Object Tracking:A Survey
Alper Yilmaz
Ohio State University
Omar Javed
ObjectVideo,Inc.
and
Mubarak Shah
University of Central Florida
The goal of this article is to review the state-of-the-art tracking methods,classify them into different cate-gories,and identify new trends.Object tracking,in general,is a challenging problem.Dif?culties in tracking objects can arise due to abrupt object motion,changing appearance patterns of both the object and the scene, nonrigid object structures,object-to-object and object-to-scene occlusions,and camera motion.Tracking is usually performed in the context of higher-level applications that require the location and/or shape of the object in every frame.Typically,assumptions are made to constrain the tracking problem in the context of a particular application.In this survey,we categorize the tracking methods on the basis of the object and motion representations used,provide detailed descriptions of representative methods in each category,and examine their pros and cons.Moreover,we discuss the important issues related to tracking including the use of appropriate image features,selection of motion models,and detection of objects.
Categories and Subject Descriptors:I.4.8[Image Processing and Computer Vision]:Scene Analysis—Tracking
General Terms:Algorithms
Additional Key Words and Phrases:Appearance models,contour evolution,feature selection,object detection, object representation,point tracking,shape tracking
ACM Reference Format:
Yilmaz,A.,Javed,O.,and Shah,M.2006.Object tracking:A survey.ACM Comput.Surv.38,4,Article13 (Dec.2006),45pages.DOI=10.1145/1177352.1177355https://www.doczj.com/doc/9a14348350.html,/10.1145/1177352.1177355
This material is based on work funded in part by the US Government.Any opinions,?ndings,and conclusions or recommendations expressed in this material are those of the authors and do not necessarily re?ect the views of the US Government.
Author’s address:A.Yilmaz,Department of CEEGS,Ohio State University;email:yilmaz.15@https://www.doczj.com/doc/9a14348350.html,; O.Javed,ObjectVideo,Inc.,Reston,VA20191;email:ojaved@https://www.doczj.com/doc/9a14348350.html,;M.Shah,School of EECS, University of Central Florida;email:shah@https://www.doczj.com/doc/9a14348350.html,.
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1.INTRODUCTION
Object tracking is an important task within the?eld of computer vision.The prolif-eration of high-powered computers,the availability of high quality and inexpensive video cameras,and the increasing need for automated video analysis has generated a great deal of interest in object tracking algorithms.There are three key steps in video analysis:detection of interesting moving objects,tracking of such objects from frame to frame,and analysis of object tracks to recognize their behavior.Therefore,the use of object tracking is pertinent in the tasks of:
—motion-based recognition,that is,human identi?cation based on gait,automatic ob-ject detection,etc;
—automated surveillance,that is,monitoring a scene to detect suspicious activities or unlikely events;
—video indexing,that is,automatic annotation and retrieval of the videos in multimedia databases;
—human-computer interaction,that is,gesture recognition,eye gaze tracking for data input to computers,etc.;
—traf?c monitoring,that is,real-time gathering of traf?c statistics to direct traf?c?ow.—vehicle navigation,that is,video-based path planning and obstacle avoidance capabilities.
In its simplest form,tracking can be de?ned as the problem of estimating the tra-jectory of an object in the image plane as it moves around a scene.In other words,a tracker assigns consistent labels to the tracked objects in different frames of a video.Ad-ditionally,depending on the tracking domain,a tracker can also provide object-centric information,such as orientation,area,or shape of an object.Tracking objects can be complex due to:
—loss of information caused by projection of the3D world on a2D image,
—noise in images,
—complex object motion,
—nonrigid or articulated nature of objects,
—partial and full object occlusions,
—complex object shapes,
—scene illumination changes,and
—real-time processing requirements.
One can simplify tracking by imposing constraints on the motion and/or appearance of objects.For example,almost all tracking algorithms assume that the object motion is smooth with no abrupt changes.One can further constrain the object motion to be of constant velocity or constant acceleration based on a priori information.Prior knowledge about the number and the size of objects,or the object appearance and shape,can also be used to simplify the problem.
Numerous approaches for object tracking have been proposed.These primarily differ from each other based on the way they approach the following questions:Which object representation is suitable for tracking?Which image features should be used?How should the motion,appearance,and shape of the object be modeled?The answers to these questions depend on the context/environment in which the tracking is performed and the end use for which the tracking information is being sought.A large number of tracking methods have been proposed which attempt to answer these questions for a variety of scenarios.The goal of this survey is to group tracking methods into broad
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Object Tracking:A Survey3 categories and provide comprehensive descriptions of representative methods in each category.We aspire to give readers,who require a tracker for a certain application, the ability to select the most suitable tracking algorithm for their particular needs. Moreover,we aim to identify new trends and ideas in the tracking community and hope to provide insight for the development of new tracking methods.
Our survey is focused on methodologies for tracking objects in general and not on trackers tailored for speci?c objects,for example,person trackers that use human kine-matics as the basis of their implementation.There has been substantial work on track-ing humans using articulated object models that has been discussed and categorized in the surveys by Aggarwal and Cai[1999],Gavrilla[1999],and Moeslund and Granum [2001].We will,however,include some works on the articulated object trackers that are also applicable to domains other than articulated objects.
We follow a bottom-up approach in describing the issues that need to be addressed when one sets out to build an object tracker.The?rst issue is de?ning a suitable rep-resentation of the object.In Section2,we will describe some common object shape representations,for example,points,primitive geometric shapes and object contours, and appearance representations.The next issue is the selection of image features used as an input for the tracker.In Section3,we discuss various image features,such as color, motion,edges,etc.,which are commonly used in object tracking.Almost all tracking algorithms require detection of the objects either in the?rst frame or in every frame. Section4summarizes the general strategies for detecting the objects in a scene.The suitability of a particular tracking algorithm depends on object appearances,object shapes,number of objects,object and camera motions,and illumination conditions.In Section5,we categorize and describe the existing tracking methods and explain their strengths and weaknesses in a summary section at the end of each category.In Section 6,important issues relevant to object tracking are discussed.Section7presents future directions in tracking research.Finally,concluding remarks are sketched in Section8.
2.OBJECT REPRESENTATION
In a tracking scenario,an object can be de?ned as anything that is of interest for further analysis.For instance,boats on the sea,?sh inside an aquarium,vehicles on a road, planes in the air,people walking on a road,or bubbles in the water are a set of objects that may be important to track in a speci?c domain.Objects can be represented by their shapes and appearances.In this section,we will?rst describe the object shape representations commonly employed for tracking and then address the joint shape and appearance representations.
—Points.The object is represented by a point,that is,the centroid(Figure1(a)) [Veenman et al.2001]or by a set of points(Figure1(b))[Serby et al.2004].In general, the point representation is suitable for tracking objects that occupy small regions in an image.(see Section5.1).
—Primitive geometric shapes.Object shape is represented by a rectangle,ellipse (Figure1(c),(d)[Comaniciu et al.2003],etc.Object motion for such representations is usually modeled by translation,af?ne,or projective(homography)transformation (see Section5.2for details).Though primitive geometric shapes are more suitable for representing simple rigid objects,they are also used for tracking nonrigid objects.—Object silhouette and contour.Contour representation de?nes the boundary of an object(Figure1(g),(h).The region inside the contour is called the silhouette of the object(see Figure1(i)).Silhouette and contour representations are suitable for track-ing complex nonrigid shapes[Yilmaz et al.2004].
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Fig.1.Object representations.(a)Centroid,(b)multiple points,(c)rectangular
patch,(d)elliptical patch,(e)part-based multiple patches,(f)object skeleton,(g)
complete object contour,(h)control points on object contour,(i)object silhouette.—Articulated shape models.Articulated objects are composed of body parts that are held together with joints.For example,the human body is an articulated object with torso,legs,hands,head,and feet connected by joints.The relationship between the parts are governed by kinematic motion models,for example,joint angle,etc.In order to represent an articulated object,one can model the constituent parts using cylinders or ellipses as shown in Figure1(e).
—Skeletal models.Object skeleton can be extracted by applying medial axis trans-form to the object silhouette[Ballard and Brown1982,Chap.8].This model is com-monly used as a shape representation for recognizing objects[Ali and Aggarwal2001]. Skeleton representation can be used to model both articulated and rigid objects(see Figure1(f).
There are a number of ways to represent the appearance features of objects.Note that shape representations can also be combined with the appearance representations [Cootes et al.2001]for tracking.Some common appearance representations in the context of object tracking are:
—Probability densities of object appearance.The probability density estimates of the object appearance can either be parametric,such as Gaussian[Zhu and Yuille1996] and a mixture of Gaussians[Paragios and Deriche2002],or nonparametric,such as Parzen windows[Elgammal et al.2002]and histograms[Comaniciu et al.2003].The probability densities of object appearance features(color,texture)can be computed from the image regions speci?ed by the shape models(interior region of an ellipse or a contour).
—Templates.Templates are formed using simple geometric shapes or silhouettes [Fieguth and Terzopoulos1997].An advantage of a template is that it carries both spatial and appearance information.Templates,however,only encode the object ap-pearance generated from a single view.Thus,they are only suitable for tracking objects whose poses do not vary considerably during the course of tracking.
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Object Tracking:A Survey5—Active appearance models.Active appearance models are generated by simultane-ously modeling the object shape and appearance[Edwards et al.1998].In general, the object shape is de?ned by a set of landmarks.Similar to the contour-based repre-sentation,the landmarks can reside on the object boundary or,alternatively,they can reside inside the object region.For each landmark,an appearance vector is stored which is in the form of color,texture,or gradient magnitude.Active appearance models require a training phase where both the shape and its associated appear-ance is learned from a set of samples using,for instance,the principal component analysis.
—Multiview appearance models.These models encode different views of an object.One approach to represent the different object views is to generate a subspace from the given views.Subspace approaches,for example,Principal Component Analysis(PCA) and Independent Component Analysis(ICA),have been used for both shape and appearance representation[Mughadam and Pentland1997;Black and Jepson1998]. Another approach to learn the different views of an object is by training a set of clas-si?ers,for example,the support vector machines[Avidan2001]or Bayesian networks [Park and Aggarwal2004].One limitation of multiview appearance models is that the appearances in all views are required ahead of time.
In general,there is a strong relationship between the object representations and the tracking algorithms.Object representations are usually chosen according to the ap-plication domain.For tracking objects,which appear very small in an image,point representation is usually appropriate.For instance,Veenman et al.[2001]use the point representation to track the seeds in a moving dish sequence.Similarly,Sha?que and Shah[2003]use the point representation to track distant birds.For the objects whose shapes can be approximated by rectangles or ellipses,primitive geometric shape representations are more https://www.doczj.com/doc/9a14348350.html,aniciu et al.[2003]use an elliptical shape representation and employ a color histogram computed from the elliptical region for modeling the appearance.In1998,Black and Jepson used eigenvectors to represent the appearance.The eigenvectors were generated from rectangular object templates.For tracking objects with complex shapes,for example,humans,a contour or a silhouette-based representation is appropriate.Haritaoglu et al.[2000]use silhouettes for object tracking in a surveillance application.
3.FEATURE SELECTION FOR TRACKING
Selecting the right features plays a critical role in tracking.In general,the most de-sirable property of a visual feature is its uniqueness so that the objects can be easily distinguished in the feature space.Feature selection is closely related to the object rep-resentation.For example,color is used as a feature for histogram-based appearance representations,while for contour-based representation,object edges are usually used as features.In general,many tracking algorithms use a combination of these features. The details of common visual features are as follows.
—Color.The apparent color of an object is in?uenced primarily by two physical factors, 1)the spectral power distribution of the illuminant and2)the surface re?ectance properties of the object.In image processing,the RGB(red,green,blue)color space is usually used to represent color.However,the RGB space is not a perceptually uni-form color space,that is,the differences between the colors in the RGB space do not correspond to the color differences perceived by humans[Paschos2001].Addition-ally,the RGB dimensions are highly correlated.In contrast,L?u?v?and L?a?b?are perceptually uniform color spaces,while HSV(Hue,Saturation,Value)is an approx-imately uniform color space.However,these color spaces are sensitive to noise[Song ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006.
6 A.Yilmaz et al. et al.1996].In summary,there is no last word on which color space is more ef?cient, therefore a variety of color spaces have been used in tracking.
—Edges.Object boundaries usually generate strong changes in image intensities.Edge detection is used to identify these changes.An important property of edges is that they are less sensitive to illumination changes compared to color features.Algorithms that track the boundary of the objects usually use edges as the representative feature. Because of its simplicity and accuracy,the most popular edge detection approach is the Canny Edge detector[Canny1986].An evaluation of the edge detection algorithms is provided by Bowyer et al.[2001].
—Optical Flow.Optical?ow is a dense?eld of displacement vectors which de?nes the translation of each pixel in a region.It is computed using the brightness constraint, which assumes brightness constancy of corresponding pixels in consecutive frames [Horn and Schunk1981].Optical?ow is commonly used as a feature in motion-based segmentation and tracking applications.Popular techniques for computing dense optical?ow include methods by Horn and Schunck[1981],Lucas and Kanade[1981], Black and Anandan[1996],and Szeliski and Couglan[1997].For the performance evaluation of the optical?ow methods,we refer the interested reader to the survey by Barron et al.[1994].
—Texture.Texture is a measure of the intensity variation of a surface which quanti?es properties such as smoothness and https://www.doczj.com/doc/9a14348350.html,pared to color,texture requires a processing step to generate the descriptors.There are various texture descriptors: Gray-Level Cooccurrence Matrices(GLCM’s)[Haralick et al.1973](a2D histogram which shows the cooccurrences of intensities in a speci?ed direction and distance), Law’s texture measures[Laws1980](twenty-?ve2D?lters generated from?ve1D ?lters corresponding to level,edge,spot,wave,and ripple),wavelets[Mallat1989] (orthogonal bank of?lters),and steerable pyramids[Greenspan et al.1994].Simi-lar to edge features,the texture features are less sensitive to illumination changes compared to color.
Mostly features are chosen manually by the user depending on the application domain.However,the problem of automatic feature selection has received signif-icant attention in the pattern recognition community.Automatic feature selection methods can be divided into?lter methods and wrapper methods[Blum and Langley 1997].The?lter methods try to select the features based on a general criteria,for ex-ample,the features should be uncorrelated.The wrapper methods select the features based on the usefulness of the features in a speci?c problem domain,for example, the classi?cation performance using a subset of features.Principal Component Analy-sis(PCA)is an example of the?lter methods for the feature reduction.PCA involves transformation of a number of(possibly)correlated variables into a(smaller)number of uncorrelated variables called the principal components.The?rst principal component accounts for as much of the variability in the data as possible,and each succeeding component accounts for as much of the remaining variability as possible.A wrapper method of selecting the discriminatory features for tracking a particular class of ob-jects is the Adaboost[Tieu and Viola2004]algorithm.Adaboost is a method for?nding a strong classi?er based on a combination of moderately inaccurate weak classi?ers. Given a large set of features,one classi?er can be trained for each feature.Adaboost, as discussed in Sections4.4,will discover a weighted combination of classi?ers(repre-senting features)that maximize the classi?cation performance of the algorithm.The higher the weight of the feature,the more discriminatory it is.One can use the?rst n highest-weighted features for tracking.
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Object Tracking:A Survey7
Table I.Object Detection Categories
Categories Representative Work
Point detectors Moravec’s detector[Moravec1979],
Harris detector[Harris and Stephens1988],
Scale Invariant Feature Transform[Lowe2004].
Af?ne Invariant Point Detector[Mikolajczyk and Schmid2002].
Segmentation Mean-shift[Comaniciu and Meer1999],
Graph-cut[Shi and Malik2000],
Active contours[Caselles et al.1995].
Background Modeling Mixture of Gaussians[Stauffer and Grimson2000],
Eigenbackground[Oliver et al.2000],
Wall?ower[Toyama et al.1999],
Dynamic texture background[Monnet et al.2003].
Supervised Classi?ers Support Vector Machines[Papageorgiou et al.1998],
Neural Networks[Rowley et al.1998],
Adaptive Boosting[Viola et al.2003].
Among all features,color is one of the most widely used feature for tracking. Comaniciu et al.[2003]use a color histogram to represent the object appearance.De-spite its popularity,most color bands are sensitive to illumination variation.Hence in scenarios where this effect is inevitable,other features are incorporated to model object appearance.Cremers et al.[2003]use optical?ow as a feature for contour track-ing.Jepson et al.[2003]use steerable?lter responses for tracking.Alternatively,a combination of these features is also utilized to improve the tracking performance. 4.OBJECT DETECTION
Every tracking method requires an object detection mechanism either in every frame or when the object?rst appears in the video.A common approach for object detection is to use information in a single frame.However,some object detection methods make use of the temporal information computed from a sequence of frames to reduce the number of false detections.This temporal information is usually in the form of frame differencing, which highlights changing regions in consecutive frames.Given the object regions in the image,it is then the tracker’s task to perform object correspondence from one frame to the next to generate the tracks.
We tabulate several common object detection methods in Table I.Although the object detection itself requires a survey of its own,here we outline the popular methods in the context of object tracking for the sake of completeness.
4.1.Point Detectors
Point detectors are used to?nd interest points in images which have an expressive texture in their respective localities.Interest points have been long used in the con-text of motion,stereo,and tracking problems.A desirable quality of an interest point is its invariance to changes in illumination and camera viewpoint.In the literature, commonly used interest point detectors include Moravec’s interest operator[Moravec 1979],Harris interest point detector[Harris and Stephens1988],KLT detector[Shi and Tomasi1994],and SIFT detector[Lowe2004].For a comparative evaluation of interest point detectors,we refer the reader to the survey by Mikolajczyk and Schmid [2003].
To?nd interest points,Moravec’s operator computes the variation of the image inten-sities in a4×4patch in the horizontal,vertical,diagonal,and antidiagonal directions and selects the minimum of the four variations as representative values for the window.
A point is declared interesting if the intensity variation is a local maximum in a12×12patch.
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Fig.2.Interest points detected by applying(a)the Harris,(b)the KLT,and(c)SIFT operators.
The Harris detector computes the?rst order image derivatives,(I x,I y),in x and y di-rections to highlight the directional intensity variations,then a second moment matrix, which encodes this variation,is evaluated for each pixel in a small neighborhood:
M=
I2x
I x I y
I x I y
I2y
.(1)
An interest point is identi?ed using the determinant and the trace of M which mea-
sures the variation in a local neighborhood R=det(M)?k·tr(M)2,where k is constant.
The interest points are marked by thresholding R after applying nonmaxima suppres-
sion(see Figure2(a)for results).The source code for Harris detector is available at
HarrisSrc.The same moment matrix M given in Equation(1)is used in the interest
point detection step of the KLT tracking method.Interest point con?dence,R,is com-
puted using the minimum eigenvalue of M,λmin.Interest point candidates are selected
by thresholding R.Among the candidate points,KLT eliminates the candidates that
are spatially close to each other(Figure2(b)).Implementation of the KLT detector is
available at KLTSrc.
Quantitatively both Harris and KLT emphasize the intensity variations using very
similar measures.For instance,R in Harris is related to the characteristic polynomial
used for?nding the eigenvalues of M:λ2+det(M)?λ·tr(M)=0,while KLT computes the eigenvalues directly.In practice,both of these methods?nd almost the same interest
points.The only difference is the additional KLT criterion that enforces a prede?ned
spatial distance between detected interest points.
In theory,the M matrix is invariant to both rotation and translation.However,it
is not invariant to af?ne or projective transformations.In order to introduce robust
detection of interest points under different transformations,Lowe[2004]introduced
the SIFT(Scale Invariant Feature Transform)method which is composed of four steps.
First,a scale space is constructed by convolving the image with Gaussian?lters at
different scales.Convolved images are used to generate difference-of-Gaussians(DoG)
images.Candidate interest points are then selected from the minima and maxima of
the DoG images across scales.The next step updates the location of each candidate by
interpolating the color values using neighboring pixels.In the third step,low contrast
candidates as well as the candidates along the edges are eliminated.Finally,remaining
interest points are assigned orientations based on the peaks in the histograms of
gradient directions in a small neighborhood around a candidate point.SIFT detector
generates a greater number of interest points compared to other interest point detec-
tors.This is due to the fact that the interest points at different scales and different
resolutions(pyramid)are accumulated.Empirically,it has been shown in Mikolajczyk
and Schmid[2003]that SIFT outperforms most point detectors and is more resilient
to image deformations.Implementation of the SIFT detector is available at SIFTSrc.
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Object Tracking:A Survey9
Fig.3.Mixture of Gaussian modeling for background subtraction.(a)Image from a sequence
in which a person is walking across the scene.(b)The mean of the highest-weighted Gaussians
at each pixels position.These means represent the most temporally persistent per-pixel color
and hence should represent the stationary background.(c)The means of the Gaussian with
the second-highest weight;these means represent colors that are observed less frequently.(d)
Background subtraction result.The foreground consists of the pixels in the current frame that
matched a low-weighted Gaussian.
4.2.Background Subtraction
Object detection can be achieved by building a representation of the scene called the background model and then?nding deviations from the model for each incoming frame. Any signi?cant change in an image region from the background model signi?es a moving object.The pixels constituting the regions undergoing change are marked for further https://www.doczj.com/doc/9a14348350.html,ually,a connected component algorithm is applied to obtain connected regions corresponding to the objects.This process is referred to as the background subtraction.
Frame differencing of temporally adjacent frames has been well studied since the late70s[Jain and Nagel1979].However,background subtraction became popular fol-lowing the work of Wren et al.[1997].In order to learn gradual changes in time,Wren et al.propose modeling the color of each pixel,I(x,y),of a stationary background with a single3D(Y,U,and V color space)Gaussian,I(x,y)～N(μ(x,y), (x,y)).The model parameters,the meanμ(x,y)and the covariance (x,y),are learned from the color observations in several consecutive frames.Once the background model is de-rived,for every pixel(x,y)in the input frame,the likelihood of its color coming from N(μ(x,y), (x,y))is computed,and the pixels that deviate from the background model are labeled as the foreground pixels.However,a single Gaussian is not a good model for outdoor scenes[Gao et al.2000]since multiple colors can be observed at a certain loca-tion due to repetitive object motion,shadows,or re?ectance.A substantial improvement in background modeling is achieved by using multimodal statistical models to describe per-pixel background color.For instance,Stauffer and Grimson[2000]use a mixture of Gaussians to model the pixel color.In this method,a pixel in the current frame is checked against the background model by comparing it with every Gaussian in the model until a matching Gaussian is found.If a match is found,the mean and vari-ance of the matched Gaussian is updated,otherwise a new Gaussian with the mean equal to the current pixel color and some initial variance is introduced into the mix-ture.Each pixel is classi?ed based on whether the matched distribution represents the background process.Moving regions,which are detected using this approach,along with the background models are shown in Figure3.
Another approach is to incorporate region-based(spatial)scene information instead of only using color-based information.Elgammal and Davis[2000]use nonparamet-ric kernel density estimation to model the per-pixel background.During the sub-traction process,the current pixel is matched not only to the corresponding pixel in the background model,but also to the nearby pixel locations.Thus,this method can handle camera jitter or small movements in the background.Li and Leung[2002] fuse the texture and color features to perform background subtraction over blocks of ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006.
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Fig.4.Eigenspace decomposition-based background subtraction(space is constructed with objects in the FOV of camera):(a)an input image with objects,(b)reconstructed image after projecting input image onto the eigenspace,(c)difference image.Note that the foreground objects are clearly identi?able.
5×5pixels.Since texture does not vary greatly with illumination changes,the method is less sensitive to illumination.Toyama et al.[1999]propose a three-tiered algorithm to deal with the background subtraction problem.In addition to the pixel-level sub-traction,the authors use the region and the frame-level information.At the pixel level, the authors propose to use Wiener?ltering to make probabilistic predictions of the expected background color.At the region level,foreground regions consisting of homo-geneous color are?lled in.At the frame level,if most of the pixels in a frame exhibit suddenly change,it is assumed that the pixel-based color background models are no longer valid.At this point,either a previously stored pixel-based background model is swapped in,or the model is reinitialized.
An alternate approach for background subtraction is to represent the intensity vari-ations of a pixel in an image sequence as discrete states corresponding to the events in the environment.For instance,for tracking cars on a highway,image pixels can be in the background state,the foreground(car)state,or the shadow state.Rittscher et al.[2000]use Hidden Markov Models(HMM)to classify small blocks of an image as belonging to one of these three states.In the context of detecting light on and off events in a room,Stenger et al.[2001]use HMMs for the background subtraction.The advantage of using HMMs is that certain events,which are hard to model correctly using unsupervised background modeling approaches,can be learned using training samples.
Instead of modeling the variation of individual pixels,Oliver et al.[2000]pro-pose a holistic approach using the eigenspace decomposition.For k input frames, I i:i=1···k,of size n×m,a background matrix B of size k×l is formed by cas-cading m rows in each frame one after the other,where l=(n×m),and eigenvalue decomposition is applied to the covariance of B,C=B T B.The background is then rep-resented by the most descriptiveηeigenvectors,u i,where i<η One limitation of the aforementioned approaches is that they require a static back-ground.This limitation is addressed by Monnet et al.[2003],and Zhong and Sclaroff [2003].Both of these methods are able to deal with time-varying background(e.g.,the waves on the water,moving clouds,and escalators).These methods model the image re-gions as autoregressive moving average(ARMA)processes which provide a way to learn and predict the motion patterns in a scene.An ARMA process is a time series model that is made up of sums of autoregressive and moving-average components,where an ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. Object Tracking:A Survey11 Fig.5.Segmentation of the image shown in(a),using mean-shift segmentation(b)and normalized cuts(c). autoregressive process can be described as a weighted sum of its previous values and a white noise error. In summary,most state-of-the-art tracking methods for?xed cameras,for example, Haritaoglu et al.[2000]and Collins et al.[2001]use background subtraction methods to detect regions of interest.This is because recent subtraction methods have the ca-pabilities of modeling the changing illumination,noise,and the periodic motion of the background regions and,therefore,can accurately detect objects in a variety of circum-stances.Moreover,these methods are computationally ef?cient.In practice,background subtraction provides incomplete object regions in many instances,that is,the objects may be spilled into several regions,or there may be holes inside the object since there are no guarantees that the object features will be different from the background features. The most important limitation of background subtraction is the requirement of station-ary cameras.Camera motion usually distorts the background models.These methods can be applied to video acquired by mobile cameras by regenerating background mod-els for small temporal windows,for instance,three frames,from scratch[Kanade et al. 1998]or by compensating sensor motion,for instance,creating background mosaics [Rowe and Blake1996;Irani and Anandan1998].However,both of these solutions require assumptions of planar scenes and small motion in successive frames. 4.3.Segmentation The aim of image segmentation algorithms is to partition the image into perceptually similar regions.Every segmentation algorithm addresses two problems,the criteria for a good partition and the method for achieving ef?cient partitioning[Shi and Malik 2000].In this section,we will discuss recent segmentation techniques that are relevant to object tracking. 4.3.1.Mean-Shift Clustering.For the image segmentation problem,Comaniciu and Meer[2002]propose the mean-shift approach to?nd clusters in the joint spatial+color space,[l,u,v,x,y],where[l,u,v]represents the color and[x,y]represents the spatial location.Given an image,the algorithm is initialized with a large number of hypoth-esized cluster centers randomly chosen from the data.Then,each cluster center is moved to the mean of the data lying inside the multidimensional ellipsoid centered on the cluster center.The vector de?ned by the old and the new cluster centers is called the mean-shift vector.The mean-shift vector is computed iteratively until the cluster centers do not change their positions.Note that during the mean-shift iterations,some clusters may get merged.In Figure5(b),we show the segmentation using the mean-shift approach generated using the source code available at MeanShiftSegmentSrc. Mean-shift clustering is scalable to various other applications such as edge detection, image regularization[Comaniciu and Meer2002],and tracking[Comaniciu et al.2003]. ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. 12 A.Yilmaz et al.Mean-shift based segmentation requires ?ne tuning of various parameters to obtain better segmentation,for instance,selection of the color and spatial kernel bandwidths,and the threshold for the minimum size of the region considerably effect the resulting segmentation. 4.3.2.Image Segmentation Using Graph-Cuts. Image segmentation can also be formu- lated as a graph partitioning problem,where the vertices (pixels),V ={u ,v ,...},of a graph (image),G ,are partitioned into N disjoint subgraphs (regions),A i , N i =1A i =V ,A i ∩A j =?,i =j ,by pruning the weighted edges of the graph.The total weight of the pruned edges between two subgraphs is called a cut.The weight is typically computed by color,brightness,or texture similarity between the nodes.Wu and Leahy [1993]use the minimum cut criterion,where the goal is to ?nd the partitions that minimize a cut.In their approach,the weights are de?ned based on the color similarity .One limitation of minimum cut is its bias toward oversegmenting the image.This effect is due to the increase in cost of a cut with the number of edges going across the two partitioned segments. Shi and Malik [2000]propose the normalized cut to overcome the oversegmentation problem.In their approach,the cut not only depends on the sum of edge weights in the cut,but also on the ratio of the total connection weights of nodes in each partition to all nodes of the graph.For image-based segmentation,the weights between the nodes are de?ned by the product of the color similarity and the spatial proximity .Once the weights between each pair of nodes are computed,a weight matrix W and a diagonal matrix D ,where D i ,i = N j =1W i ,j ,are constructed.The segmentation is performed ?rst by computing the eigenvectors and the eigenvalues of the generalized eigensystem (D ?W )y =λDy ,then the second-smallest eigenvector is used to divide the image into two segments.For each new segment,this process is recursively performed until a threshold is reached.In Figure 5(c),we show the segmentation results obtained by the normalized cuts approach. In normalized cuts-based segmentation,the solution to the generalized eigensystem for large images can be expensive in terms of processing and memory requirements.However,this method requires fewer manually selected parameters,compared to mean-shift segmentation.Normalized cuts have also been used in the context of tracking object contours [Xu and Ahuja 2002].4.3.3.Active Contours. In an active contour framework,object segmentation is achieved by evolving a closed contour to the object’s boundary ,such that the contour tightly encloses the object region.Evolution of the contour is governed by an energy functional which de?nes the ?tness of the contour to the hypothesized object region.Energy functional for contour evolution has the following common form: E ( )= 1 E int (v )+E im (v )+E ext (v )ds ,(2)where s is the arc-length of the contour ,E int includes regularization constraints,E im includes appearance-based energy ,and E ext speci?es additional constraints.E int usu-ally includes a curvature term,?rst-order (?v )or second-order (?2v )continuity terms to ?nd the shortest contour.Image-based energy ,E im ,can be computed locally or globally .Local information is usually in the form of an image gradient and is evaluated around the contour [Kass et al.1988;Caselles et al.1995].In contrast,global features are com-puted inside and outside of the object region.Global features include color [Zhu and Yuille 1996;Yilmaz et al.2004;Ronfard 1994]and texture [Paragios and Deriche 2002]. ACM Computing Surveys,Vol.38,No.4,Article 13,Publication date:December 2006. Object Tracking:A Survey13 Different researchers have used different energy terms in Equation(2).In1995, Caselles et al.exclude the E ext and use only the image gradient as the image energy E im=g(|?I|),where g is the sigmoid https://www.doczj.com/doc/9a14348350.html,pared to the gradient,a function of the gradient de?nes the object contour as a geodesic curve in the Riemannian space [Caselles et al.1995].However,image gradients provide very local information and are sensitive to local minima.In order to overcome this problem,researchers introduced region-based image energy terms.In1996,Zhu and Yuille proposed using region infor-mation instead of the image gradient.However,the use of regional terms in the energy functional does not result in good localization of the object contour.Recently,methods that combine both region-based and gradient-based image energy have become popular. Paragios and Deriche[2002]propose using a convex combination of the gradient and region-based energies,E image=λE boundary+(1?λ)E region.In particular,the authors model the appearance in E region by mixture of Gaussians.Contour evolution is?rst performed globally,then locally by varying theαfrom0to1at each iteration. An important issue in contour-based methods is the contour initialization.In im-age gradient-based approaches,a contour is typically placed outside the object region and shrunk until the object boundary is encountered[Kass et al.1988;Caselles et al. 1995].This constraint is relaxed in region-based methods such that the contour can be initialized either inside or outside the object so that the contour can either expand or shrink,respectively,to?t the object boundary.However,these approaches require prior object or background knowledge[Paragios and Deriche2002].Using multiple frames or a reference frame,initialization can be performed without building region priors. For instance,in Paragios and Deriche[2000],the authors use background subtraction to initialize the contour. Besides the selection of the energy functional and the initialization,another im-portant issue is selecting the right contour representation.Object contour, ,can be represented either explicitly(control points,v)or implicitly(level sets,φ).In the explicit representation,the relation between the control points are de?ned by spline equations. In the level sets representation,the contour is represented on a spatial grid which encodes the signed distances of the grids from the contour with opposite signs for the object and the background regions.The contour is implicitly de?ned as the zero cross-ings in the level set grid.The evolution of the contour is governed by changing the grid values according to the energy computed using Equation(2),evaluated at each grid po-sition.The changes in the grid values result in new zero crossings,hence,a new contour positions(more details are given in Section5.3).The source code for generic level sets, which can be used for various applications by specifying the contour evolution speed, for instance,segmentation,tracking,heat?ow etc.,is available at LevelSetSrc.The most important advantage of implicit representation over the explicit representation is its?exibility in allowing topology changes(split and merge). 4.4.Supervised Learning Object detection can be performed by learning different object views automatically from a set of examples by means of a supervised learning mechanism.Learning of different object views waives the requirement of storing a complete set of templates.Given a set of learning examples,supervised learning methods generate a function that maps inputs to desired outputs.A standard formulation of supervised learning is the classi?cation problem where the learner approximates the behavior of a function by generating an output in the form of either a continuous value,which is called regression,or a class label,which is called classi?cation.In context of object detection,the learning examples are composed of pairs of object features and an associated object class where both of these quantities are manually de?ned. ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. 14 A.Yilmaz et al. Selection of features plays an important role in the performance of the classi?ca-tion,hence,it is important to use a set of features that discriminate one class from the other.In addition to the features discussed in Section3,it is also possible to use other features such as object area,object orientation,and object appearance in the form of a density function,for example,histogram.Once the features are selected,different appearances of an object can be learned by choosing a supervised learning approach. These learning approaches include,but are not limited to,neural networks[Rowley et al.1998],adaptive boosting[Viola et al.2003],decision trees[Grewe and Kak1995], and support vector machines[Papageorgiou et al.1998].These learning methods com-pute a hypersurface that separates one object class from the other in a high dimensional space. Supervised learning methods usually require a large collection of samples from each object class.Additionally,this collection must be manually labeled.A possible approach to reducing the amount of manually labeled data is to accompany cotraining with su-pervised learning[Blum and Mitchell1998].The main idea behind cotraining is to train two classi?ers using a small set of labeled data where the features used for each classi?er are independent.After training is achieved,each classi?er is used to assign unlabeled data to the training set of the other classi?er.It was shown that,starting from a small set of labeled data with two sets of statistically independent features, cotraining can provide a very accurate classi?cation rule[Blum and Mitchell1998]. Cotraining has been successfully used to reduce the amount of manual interaction re-quired for training in the context of adaboost[Levin et al.2003]and support vector machines[Kockelkorn et al.2003].Following we will discuss the adaptive boosting and the support vector machines due to their applicability to object tracking. 4.4.1.Adaptive Boosting.Boosting is an iterative method of?nding a very accurate classi?er by combining many base classi?ers,each of which may only be moderately accurate[Freund and Schapire1995].In the training phase of the Adaboost algorithm, the?rst step is to construct an initial distribution of weights over the training set. The boosting mechanism then selects a base classi?er that gives the least error,where the error is proportional to the weights of the misclassi?ed data.Next,the weights associated with the data misclassi?ed by the selected base classi?er are increased.Thus the algorithm encourages the selection of another classi?er that performs better on the misclassi?ed data in the next iteration.For interested readers tutorials on boosting are available at https://www.doczj.com/doc/9a14348350.html,. In the context of object detection,weak classi?ers can be simple operators such as a set of thresholds,applied to the object features extracted from the image.In2003, Viola et https://www.doczj.com/doc/9a14348350.html,ed the Adaboost framework to detect pedestrians.In their approach, perceptrons were chosen as the weak classi?ers which are trained on image features extracted by a combination of spatial and temporal operators.The operators for feature extraction are in the form of simple rectangular?lters,and are shown in Figure6. The operators in the temporal domain are in the form of frame differencing which encode some form of motion information.Frame differencing,when used as an operator in the temporal domain,reduces the number of false detections by enforcing object detection in the regions where the motion occurs. 4.4.2.Support Vector Machines.As a classi?er,Support Vector Machines(SVM)are used to cluster data into two classes by?nding the maximum marginal hyperplane that separates one class from the other[Boser et al.1992].The margin of the hyperplane, which is maximized,is de?ned by the distance between the hyperplane and the closest data points.The data points that lie on the boundary of the margin of the hyperplane are called the support vectors.In the context of object detection,these classes correspond ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. Object Tracking:A Survey15 Fig.6.A set of rectangular?lters used by Viola et al.[2003]to extract features used in the Adaboost framework.Each?lter is composed of three regions:white,light gray,and dark gray,with associated weights0,?1,and1respectively.In order to compute the feature in a window,these?lters are convolved with the image. to the object class(positive samples)and the nonobject class(negative samples).From manually generated training examples labeled as object and nonobject,computation of the hyperplane from among an in?nite number of possible hyperplanes is carried out by means of quadratic programming. Despite being a linear classi?er,SVM can also be used as a nonlinear classi?er by ap-plying the kernel trick to the input feature vector extracted from the input.Application of the kernel trick to a set of data that is not linearly separable,transforms the data to a higher dimensional space which is likely to be separable.The kernels used for kernel trick are polynomial kernels or radial basis functions,for example,Gaussian kernel and two-layer perceptron,for instance,a sigmoid function.However,the selection of the right kernel for the problem at hand is not easy.Once a kernel is chosen,one has to test the classi?cation performance for a set of parameters which may not work as well when new observations are introduced to the sample set. In the context of object detection,Papageorgiou et al.[1998]use SVM for detecting pedestrians and faces in images.The features used to discriminate between the classes are extracted by applying Haar wavelets to the sets of positive and negative training examples.In order to reduce the search space,temporal information is utilized by com-puting the optical?ow?eld in the image.Particularly,the discontinuities in the optical ?ow?eld are used to initiate the search for possible objects resulting in a decreased number of false positives. 5.OBJECT TRACKING The aim of an object tracker is to generate the trajectory of an object over time by locat-ing its position in every frame of the video.Object tracker may also provide the complete region in the image that is occupied by the object at every time instant.The tasks of de-tecting the object and establishing correspondence between the object instances across frames can either be performed separately or jointly.In the?rst case,possible object regions in every frame are obtained by means of an object detection algorithm,and then the tracker corresponds objects across frames.In the latter case,the object region and correspondence is jointly estimated by iteratively updating object location and region information obtained from previous frames.In either tracking approach,the objects are represented using the shape and/or appearance models described in Section2.The model selected to represent object shape limits the type of motion or deformation it can undergo.For example,if an object is represented as a point,then only a translational model can be used.In the case where a geometric shape representation like an ellipse is used for the object,parametric motion models like af?ne or projective transformations are appropriate.These representations can approximate the motion of rigid objects in the scene.For a nonrigid object,silhouette or contour is the most descriptive representa-tion and both parametric and nonparametric models can be used to specify their motion. ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. 16 A.Yilmaz et al. Fig.7.Taxonomy of tracking methods. Table II.T racking Categories Categories Representative Work Point Tracking ?Deterministic methods MGE tracker[Salari and Sethi1990], GOA tracker[Veenman et al.2001]. ?Statistical methods Kalman?lter[Broida and Chellappa1986], JPDAF[Bar-Shalom and Foreman1988], PMHT[Streit and Luginbuhl1994]. Kernel Tracking ?Template and density based Mean-shift[Comaniciu et al.2003], appearance models KLT[Shi and Tomasi1994], Layering[Tao et al.2002]. ?Multi-view appearance models Eigentracking[Black and Jepson1998], SVM tracker[Avidan2001]. Silhouette Tracking ?Contour evolution State space models[Isard and Blake1998], Variational methods[Bertalmio et al.2000], Heuristic methods[Ronfard1994]. ?Matching shapes Hausdorff[Huttenlocher et al.1993], Hough transform[Sato and Aggarwal2004], Histogram[Kang et al.2004]. In view of the aforementioned discussion,we provide a taxonomy of tracking methods in Figure7.Representative work for each category is tabulated in Table II.We now brie?y introduce the main tracking categories,followed by a detailed section on each category. —Point Tracking.Objects detected in consecutive frames are represented by points, and the association of the points is based on the previous object state which can include object position and motion.This approach requires an external mechanism to detect the objects in every frame.An example of object correspondence is shown in Figure8(a). ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. Object Tracking:A Survey17 Fig.8.(a)Different tracking approaches.Multipoint correspondence,(b)parametric transformation of a rectangular patch,(c,d)Two examples of contour evolution. —Kernel Tracking.Kernel refers to the object shape and appearance.For example, the kernel can be a rectangular template or an elliptical shape with an associated histogram.Objects are tracked by computing the motion of the kernel in consecutive frames(Figure8(b)).This motion is usually in the form of a parametric transformation such as translation,rotation,and af?ne. —Silhouette Tracking.Tracking is performed by estimating the object region in each frame.Silhouette tracking methods use the information encoded inside the object region.This information can be in the form of appearance density and shape models which are usually in the form of edge maps.Given the object models,silhouettes are tracked by either shape matching or contour evolution(see Figure8(c),(d)).Both of these methods can essentially be considered as object segmentation applied in the temporal domain using the priors generated from the previous frames. 5.1.Point Tracking Tracking can be formulated as the correspondence of detected objects represented by points across frames.Point correspondence is a complicated problem-specially in the presence of occlusions,misdetections,entries,and exits of objects.Overall,point cor-respondence methods can be divided into two broad categories,namely,deterministic and statistical methods.The deterministic methods use qualitative motion heuristics [Veenman et al.2001]to constrain the correspondence problem.On the other hand, probabilistic methods explicitly take the object measurement and take uncertainties into account to establish correspondence. 5.1.1.Deterministic Methods for Correspondence.Deterministic methods for point corre-spondence de?ne a cost of associating each object in frame t?1to a single object in frame t using a set of motion constraints.Minimization of the correspondence cost is formulated as a combinatorial optimization problem.A solution,which consists of one-to-one correspondences(Figure9(b))among all possible associations(Figure9(a)),can be obtained by optimal assignment methods,for example,Hungarian algorithm,[Kuhn 1955]or greedy search methods.The correspondence cost is usually de?ned by using a combination of the following constraints. —Proximity assumes the location of the object would not change notably from one frame to other(see Figure10(a)). —Maximum velocity de?nes an upper bound on the object velocity and limits the possi-ble correspondences to the circular neighborhood around the object(see Figure10(b)).—Small velocity change(smooth motion)assumes the direction and speed of the object does not change drastically(see Figure10(c)). —Common motion constrains the velocity of objects in a small neighborhood to be sim-ilar(see Figure10(d)).This constraint is suitable for objects represented by multiple points. ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. 18 A.Yilmaz et al. Fig.9.Point correspondence.(a)All possible associations of a point(object)in frame t?1with points (objects)in frame t,(b)unique set of associations plotted with bold lines,(c)multiframe correspondences. Fig.10.Different motion constraints.(a)proximity,(b)maximum velocity(r denotes radius),(c)small velocity-change,(d)common motion,(e)rigidity constraints. denotes object position at frame t?2,?denotes object position at frame t?1,and?nally×denotes object position at frame t. —Rigidity assumes that objects in the3D world are rigid,therefore,the distance be-tween any two points on the actual object will remain unchanged(see Figure10(e)).—Proximal uniformity is a combination of the proximity and the small,velocity change constraints. We should,however,note that these constraints are not speci?c to the deterministic methods,and they can also be used in the context of point tracking using statistical methods. Here we present a sample of different methods proposed in the literature in this category.Sethi and Jain[1987]solve the correspondence by a greedy approach based on the proximity and rigidity constraints.Their algorithm considers two consecutive frames and is initialized by the nearest neighbor criterion.The correspondences are exchanged iteratively to minimize the cost.A modi?ed version of the same algorithm which computes the correspondences in the backward direction(from the last frame to the?rst frame)in addition to the forward direction is also analyzed.This method cannot handle occlusions,entries,or exits.Salari and Sethi[1990]handle these prob-lems,by?rst establishing correspondence for the detected points and then extending the tracking of the missing objects by adding a number of hypothetical points.Ran-garajan and Shah[1991]propose a greedy approach,which is constrained by proximal uniformity.Initial correspondences are obtained by computing optical?ow in the?rst two frames.The method does not address entry and exit of objects.If the number of detected points decrease,occlusion or misdetection is assumed.Occlusion is handled by establishing the correspondence for the detected objects in the current frame.For the remaining objects,position is predicted based on a constant velocity assumption.In the work by Intille et al.[1997],which uses a slightly modi?ed version of Rangarajan ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. Object Tracking:A Survey19 Fig.11.Results of two point correspondence algorithms.(a)Tracking using the algorithm proposed by Veenman et al.[2001]in the rotating dish sequence color segmentation was used to detect black dots on a white dish(c 2001IEEE).(b)Tracking birds using the algorithm proposed by Sha?que and Shah[2003];birds are detected using background subtraction(c 2003IEEE). and Shah[1991]for matching object centroids,the objects are detected by using back- ground subtraction.The authors explicitly handle the change in the number of objects by examining speci?c regions in the image,for example,a door,to detect entries/exits before computing the correspondence. Veenman et al.[2001]extend the work of Sethi and Jain[1987],and Rangarajan and Shah[1991]by introducing the common motion constraint for correspondence.The common motion constraint provides a strong constraint for coherent tracking of points that lie on the same object;however,it is not suitable for points lying on isolated objects moving in different directions.The algorithm is initialized by generating the initial tracks using a two-pass algorithm,and the cost function is minimized by Hungarian assignment algorithm in two consecutive frames.This approach can handle occlusion and misdetection errors,however,it is assumed that the number of objects are the same throughout the sequence,that is,no object entries or exits.See Figure11(a)for tracking results. Sha?que and Shah[2003]propose a multiframe approach to preserve temporal co- herency of the speed and position(Figure9(c)).They formulate the correspondence as a graph theoretic problem.Multiple frame correspondence relates to?nding the best unique path P i={x0,...,x k}for each point(the superscript represents the frame num-ber).For misdetected or occluded objects,the path will consist of missing positions in corresponding frames.The directed graph,which is generated using the points in k frames,is converted to a bipartite graph by splitting each node(object)into two(+ and?)nodes and representing directed edges as undirected edges from+to?nodes. The correspondence is then established by a greedy algorithm.They use a window of frames during point correspondence to handle occlusions whose durations are shorter than the temporal window used to perform matching.See Figure11(b)for results on this algorithm for the tracking of birds. 5.1.2.Statistical Methods for Correspondence.Measurements obtained from video sen-sors invariably contain noise.Moreover,the object motions can undergo random pertur-bations,for instance,maneuvering vehicles.Statistical correspondence methods solve these tracking problems by taking the measurement and the model uncertainties into account during object state estimation.The statistical correspondence methods use the ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. 20 A.Yilmaz et al. state space approach to model the object properties such as position,velocity,and ac-celeration.Measurements usually consist of the object position in the image,which is obtained by a detection mechanism.Followings,we will discuss the state estimation methods in the context of point tracking,however,it should be noted that these methods can be used in general to estimate the state of any time varying system.For example, these methods have extensively been used for tracking contours[Isard and Blake1998], activity recognition[Vaswani et al.2003],object identi?cation[Zhou et al.2003],and structure from motion[Matthies et al.1989]. Consider a moving object in the scene.The information representing the object,for example,location,is de?ned by a sequence of states X t:t=1,2,....The change in state over time is governed by the dynamic equation, X t=f t(X t?1)+W t,(3) where W t:t=1,2,...is white noise.The relationship between the measurement and the state is speci?ed by the measurement equation Z t=h t(X t,N t),where N t is the white noise and is independent of W t.The objective of tracking is to estimate the state X t given all the measurements up to that moment or,equivalently,to construct the probability density function p(X t|Z1,...,t).A theoretically optimal solution is provided by a recursive Bayesian?lter which solves the problem in two steps.The prediction step uses a dynamic equation and the already computed pdf of the state at time t?1 to derive the prior pdf of the current state,that is,p(X t|Z1,...,t?1).Then,the correction step employs the likelihood function p(Z t|X t)of the current measurement to compute the posterior pdf p(X t|Z1,...,t).In the case where the measurements only arise due to the presence of a single object in the scene,the state can be simply estimated by the two steps as de?ned.On the other hand,if there are multiple objects in the scene, measurements need to be associated with the corresponding object states.We now discuss the two cases. 5.1.2.1.Single Object State Estimation.For the single object case,if f t and h t are linear functions and the initial state X1and noise have a Gaussian distribution,then the optimal state estimate is given by the Kalman Filter.In the general case,that is,object state is not assumed to be a Gaussian,state estimation can be performed using particle ?lters[Tanizaki1987]. —Kalman Filters.A Kalman?lter is used to estimate the state of a linear system where the state is assumed to be distributed by a Gaussian.Kalman?ltering is composed of two steps,prediction and correction.The prediction step uses the state model to predict the new state of the variables: X t=D X t?1+W, t=D t?1D T+Q t, where X t and t are the state and the covariance predictions at time t.D is the state transition matrix which de?nes the relation between the state variables at time t and t?1.Q is the covariance of the noise W.Similarly,the correction step uses the current observations Z t to update the object’s state: K t= t M T[M t M T+R t]?1,(4) ,(5) X t=X t+K t[Z t?M X t] v t= t?K t M t, ACM Computing Surveys,Vol.38,No.4,Article13,Publication date:December2006. 一、工程项目进度控制管理基本论述 1·1 工程项目进度管理控制含义及作用 工程项目进度管理控制是对工程项目在施工阶段的作业程序和作业时间进行规划、实施、检查、调查等一系列活动的总称，即在施工项目实施过程中，按照已经核准的工程进度计划，采用科学的方法定期追踪和检验项目的实际进度情况，并参照项目先期进度计划，找出两者之间的偏差，并对产生偏差的各种因素及影响工期的程度进行分析与评估；而后组织、指导、协调和监督监理单位、承包商及相关单位三方，帮助其及时采取有效措施调整项目进度，使工期在计划执行中不断循环往复，直至该项目按合同约定的工期如期完工，或在保证工程质量和不增加原先预算的工程造价的条件下，使该项目提前完工并交付使用。 施工工程项目进度控制是影响工程项目管理中成本、进度、质量三大控制因素中的主要控制因素，贯穿于整个施工工程项目的投标、设计、施工、投产等所有阶段，尤其是在项目施工阶段，监理方、承包商以及相关部门对该项目进度的把控管理力度居于首位，不容忽视。 施工工程项目的进度控制管理，是工程建设过程中一项兼具实施复杂性和监管重要性的复合任务，是工程建设的三大目标的重要部分。对工程项目进度进行合理有效的控制管理，有利于尽快发挥投资者投入产出比，有利于经济秩序的良好维持，同时有利于提高企业效益。 1·2 影响工程项目进度控制的背景因素 长期以来，施工工程项目在进度控制管理方面，由于自然环境因素的制约性，面临着多重不可抗力，同时由于社会环境因素和企业管理作风因素，面临着不少压力和问题。 自然环境因素方面 工程地质条件和水文地质条件，如地质断层、溶洞、地下障碍物、软弱地基及恶劣气候、暴雨和洪涝灾害等都会对施工进度产生影响。 另外，施工中如果出现意外的事件，如战争、地震、火灾、重大工程事故、 设备的管理工作一直是大家共同关注的问题，车间设备档案不健全，对设备的运行周期不能及时了解，设备维修计划不能及时实施，其二是设备故障的诊断不及时，造成设备得不到预防修理，以上原因是导致设备使用周期短的一个根本性原因，当然还有其他原因，如：过度运行设备，维修水平不过关，粗暴对待设备等等都是导致设备运行周期达不到预期的原因。 设备管理的新潮流——全系统，全效率，全员参与 全系统是指：设备寿命周期为研究对象进行系统研究与管理，做到智能化设备管理，提高设备生命周期，加强设备的使用率。全效率是指：设备的综合效率。全员参与：设备管理有关的人员和部门都要参与，加强设备定期管理意识 实现设备的全系统管理推荐：设备管理系统 重庆六业科技根据长期的市场调研，总结各大工厂、国企、大中型企事业单位设备管理出现的问题，自主研发的设备管理系统，具有设备文档的管理，设备缺陷分析及事故管理，维修计划排程和成本核算，预防性维修以及统计报表等功能，是目前企事业设备管理最好的帮手。 设备管理系统有什么功能： 设备资产及技术管理：建立设备信息库，实现设备前期的选型、采购、安装测试、转固；设备转固后的移装、封存、启封、闲置、租赁、转让、报废，设备运行过程中的技术状态、维护、保养、润滑情况记录。 设备文档管理：设备相关档案的登录、整理以及与设备的挂接。 设备缺陷及事故管理：设备缺陷报告、跟踪、统计，设备紧急事故处理。 预防性维修：以可靠性技术为基础的定期维修、维护，维修计划分解，自动生成预防性维修工作单。 维修计划排程：根据日程表中设备运行记录和维修人员工作记录，编制整体维修、维护任务进度的安排计划，根据任务的优先级和维修人员工种情况来确定维修工人。工单的生成与跟踪：对自动生成的预防性、预测性维修工单和手工录入的请求工单，进行人员、备件、工具、工作步骤、工作进度等的计划、审批、执行、检查、完工报告，跟踪工单状态。 备品、备件管理：建立备件台帐，编制备件计划，处理备件日常库存事务（接受、发料、移动、盘点等），根据备件最小库存量或备件重订货点自动生成采购计划，跟踪备件与设备的关系。 维修成本核算：凭借工作单上人员时间、所耗物料、工具和服务等信息，汇总维修、维护任务成本，进行实际成本与预算的分析比较。 最小二乘法及其应用 1． 引言 最小二乘法在19世纪初发明后,很快得到欧洲一些国家的天文学家和测地学家的广泛关注。据不完全统计,自1805年至1864年的60年间,有关最小二乘法的研究论文达256篇,一些百科全书包括1837年出版的大不列颠百科全书第7版,亦收入有关方法的介绍。同时,误差的分布是“正态”的,也立刻得到天文学家的关注及大量经验的支持。如贝塞尔( F. W. Bessel, 1784—1846)对几百颗星球作了三组观测,并比较了按照正态规律在给定范围内的理论误差值和实际值,对比表明它们非常接近一致。拉普拉斯在1810年也给出了正态规律的一个新的理论推导并写入其《分析概论》中。正态分布作为一种统计模型,在19世纪极为流行,一些学者甚至把19世纪的数理统计学称为正态分布的统治时代。在其影响下,最小二乘法也脱出测量数据意义之外而发展成为一个包罗极大,应用及其广泛的统计模型。到20世纪正态小样本理论充分发展后,高斯研究成果的影响更加显著。最小二乘法不仅是19世纪最重要的统计方法,而且还可以称为数理统计学之灵魂。相关回归分析、方差分析和线性模型理论等数理统计学的几大分支都以最小二乘法为理论基础。正如美国统计学家斯蒂格勒( S. M. Stigler)所说,“最小二乘法之于数理统计学犹如微积分之于数学”。最小二乘法是参数回归的最基本得方法所以研究最小二乘法原理及其应用对于统计的学习有很重要的意义。 2. 最小二乘法 所谓最小二乘法就是：选择参数10,b b ,使得全部观测的残差平方和最小. 用数学公式表示为： 21022)()(m in i i i i i x b b Y Y Y e --=-=∑∑∑∧ 为了说明这个方法，先解释一下最小二乘原理，以一元线性回归方程为例. i i i x B B Y μ++=10 （一元线性回归方程） 曲线拟合及其应用综述 摘要：本文首先分析了曲线拟合方法的背景及在各个领域中的应用，然后详细介绍了曲线拟合方法的基本原理及实现方法，并结合一个具体实例，分析了曲线拟合方法在柴油机故障诊断中的应用，最后对全文内容进行了总结，并对曲线拟合方法的发展进行了思考和展望。 关键词：曲线拟合最小二乘法故障模式识别柴油机故障诊断 1背景及应用 在科学技术的许多领域中，常常需要根据实际测试所得到的一系列数据，求出它们的函数关系。理论上讲，可以根据插值原则构造n 次多项式Pn(x)，使得Pn(x)在各测试点的数据正好通过实测点。可是, 在一般情况下，我们为了尽量反映实际情况而采集了很多样点，造成了插值多项式Pn(x)的次数很高，这不仅增大了计算量，而且影响了函数的逼近程度；再就是由于插值多项式经过每一实测样点，这样就会保留测量误差，从而影响逼近函数的精度，不易反映实际的函数关系。因此，我们一般根据已知实际测试样点，找出被测试量之间的函数关系，使得找出的近似函数曲线能够充分反映实际测试量之间的关系，这就是曲线拟合。 曲线拟合技术在图像处理、逆向工程、计算机辅助设计以及测试数据的处理显示及故障模式诊断等领域中都得到了广泛的应用。 2 基本原理 2.1 曲线拟合的定义 解决曲线拟合问题常用的方法有很多，总体上可以分为两大类：一类是有理论模型的曲线拟合，也就是由与数据的背景资料规律相适应的解析表达式约束的曲线拟合；另一类是无理论模型的曲线拟合，也就是由几何方法或神经网络的拓扑结构确定数据关系的曲线拟合。 2.2 曲线拟合的方法 解决曲线拟合问题常用的方法有很多，总体上可以分为两大类：一类是有理论模型的曲线拟合，也就是由与数据的背景资料规律相适应的解析表达式约束的曲线拟合；另一类是无理论模型的曲线拟合，也就是由几何方法或神经网络的拓扑结构确定数据关系的曲线拟合。 2.2.1 有理论模型的曲线拟合 有理论模型的曲线拟合适用于处理有一定背景资料、规律性较强的拟合问题。通过实验或者观测得到的数据对（x i,y i）（i=1,2, …,n），可以用与背景资料规律相适应的解析表达式y=f(x,c)来反映x、y之间的依赖关系，y=f(x,c)称为拟合的理论模型，式中c=c0,c1,…c n是待定参数。当c在f中线性出现时，称为线性模型，否则称为非线性模型。有许多衡量拟合优度的标准，最常用的方法是最小二乘法。 2.2.1.1 线性模型的曲线拟合 线性模型中与背景资料相适应的解析表达式为： ε β β+ + =x y 1 （1） 式中，β0，β1未知参数，ε服从N(0，σ2)。 将n个实验点分别带入表达式（1）得到： i i i x yε β β+ + = 1 （2） 式中i=1,2,…n，ε1, ε2,…, εn相互独立并且服从N(0，σ2)。 根据最小二乘原理，拟合得到的参数应使曲线与试验点之间的误差的平方和达到最小，也就是使如下的目标函数达到最小： 2 1 1 ) ( i i n i i x y Jε β β- - - =∑ = （3） 将试验点数据点入之后，求目标函数的最大值问题就变成了求取使目标函数对待求参数的偏导数为零时的参数值问题，即： ) ( 2 1 1 = - - - - = ? ?∑ = i i n i i x y J ε β β β （4） 销售部月度工作计划表范文 一、对于销售工作的认识 1.市场分析，根据市场容量和个人能力，客观、科学的制定出销售任务。暂订年任务：销售额100万元。 2.适时作出工作计划，制定出月计划和周计划。并定期与业务相关人员会议沟通，确保各专业负责人及时跟进。 3.注重绩效管理，对绩效计划、绩效执行、绩效评估进行全程的关注与跟踪。 4.目标市场定位，区分大客户与一般客户，分别对待，加强对大客户的沟通与合作，用相同的时间赢取的市场份额。 5.不断学习行业新知识，新产品，为客户带来实用的资讯，更好为客户服务。并结识弱电各行业各档次的优秀产品提供商，以备工程商需要时能及时作好项目配合，并可以和同行分享行业人脉和项目信息，达到多赢。 6.先友后单，与客户发展良好的友谊，处处为客户着想，把客户当成自己的好朋友，达到思想和情感上的交融。 7.对客户不能有隐瞒和欺骗，答应客户的承诺要及时兑现，讲诚信不仅是经商之本，也是为人之本。 8.努力保持***的同事关系，善待同事，确保各部门在项目实施中各项职能的顺利执行。 二、销售工作具体量化任务 1.制定出月计划和周计划、及每日的工作量。每天至少打30个电话，每周至少拜访20位客户，促使潜在客户从量变到质变。上午重点电话回访和预约客户，下午时间长可安排拜访客户。考虑北京市地广人多，交通涌堵，预约时选择客户在相同或接近的地点。 2.见客户之前要多了解客户的主营业务和潜在需求，先了解决策人的个人爱好，准备一些有对方感兴趣的话题，并为客户提供针对性的解决方案。 3、从招标网或其他渠道多搜集些项目信息供工程商投标参考，并为工程商出谋划策，配合工程商技术和商务上的项目运作。 4、做好每天的工作记录，以备遗忘重要事项，并标注重要未办理事项。 5.填写项目跟踪表，根据项目进度：前期设计、投标、深化设计、备货执行、验收等跟进，并完成各阶段工作。 计划跟踪与进度控制 当项目计划编制完成后，项目将进入执行阶段。项目在执行过程中，由于各种内外环境的变化，使得项目不能按照预先拟定的计划进行，项目实际执行结果与计划蓝图之间总会出现一定偏差。这种偏差的存在可能会影响我们对项目计划的实施。这就需要我们定期的收集项目的有关信息，利用软件工具对计划进度、资源、费用进行监控，得到当前计划活动与目标计划活动的监控差值，从而为分析项目计划各种指标提供依据，及早发现问题，纠正偏差，使项目计划回到正常的执行轨道上。 在执行过程中，软件提供了丰富的图表、临界值、报表过滤器等主要分析工具，为用户提供有效的辅助决策方案数据。这些工具都可以直接挂接在WBS/项目下，对当前WBS/项目进行监控分析，符合项目管理的范围管理思想。 1、每一更新周期应提供的书面报告内容 1.1、作业清单，包括以下内容： a.作业清单(作业代码名称、原定工期、紧前作业、紧后作业) (作业清单报表) b.尚需工期、实际工期 c.最早开始时间、最早完成时间、最晚开始时间、最晚完成时间 d.实际开始时间、实际完成时间 e.自由时差、总时差 (作业时间工期报表) (作业时间分析报表) 1.2、工程量完成情况报表、资源使用情况报表 工程量完成情况报表应该包括以下内容：作业编码/名称、工程量名称、单位、单价、本期单价、本期数量、本期完成费用、累计完成数量、累计完成费用、尚需数量、尚需费用、完成时数量、完成时费用预算、计划完成百分比、实 际完成百分比。 (工程量完成情况报表) 资源使用情况报表应该包括以下内容：作业编码/名称、工程量名称、单位、单价、本期单价、本期数量、本期完成费用、累计完成数量、累计完成费用、 尚需数量、尚需费用、完成时数量、完成时费用。 (资源使用情况报表) 1.3、挣值分析报表 通过挣值分析报表可以动态的从进度/成本的角度去分析作业的执行情 况，将项目的不良执行情况扼杀于萌芽状态。 a.作业完成百分比分析报表(应包括以下内容：作业编码/名称、计划完成百分 比、实际完成百分比、进度完成百分比、费用消耗百分比) 毕业论文文献综述 信息与计算科学 最小二乘法的原理及应用 一、国内外状况 国际统计学会第56届大会于2007年8月22-29日在美丽的大西洋海滨城市、葡萄牙首都里斯本如期召开。应大会组委会的邀请，以会长李德水为团长的中国统计学会代表团一行29人注册参加了这次大会。北京市统计学会、山东省统计学会，分别组团参加了这次大会。中国统计界（不含港澳台地区）共有58名代表参加了这次盛会。本届大会的特邀论文会议共涉及94个主题，每个主题一般至少有3-5位代表做学术演讲和讨论。通过对大会论文按研究内容进行归纳，特邀论文大致可以分为四类：即数理统计，经济、社会统计和官方统计，统计教育和统计应用。 数理统计方面。数理统计作为统计科学的一个重要部分，特别是随机过程和回归分析依然展现着古老理论的活力，一直受到统计界的重视并吸引着众多的研究者。本届大会也不例外。 二、进展情况 数理统计学19世纪的数理统计学史, 就是最小二乘法向各个应用领域拓展的历史席卷了统计大部分应用的几个分支——相关回归分析, 方差分析和线性模型理论等, 其灵魂都在于最小二乘法; 不少近代的统计学研究是在此法的基础上衍生出来, 作为其进一步发展或纠正其不足之处而采取的对策, 这包括回归分析中一系列修正最小二乘法而导致的估计方法。 数理统计学的发展大致可分 3 个时期。① 20 世纪以前。这个时期又可分成两段，大致上可以把高斯和勒让德关于最小二乘法用于观测数据的误差分析的工作作为分界线，前段属萌芽时期，基本上没有超出描述性统计量的范围。后一阶段可算作是数理统计学的幼年阶段。首先，强调了推断的地位，而摆脱了单纯描述的性质。由于高斯等的工作揭示了最小二乘法的重要性，学者们普遍认为，在实际问题中遇见的几乎所有的连续变量，都可以满意地用最小二乘法来刻画。这种观点使关于最小二乘法得到了深入的发展，②20世纪初到第二次世界大战结束。这是数理统计学蓬勃发展达到成熟的时期。许多重要的基本观点和方法，以及数理统计学的主要分支学科，都是在这个时期建立和发展起来的。这个时期的成就，包含了至今仍在广泛使用的大多数统计方法。在其发展中，以英国统计学家、生物学家费希尔为代表的英国学派起了主导作用。③战后时期。这一时期中，数理统计学在应用和理论两方面继续获得很大的进展。 人事月度工作计划表 为了确保公司的高速发展，为公司提供强有力的人力资源及后勤保障，人事行政部20xx年度工作目标是：认真学习，落实公司的经营的长远规划，以求真务实的态度，落实公司对人事行政部的人力资助人源及工后勤力工作的布置，统一思想，加强服务意识，做好本部门承担的工作。 第一部分：人力资源工作计划 20xx年将是公司高速发展的一年，发展中最首要的保障就是人力资源保障，人力是根本。所以20xx年，人事行政部将根据公司经营策略的需要，在人力资源工作中将围绕以下几方面开展工作： 一、人事招聘、人力资源开发以及组织结构完善。 1、20xx年将根据公司职位设置及人员配置计划，确定招聘需求及人力资源开发计划。 2、招聘方式及渠道。 ⑴、主管以上管理人员，人事行政部将会同集团人力资源中心一起沟通、协作招聘，主要渠道以内部提升、网站招聘、猎头公司为主。 ⑵、一般员工，由人事行政部自主招聘，主要渠道以公司内部提升、同周边人才市场、职介所合作、招聘网站发布、及张贴小广告的方式进行招聘。 3、招聘政策。 ⑴、内部提升优先，公司职位空缺，优先从基层员工中挑选有能力胜任该职位的员工进行竞聘，选拔提升。 ⑵、德才兼备者优先，在人员的选择中，注重员工的个人品德、工作能力、团队协作精神，让品德优秀、有才干、集体观念强的人才进入公司。 ⑶、对公司忠诚度高的人才优先，为了保持员工的稳定性，减少不确定因素的流失，在人员选拔过程式中，对公司忠诚度高的员工优先选拔及重用。 4、招聘费用预算。 ⑴、网络招聘费用：（无），网络招聘利用集团招聘网站及资源，由集团承担费用。 ⑵、人才市场招聘费用：按全年到人才市场招聘6次左右计算，预计费用为：2280.00元左右。 ⑶、猎头费用：（无），高层职位如果需要与猎头公司合作，人事行政部将与集团人力资源中心沟通与集团共同完成。 ⑷、全年总计费用：2280.00元左右。 5、组织结构完善。 ⑴、根据因事设人的原则，确定20xx年度公司组织结构。 ⑵、根据公司发展的需求设定组织结构的原则及时调整公司组织结构。 ⑶、精简臃肿的组织机构，压缩非必要的编制人员，减少管理层级，确保工作效率的提升及工作汇报、沟通的及时有效。 ⑷、对市场硬件设施进行改善及添置，增加安全防范设备，减少人员编制，降低运营成本，加强人员培训，精兵强将，不断提升市场管理水平及服务水平。 二、培训 最小二乘法综述及算例 一最小二乘法的历史简介 1801年，意大利天文学家朱赛普·皮亚齐发现了第一颗小行星谷神星。经过40天的跟踪观测后，由于谷神星运行至太阳背后，使得皮亚齐失去了谷神星的位置。随后全世界的科学家利用皮亚齐的观测数据开始寻找谷神星，但是根据大多数人计算的结果来寻找谷神星都没有结果。时年24岁的高斯也计算了谷神星的轨道。奥地利天文学家海因里希·奥尔伯斯根据高斯计算出来的轨道重新发现了谷神星。 高斯使用的最小二乘法的方法发表于1809年他的著作《天体运动论》中。 经过两百余年后，最小二乘法已广泛应用与科学实验和工程技术中，随着现代电子计算机的普及与发展，这个方法更加显示出其强大的生命力。 二最小二乘法原理 最小二乘法的基本原理是：成对等精度测得的一组数据),...,2,1(,n i y x i i =，是找出一条最佳的拟合曲线，似的这条曲线上的个点的值与测量值的差的平方和在所有拟合曲线中最小。 设物理量y 与1个变量l x x x ,...,2,1间的依赖关系式为:)(,...,1,0;,...,2,1n l a a a x x x f y =。 其中n a a a ,...,1,0是n +l 个待定参数,记()2 1 ∑=- = m i i i y v s 其中 是测量值, 是由己求 得的n a a a ,...,1,0以及实验点),...,2,1)(,...,(;,2,1m i v x x x i il i i =得出的函数值 )(,...,1,0;,...,2,1n il i i a a a x x x f y =。 在设计实验时, 为了减小误差, 常进行多点测量, 使方程式个数大于待定参数的个数, 此时构成的方程组称为矛盾方程组。通过最小二乘法转化后的方程组称为正规方程组(此时方程式的个数与待定参数的个数相等) 。我们可以通过正规方程组求出a 最小二乘法又称曲线拟合, 所谓“ 拟合” 即不要求所作的曲线完全通过所有的数据点, 只要求所得的曲线能反映数据的基本趋势。 三曲线拟合 曲线拟合的几何解释: 求一条曲线, 使数据点均在离此曲线的上方或下方不远处。 （1）一元线性拟合 设变量y 与x 成线性关系x a a y 10+=,先已知m 个实验点),...,2,1(,m i v x i i =，求两个未知参数1,0a a 。 令()2 1 10∑ =--=m i i i x a a y s ，则1,0a a 应满足1,0,0==??i a s i 。 即 i v i v 编号：YB-JH-0989 ( 工作计划) 部门：_____________________ 姓名：_____________________ 日期：_____________________ WORD文档/ A4打印/ 可编辑 德育月度工作计划表(2021 版) Frequently formulating work plans can make people’s life, work and study more regular, and develop good habits, which is a habit necessary for success in doing things 德育月度工作计划表(2021版) 摘要：经常制订工作计划，可以使人的生活、工作和学习比较有规律性，养成良好的习惯，因为习惯了制订 工作计划，于是让人变得不拖拉、不懒惰、不推诿、不依赖，养成一种做事成功必须具备的习惯。本内容可 以放心修改调整或直接使用。 一、指导思想 围绕德育工作思路和要点，加大德育创新力度，深化教育改革，全面推进素质教育。进一步加强学生的政治思想教育、道德教育、纪律教育、法制教育，增强学生的爱国主义、集体主义和社会主义的思想。巩固校园文化建设成果，强化学生良好品德行为习惯的养成，探索学生良好心理素质形成的规律与方法，完善美育和劳动教育，促进学生全面发展和健康成长。以科研带队伍，突出特色，务求实效，探索培养具有创新精神和实践能力的新型人才培养模式。 二、工作目标: (一)加强学生日常行为规范教育，保持学生良好的行为习惯; (二)加强法制教育，加强安全教育，确保学期内无责任事故发生; (三)深化团队活动，从活动中培养和提高学生的素质。组织开展综合实践活动，不断提高学生综合素质; 智能物流跟踪与仓储管理系统 2016年9月23日 目录 1、产品方案介绍 0 1.1概述 0 1.2业务流程图 (1) 1.3 业务流程简介 0 1.4 主要硬件设备简介 (6) 2、实验内容 (10) 3、配置清单及技术指标 (11) 1、产品方案介绍 1.1概述 “互联网+”浪潮让一切传统行业和产业都在发生改变，物流业也开始进入智能时代。目前，我国物流系统虽然跨越了简单送货上门的阶段，但层次上仍是传统意义上的物流配送，先进信息技术在物流行业的应用和推广水平仍然较低，且存在物流企业规模较小且布局散乱、物流信息标准滞后等问题，物流配送的许多环节造成巨大的成本、人力、时间浪费。总体来说，我国智慧物流尚处于发展的初级阶段，运输及仓储信息化低等仍需突破。而智能物流能使整个物流系统能模仿人的智能，具有思维、感知、学习、推理判断和自行解决物流中某些问题的能力，标志着信息化在整合网络和管控流程中进入到一个新的阶段，即进入到一个动态的，实时进行选择和控制的管理水平，并成为未来发展的方向。 智能物流跟踪与仓储管理系统是利用无线射频识别技术将物联网的思想转换成实际应用的典型方案；智能物流跟踪与仓储管理系统模拟了从生产企业包装至仓储物流、商超存储，乃至消费购物、收银等整个流程。利用先进的RFID技术、AGV自动车辆导航技术和计算机网络、数据库、软件等技术，真实的展现了典型的商业运作的业务流程，实现智能仓储、智能物流、智能收银等功能，全面实现“从仓储物流到顾客购物”的智能化及零售业务管理的智能化，学生通过在智能物流跟踪与仓储物流系统实训室内各种活动及作业的模拟可以掌握现代物流信息，了解智能物流跟踪与仓储物流系统的总体流程，增强管理意识，提高团队意识和沟通能力。 智能物流输送系统可广泛应用于汽车制造、工程机械、服装家电、农用机械、 ( 工作计划 ) 单位：_________________________ 姓名：_________________________ 日期：_________________________ 精品文档 / Word文档 / 文字可改 销售部门月度工作计划表Monthly work schedule of Sales Department 销售部门月度工作计划表 【篇一】 一、销量指标： 至20xx年11月31日，山东区销售任务560万元，销售目标700万元(20xx年度销售计划表附后); 二、计划拟定： 1、年初拟定《年度销售总体计划》; 2、年终拟定《年度销售总结》; 3、月初拟定《月销售计划表》和《月访客户计划表》; 4、月末拟定《月销售统计表》和《月访客户统计表》; 三、客户分类： 根据xx年度销售额度，对市场进行细分化，将现有客户分为VIP 用户、一级用户、二级用户和其它用户四大类，并对各级用户进行 全面分析。 四、实施措施： 1、技术交流： (1)本年度针对VIP客户的技术部、售后服务部开展一次技术交流研讨会; (2)参加相关行业展会两次，其中展会期间安排一场大型联谊座谈会; 2、客户回访： 目前在国内市场上流通的相似品牌有七八种之多，与我司品牌相当的有三四种，技术方面不相上下，竞争愈来愈激烈,已构成市场威胁。为稳固和拓展市场，务必加强与客户的交流，协调与客户、直接用户之间的关系。 (1)为与客户加强信息交流，增近感情，对VIP客户每月拜访一次;对一级客户每两月拜访一次;对于二级客户根据实际情况另行安排拜访时间; (2)适应把握形势，销售工作已不仅仅是销货到我们的客户方即 误差理论综述与最小二乘法讨论 摘要：本文对误差理论和有关数据处理的方法进行综述。并且针对最小二乘法（LS）的创立、发展、思想方法等相关方面进行了研究和总结。同时，将近年发展起来的全面最小二乘法(TLS)同传统最小二乘法进行了对比。 1.误差的有关概念 对科学而言，各种物理量都需要经过测量才能得出结果。许多物理量的发现，物理常数的确定，都是通过精密测量得到的。任何测试结果，都含有误差，因此，必须研究，估计和判断测量结果是否可靠，给出正确评定。对测量结果的分析、研究、判断，必须采用误差理论，它是我们客观分析的有力工具 测量基本概念 一个物理量的测量值应由数值和单位两部分组成。按实验数据处理的方式，测量可分为直接测量、间接测量和组合测量。 直接测量:可以用测量仪表直接读出测量值的测量。 间接测量:有些物理量无法直接测得，需要依据待测物理量与若干直接测量量的函数关系求出。 组合测量:如有若干个待求量，把这些待求量用不同方法组合起来进行测量，并把测量结果与待求量之间的函数关系列成方程组，用最小二乘法求出这个待求量的数值，即为组合测量。 误差基本概念 误差是评定测量精度的尺度，误差越小表示精度越高。若某物理量的测量值为y，真值为Y，则测量误差dy=y-Y。虽然真值是客观存在的，但实际应用时它一般无从得知。按照误差的性质，可分为随机误差，系统误差和粗大误差三类。 随机误差:是同一测量条件下，重复测量中以不可预知方式变化的测量误差分量。 系统误差:是同一测量条件下，重复测量中保持恒定或以可预知方式变化的测量误差分量。 粗大误差:指超出在规定条件下预期的误差。 等精度测量的随机误差 当对同一量值进行多次等精度的重复测量，得到一系列的测量值，每个测量 设备管理系统设计 方案 冠唐设备管理系统 设计方案 成都冠唐科技有限公司 8月 目录 一，项目背景........................................................................... 错误!未定义书签。 1.1 企业概述 ...................................................................... 错误!未定义书签。 1.2 传统设备管理模式存在的问题 ................................... 错误!未定义书签。 1.3 实施设备管理系统的目标 ........................................... 错误!未定义书签。 1.4 需求要点 ...................................................................... 错误!未定义书签。二，系统设计原则 ................................................................... 错误!未定义书签。三，总体设计........................................................................... 错误!未定义书签。 3.1 技术基础 ...................................................................... 错误!未定义书签。 3.1 系统安全 ...................................................................... 错误!未定义书签。 3.2 管理权限划分............................................................... 错误!未定义书签。四，功能模块设计 ................................................................... 错误!未定义书签。 4.1 设备信息 ...................................................................... 错误!未定义书签。 4.2 设备台帐 ...................................................................... 错误!未定义书签。 4.3 维修保养计划............................................................... 错误!未定义书签。 4.4 维修保养记录............................................................... 错误!未定义书签。 4.5 维修经验库 .................................................................. 错误!未定义书签。 4.6 设备申购 ...................................................................... 错误!未定义书签。 4.7 设备调拨 ...................................................................... 错误!未定义书签。 4.8 设备报废 ...................................................................... 错误!未定义书签。 4.9 备品配件信息管理....................................................... 错误!未定义书签。 精心整理 人事工作月度工作计划表 为了确保公司的高速发展，为公司提供强有力的人力资源及后勤保障，人事行政部20xx08年度工作目标是：认真学习，落实公司的经营的长远规划，以求真务实的态度，落实公司对人事行政部的人力资助人源及工后勤力工作的布置，统一思想，加强服务意识，做好本部门承担的工作。 第一部分：人力资源工作计划 20xx 1、2⑴⑵3⑴ ⑵⑶4⑴、网络招聘费用：（无），网络招聘利用集团招聘网站及资源，由集团承担费用。 ⑵、人才市场招聘费用：按全年到人才市场招聘6次左右计算，预计费用为：2280.00元左右。 ⑶、猎头费用：（无），高层职位如果需要与猎头公司合作，人事行政部将与集团人力资源中心沟通与集团共同完成。 ⑷、全年总计费用：2280.00元左右。 5、组织结构完善。 ⑴、根据因事设人的原则，确定2008年度公司组织结构。 ⑵、根据公司发展的需求设定组织结构的原则及时调整公司组织结构。 ⑶、精简臃肿的组织机构，压缩非必要的编制人员，减少管理层级，确保工作效率的提升及工作汇报、沟通的及时有效。 ⑷、对市场硬件设施进行改善及添置，增加安全防范设备，减少人员编制，降低运营成本，加强人员培训，精兵强将，不断提升市场管理水平及服务水平。 二、培训 1 ⑴ ⑵ 2 ⑴ — — ⑵ ⑶、加强晋升培训体系： 要求每位晋升或即将晋升的员，都必须参加相应的管理技能、专业知识的培训，并且在考试合格后，才能担任相应的职务。 ⑷、外部培训体系的建立： 加强与行业主管部门、行业培训机构、咨询顾问公司、高等院校的沟通交流。 根据外部培训的不同科目，选派不同的人员参加外部培训，学习先进的生产、管理方法，提升公司内部的管理水平，对参加外部培训的人员必须要签订培训协议。 计划管理、实施及进度跟踪 我们开发工具项目组是用PROJECT进行项目计划制定和进度监控的，书上说结合这个工具可以很方便地进行计划管理、实施及进度跟踪，不过这个方便性体现在哪里呢?这个问题一直困扰着我，而且百思不能其解。最近突发奇想，制定了一套计划管理的方法，我把它介绍给你，希望可以帮到您。 首先项目组要对用户需求进行整理，根据整理出的用户需求，可以大致整理出一份功能列表。一般这份功能列表会记录在一份EXCEL文档中，其中可定义以下几个字段列：任务分类、任务名称、备注、工作量——一般单位是人/天、优先级、责任人。这些信息，其实跟我们下一步需要做的工作是息息相关的。那具体我们要怎么做呢?我认为排好计划的重中之重就是要把工作量估算好并且把任务按优先级安排好顺序。但是，在这个之前，如果有时间的话，最好做一下需求规格的整理，只有这样子我们的估算量才会比较准确。当然，在需求规格说明书整理好之后，进行需求规格说明书的文档评审那是再好不过的了。评审可以根据实际需要邀请相关的用户专家或人员参与。如果可能的话，一次通过评审固然好，不过现实中的实际情况往往没有这么理想。相反地，要不断对文档进行调整和再评审，才能整理出一份完整且完善并对设计和编码工作有真正指导意义的需求文档。如果条件允许的话，最好测试人员也能同时参加一下。 然而，实际的项目开发中，往往由于工期紧张，而不得不压缩需求、设计的时间，甚至有的项目抛弃了需求和设计阶段而直接进入编码开发阶段。在这里，我不想辩证这种做法有多少多少的不好(而且我敢肯定地说——这肯定是不好的)，关键是如果没有时间做这些工作，我们应该怎样更好的控制好需求，同时 题目:最小二乘法的综述及算例院系：航天学院自动化 班级： 学号： 学生签名： 指导教师签名： 日期：2011年12月6日 目录 1．综述 (3) 2．概念 (3) 3．原理 (4) 4．算例 (6) 5．总结 (10) 参考文献 (10) 1．综述 最小二乘法最早是由高斯提出的，这是数据处理的一种很有效的统计方法。高斯用这种方法解决了天文学方面的问题，特别是确定了某些行星和彗星的天体轨迹。这类天体的椭圆轨迹由5个参数确定，原则上，只要对它的位置做5次测量就足以确定它的整个轨迹。但由于存在测量误差，由5次测量所确定的运行轨迹极不可靠，相反，要进行多次测量，用最小二乘法消除测量误差，得到有关轨迹参数的更精确的值。最小二乘法近似将几十次甚至上百次的观察所产生的高维空间问题降到了椭圆轨迹模型的五维参数空间。 最小二乘法普遍适用于各个科学领域，它在解决实际问题中发挥了重要的作用。它在生产实践、科学实验及经济活动中均有广泛应用。比如说，我们引入等效时间的概念,根据Arrhenius 函数和指数函数研究水化热化学反应速率随温度的变化,最后采用最小二乘法回归分析试验数据,确定绝热温升和等效时间的关系式。 为了更好地掌握最小二乘法，我们引入以下两个问题： (1)假设已知一组二维数据（i i y x ,），（i=1,2,3···n ），怎样确定它的拟合曲线y=f(x)（假设为多项式形式f(x)=n n x a x a a +++...10）,使得这些点与曲线总体来说尽量接近？ (2)若拟合模型为非多项式形式bx ae y =，怎样根据已知的二维数据用最小二乘线性拟合确定其系数，求出曲线拟合函数？ 怎样从给定的二维数据出发，寻找一个简单合理的函数来拟合给定的一组看上去杂乱无章的数据，正是我们要解决的问题。 2．概念 在科学实验的统计方法研究中，往往要从一组实验数（i i y x ,）（i=1,2,3···m ）中寻找自变量x 与y 之间的函数关系y=F(x).由于观测数据往往不准确，此时不要求y=F(x)经过所有点（i i y x ,），而只要求在给定i x 上误差i δ=F （i x ）i y -（i=1,2,3···m ）按某种标准最小。 若记δ=( )δδδm T 2 ,1,就是要求向量δ的范数δ 最小。如果用最大范数，计算上困 难较大，通常就采用Euclid 范数2 δ 作为误差度量的标准。 关于最小二乘法的一般提法是：对于给定的一组数据（i i y x ,） (i=0,1,…m)要求在函数空间Φ=span{ n ???,....,,10}中找一个函数S*(x)，使加权的误差平方和22 δ = 1.引言 1.1编写目的： 设备管理系统是一个以设备为中心，对设备从统计到报废的一个全生命周期中所发生的各种事件进行跟踪的一个管理信息系统。系统可以为企业提供一个简便实用的管理平台，将设备全生命周期的管理工作信息化，有效地进行设备管理工作，以提高设备生命周期的利润率，直接为企业创造价值。设计优良的设备管理系统，实现安全性和高质量，防止故障发生，从而使企业达到降低成本和全面生产效率的提高。 1.2背景 ●企业设备管理系统开发 用户：企业及工厂 ●设备管理系统要实现对设备的管理要求，包括： 录入、浏览、删除、修改、检索和统计等。不同 的企业只需要对其稍作修改即可开发出符合本 企业要求的设备管理系统 1.3定义 SQL server2005的定义： SQL Server2005是当前最广泛的数据库之一，SQL Server 2005 通过在可伸缩性、数据集成、开发工 具和强大的分析等方面的革新更好的确立了微软在BI领域的领导地位。SQL Server 2005 能够把关键的信息及时的传递到组织内员工的手中，从而实现了可伸缩的商业智能。从CEO 到信息工作者，员工可以快速的、容易的处理数据，以更快更好的做出决策。SQL Server 2005全面的集成、分析和报表功能使企业能够提高他们已有应用的价值，即便这些应用是在不同的平台上。 1.4参考资料 SQL server教程 2外部设计 2.1标识符和状态 4.2.2数据完整性约束 （1）主键约束、非空值约束 八个表中都有主键，在设备表和用户表中，设备号和用户名是主键，因为一个公司中可能一种设备不只只有一个，也许有多个，用户密码也可能会一样的，所 文献综述 信息与计算科学 最小二乘法的原理及应用 一、国内外状况 国际统计学会第56届大会于2007年8月22-29日在美丽的大西洋海滨城市、葡萄牙首都里斯本如期召开。应大会组委会的邀请，以会长李德水为团长的中国统计学会代表团一行29人注册参加了这次大会。北京市统计学会、山东省统计学会，分别组团参加了这次大会。中国统计界（不含港澳台地区）共有58名代表参加了这次盛会。本届大会的特邀论文会议共涉及94个主题，每个主题一般至少有3-5位代表做学术演讲和讨论。通过对大会论文按研究内容进行归纳，特邀论文大致可以分为四类：即数理统计，经济、社会统计和官方统计，统计教育和统计应用。 数理统计方面。数理统计作为统计科学的一个重要部分，特别是随机过程和回归分析依然展现着古老理论的活力，一直受到统计界的重视并吸引着众多的研究者。本届大会也不例外。 二、进展情况 数理统计学19世纪的数理统计学史, 就是最小二乘法向各个应用领域拓展的历史席卷了统计大部分应用的几个分支——相关回归分析, 方差分析和线性模型理论等, 其灵魂都在于最小二乘法; 不少近代的统计学研究是在此法的基础上衍生出来, 作为其进一步发展或纠正其不足之处而采取的对策, 这包括回归分析中一系列修正最小二乘法而导致的估计方法。 数理统计学的发展大致可分 3 个时期。① 20 世纪以前。这个时期又可分成两段，大致上可以把高斯和勒让德关于最小二乘法用于观测数据的误差分析的工作作为分界线，前段属萌芽时期，基本上没有超出描述性统计量的范围。后一阶段可算作是数理统计学的幼年阶段。首先，强调了推断的地位，而摆脱了单纯描述的性质。由于高斯等的工作揭示了最小二乘法的重要性，学者们普遍认为，在实际问题中遇见的几乎所有的连续变量，都可以满意地用最小二乘法来刻画。这种观点使关于最小二乘法得到了深入的发展，②20世纪初到第二次世界大战结束。这是数理统计学蓬勃发展达到成熟的时期。许多重要的基本观点和方法，以及数理统计学的主要分支学科，都是在这个时期建立和发展起来的。这个时期的成就，包含了至今仍在广泛使用的大多数统计方法。在其发展中，以英国统计学家、生物学家费希尔为代表的英国学派起了主导作用。③战后时期。这一时期中，数理统计学在应用和理论两方面继续获得很大的进展。 生产部月工作计划表 工作计划实际上有许多不同种类，它们不仅有时间长短之分，而且有范围大小之别。下面是小编为您整理的关于生产部月工作计划表的相关资料，欢迎阅读！ 生产部月工作计划表例1 为了贯彻落实"安全第一，预防为主，综合治理"的方针，强化安全生产目标管理，生产部月工作计划。结合工厂实际，特制定201X年安全生产工作计划，将安全生产工作纳入重要议事日程，警钟长鸣，常抓不懈。 一、全年目标 全年实现无死亡、无重伤、无重大生产设备事故，无重大事故隐患，工伤事故发生率低于厂规定指标，综合粉尘浓度合格率达80%以上(如下表)。 二、指导思想 要以公司对201X年安全生产目标管理责任为指导，以工厂安全工作管理制度为标准，以安全工作总方针"安全第一，预防为主。"为原则，以车间、班组安全管理为基础，以预防重点单位、重点岗位重大事故为重点，以纠正岗位违章指挥，违章操作和员工劳动保护穿戴为突破口，落实各项规章制度，开创安全工作新局面，实现安全生产根本好转。 三、牢固树立"安全第一"的思想意识 各单位部门要高度重视安全生产工作，把安全生产工作 作为重要的工作来抓，认真贯彻"安全第一，预防为主"的方针，进一步增强安全生产意识，出实招、使真劲，把"安全第一"的方针真正落到实处，通过进一步完善安全生产责任制，首先解决领导意识问题，真正把安全生产工作列入重要议事日程，摆到"第一"的位置上，只有从思想上重视安全，责任意识才能到位，才能管到位、抓到位，才能深入落实安全责任，整改事故隐患，严格执行"谁主管，谁负责"和"管生产必须管安全"的原则，力保安全生产。 四、深入开展好安全生产专项整治工作 根据工厂现状，确定出201X年安全生产工作的重点单位、重点部位，完善各事故处理应急预案，加大重大隐患的监控和整改力度，认真开展厂级月度安全检查和专项安全检查，车间每周进行一次安全检查，班组坚持班中的三次安全检查，并要求生产科、车间领导及管理人员加强日常安全检查，对查出的事故隐患，要按照"三定四不推"原则，及时组织整改，暂不能整改的，要做好安全防范措施，尤其要突出对煤气炉、锅炉、硫酸罐、液氨罐等重要部位的安全防范，做好专项整治工作，加强对易燃易爆、有毒有害等危险化学品的管理工作，要严格按照《安全生产法》、《危险化学品安全管理条例》强化专项整治，加强对岗位现场的安全管理，及时查处违章指挥，违章操作等现象，最大限度降低各类事故的发生，确保工厂生产工作正常运行，工作计划《生产部项目进度计划控制管理
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最小二乘法及其应用..
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最小二乘法原理及应用【文献综述】
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智能物流跟踪及仓储管理系统
销售部门月度工作计划表
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人事工作月度工作计划表
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最小二乘法的综述及算例
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【文献综述】最小二乘法原理及应用
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