Motion Segmentation in the Presence of Outlying, Incomplete, or Corrupted Trajectories

人工智能是一门新兴的具有挑战力的学科。

自人工智能诞生以来,发展迅速,产生了许多分支。

诸如强化学习、模拟环境、智能硬件、机器学习等。

但是,在当前人工智能技术迅猛发展,为人们的生活带来许多便利。

下面是搜索整理的人工智能英文参考文献的分享，供大家借鉴参考。

人工智能英文参考文献一：[1]Lars Egevad,Peter Str?m,Kimmo Kartasalo,Henrik Olsson,Hemamali Samaratunga,Brett Delahunt,Martin Eklund. The utility of artificial intelligence in the assessment of prostate pathology[J]. Histopathology,2020,76(6).[2]Rudy van Belkom. The Impact of Artificial Intelligence on the Activities ofa Futurist[J]. World Futures Review,2020,12(2).[3]Reza Hafezi. How Artificial Intelligence Can Improve Understanding in Challenging Chaotic Environments[J]. World Futures Review,2020,12(2).[4]Alejandro Díaz-Domínguez. How Futures Studies and Foresight Could Address Ethical Dilemmas of Machine Learning and Artificial Intelligence[J]. World Futures Review,2020,12(2).[5]Russell T. Warne,Jared Z. Burton. Beliefs About Human Intelligence in a Sample of Teachers and Nonteachers[J]. Journal for the Education of the Gifted,2020,43(2).[6]Russell Belk,Mariam Humayun,Ahir Gopaldas. Artificial Life[J]. Journal of Macromarketing,2020,40(2).[7]Walter Kehl,Mike Jackson,Alessandro Fergnani. Natural Language Processing and Futures Studies[J]. World Futures Review,2020,12(2).[8]Anne Boysen. Mine the Gap: Augmenting Foresight Methodologies with Data Analytics[J]. World Futures Review,2020,12(2).[9]Marco Bevolo,Filiberto Amati. The Potential Role of AI in Anticipating Futures from a Design Process Perspective: From the Reflexive Description of “Design” to a Discussion of Influences by the Inclusion of AI in the Futures Research Process[J]. World Futures Review,2020,12(2).[10]Lan Xu,Paul Tu,Qian Tang,Dan Seli?teanu. Contract Design for Cloud Logistics (CL) Based on Blockchain Technology (BT)[J]. Complexity,2020,2020.[11]L. Grant,X. Xue,Z. Vajihi,A. Azuelos,S. Rosenthal,D. Hopkins,R. Aroutiunian,B. Unger,A. Guttman,M. Afilalo. LO32: Artificial intelligence to predict disposition to improve flow in the emergency department[J]. CJEM,2020,22(S1).[12]A. Kirubarajan,A. Taher,S. Khan,S. Masood. P071: Artificial intelligence in emergency medicine: A scoping review[J]. CJEM,2020,22(S1).[13]L. Grant,P. Joo,B. Eng,A. Carrington,M. Nemnom,V. Thiruganasambandamoorthy. LO22: Risk-stratification of emergency department syncope by artificial intelligence using machine learning: human, statistics or machine[J]. CJEM,2020,22(S1).[14]Riva Giuseppe,Riva Eleonora. OS for Ind Robots: Manufacturing Robots Get Smarter Thanks to Artificial Intelligence.[J]. Cyberpsychology, behavior and social networking,2020,23(5).[15]Markus M. Obmann,Aurelio Cosentino,Joshy Cyriac,Verena Hofmann,Bram Stieltjes,Daniel T. Boll,Benjamin M. Yeh,Matthias R. Benz. Quantitative enhancement thresholds and machine learning algorithms for the evaluation of renal lesions using single-phase split-filter dual-energy CT[J]. Abdominal Radiology,2020,45(1).[16]Haytham H. Elmousalami,Mahmoud Elaskary. Drilling stuck pipe classification and mitigation in the Gulf of Suez oil fields using artificial intelligence[J]. Journal of Petroleum Exploration and Production Technology,2020,10(10).[17]Rüdiger Schulz-Wendtland,Karin Bock. Bildgebung in der Mammadiagnostik –Ein Ausblick <trans-title xml:lang="en">Imaging in breast diagnostics—an outlook [J]. Der Gyn?kologe,2020,53(6).</trans-title>[18]Nowakowski Piotr,Szwarc Krzysztof,Boryczka Urszula. Combining an artificial intelligence algorithm and a novel vehicle for sustainable e-waste collection[J]. Science of the Total Environment,2020,730.[19]Wang Huaizhi,Liu Yangyang,Zhou Bin,Li Canbing,Cao Guangzhong,Voropai Nikolai,Barakhtenko Evgeny. Taxonomy research of artificial intelligence for deterministic solar power forecasting[J]. Energy Conversion and Management,2020,214.[20]Kagemoto Hiroshi. Forecasting a water-surface wave train with artificial intelligence- A case study[J]. Ocean Engineering,2020,207.[21]Tomonori Aoki,Atsuo Yamada,Kazuharu Aoyama,Hiroaki Saito,Gota Fujisawa,Nariaki Odawara,Ryo Kondo,Akiyoshi Tsuboi,Rei Ishibashi,Ayako Nakada,Ryota Niikura,Mitsuhiro Fujishiro,Shiro Oka,Soichiro Ishihara,Tomoki Matsuda,Masato Nakahori,Shinji Tanaka,Kazuhiko Koike,Tomohiro Tada. Clinical usefulness of a deep learning‐based system as the first screening on small‐bowel capsule endoscopy reading[J]. Digestive Endoscopy,2020,32(4).[22]Masashi Fujii,Hajime Isomoto. Next generation of endoscopy: Harmony with artificial intelligence and robotic‐assisted devices[J]. Digestive Endoscopy,2020,32(4).[23]Roberto Verganti,Luca Vendraminelli,Marco Iansiti. Innovation and Design in the Age of Artificial Intelligence[J]. Journal of Product Innovation Management,2020,37(3).[24]Yuval Elbaz,David Furman,Maytal Caspary Toroker. Modeling Diffusion in Functional Materials: From Density Functional Theory to Artificial Intelligence[J]. Advanced Functional Materials,2020,30(18).[25]Dinesh Visva Gunasekeran,Tien Yin Wong. Artificial Intelligence in Ophthalmology in 2020: A Technology on the Cusp for Translation and Implementation[J]. Asia-Pacific Journal of Ophthalmology,2020,9(2).[26]Fu-Neng Jiang,Li-Jun Dai,Yong-Ding Wu,Sheng-Bang Yang,Yu-Xiang Liang,Xin Zhang,Cui-Yun Zou,Ren-Qiang He,Xiao-Ming Xu,Wei-De Zhong. The study of multiple diagnosis models of human prostate cancer based on Taylor database by artificial neural networks[J]. Journal of the Chinese Medical Association,2020,83(5).[27]Matheus Calil Faleiros,Marcello Henrique Nogueira-Barbosa,Vitor Faeda Dalto,JoséRaniery Ferreira Júnior,Ariane Priscilla Magalh?es Tenório,Rodrigo Luppino-Assad,Paulo Louzada-Junior,Rangaraj Mandayam Rangayyan,Paulo Mazzoncini de Azevedo-Marques. Machine learning techniques for computer-aided classification of active inflammatory sacroiliitis in magnetic resonance imaging[J]. Advances in Rheumatology,2020,60(1078).[28]Balamurugan Balakreshnan,Grant Richards,Gaurav Nanda,Huachao Mao,Ragu Athinarayanan,Joseph Zaccaria. PPE Compliance Detection using Artificial Intelligence in Learning Factories[J]. Procedia Manufacturing,2020,45.[29]M. Stévenin,V. Avisse,N. Ducarme,A. de Broca. Qui est responsable si un robot autonome vient à entra?ner un dommage ?[J]. Ethique et Santé,2020.[30]Fatemeh Barzegari Banadkooki,Mohammad Ehteram,Fatemeh Panahi,Saad Sh. Sammen,Faridah Binti Othman,Ahmed EL-Shafie. Estimation of Total Dissolved Solids (TDS) using New Hybrid Machine Learning Models[J]. Journal of Hydrology,2020.[31]Adam J. Schwartz,Henry D. Clarke,Mark J. Spangehl,Joshua S. Bingham,DavidA. Etzioni,Matthew R. Neville. Can a Convolutional Neural Network Classify Knee Osteoarthritis on Plain Radiographs as Accurately as Fellowship-Trained Knee Arthroplasty Surgeons?[J]. The Journal of Arthroplasty,2020.[32]Ivana Nizetic Kosovic,Toni Mastelic,Damir Ivankovic. 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Artificial Intelligence in Vascular Surgery: moving from Big Data to Smart Data[J]. Annals of Vascular Surgery,2020.[37]Ilesanmi Daniyan,Khumbulani Mpofu,Moses Oyesola,Boitumelo Ramatsetse,Adefemi Adeodu. Artificial intelligence for predictive maintenance in the railcar learning factories[J]. Procedia Manufacturing,2020,45.[38]Janet L. McCauley,Anthony E. Swartz. Reframing Telehealth[J]. Obstetrics and Gynecology Clinics of North America,2020.[39]Jean-Emmanuel Bibault,Lei Xing. Screening for chronic obstructive pulmonary disease with artificial intelligence[J]. The Lancet Digital Health,2020,2(5).[40]Andrea Laghi. Cautions about radiologic diagnosis of COVID-19 infection driven by artificial intelligence[J]. The Lancet Digital Health,2020,2(5).人工智能英文参考文献二：[41]K. Orhan,I. S. Bayrakdar,M. Ezhov,A. Kravtsov,T. ?zyürek. Evaluation of artificial intelligence for detecting periapical pathosis on cone‐beam computed tomography scans[J]. International Endodontic Journal,2020,53(5).[42]Avila A M,Mezi? I. Data-driven analysis and forecasting of highway traffic dynamics.[J]. Nature communications,2020,11(1).[43]Neri Emanuele,Miele Vittorio,Coppola Francesca,Grassi Roberto. Use of CT andartificial intelligence in suspected or COVID-19 positive patients: statement of the Italian Society of Medical and Interventional Radiology.[J]. La Radiologia medica,2020.[44]Tau Noam,Stundzia Audrius,Yasufuku Kazuhiro,Hussey Douglas,Metser Ur. Convolutional Neural Networks in Predicting Nodal and Distant Metastatic Potential of Newly Diagnosed Non-Small Cell Lung Cancer on FDG PET Images.[J]. AJR. American journal of roentgenology,2020.[45]Coppola Francesca,Faggioni Lorenzo,Regge Daniele,Giovagnoni Andrea,Golfieri Rita,Bibbolino Corrado,Miele Vittorio,Neri Emanuele,Grassi Roberto. Artificial intelligence: radiologists' expectations and opinions gleaned from a nationwide online survey.[J]. La Radiologia medica,2020.[46]?. ? ? ? ? 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Clinical Implementation of Deep Learning in Thoracic Radiology: Potential Applications and Challenges.[J]. Korean journal of radiology,2020,21(5).[55]Mateen Bilal A,David Anna L,Denaxas Spiros. Electronic Health Records to Predict Gestational Diabetes Risk.[J]. Trends in pharmacological sciences,2020,41(5).[56]Yao Xiang,Mao Ling,Lv Shunli,Ren Zhenghong,Li Wentao,Ren Ke. CT radiomics features as a diagnostic tool for classifying basal ganglia infarction onset time.[J]. Journal of the neurological sciences,2020,412.[57]van Assen Marly,Banerjee Imon,De Cecco Carlo N. Beyond the Artificial Intelligence Hype: What Lies Behind the Algorithms and What We Can Achieve.[J]. Journal of thoracic imaging,2020,35 Suppl 1.[58]Guzik Tomasz J,Fuster Valentin. Leaders in Cardiovascular Research: Valentin Fuster.[J]. 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Journal of Cleaner Production,2020,258.[66]Siva Teja Kakileti,Himanshu J. Madhu,Geetha Manjunath,Leonard Wee,Andre Dekker,Sudhakar Sampangi. Personalized risk prediction for breast cancer pre-screening using artificial intelligence and thermal radiomics[J]. Artificial Intelligence In Medicine,2020,105.[67]. Evaluation of Payer Budget Impact Associated with the Use of Artificial Intelligence in Vitro Diagnostic, Kidneyintelx, to Modify DKD Progression:[J]. American Journal of Kidney Diseases,2020,75(5).[68]Rohit Nishant,Mike Kennedy,Jacqueline Corbett. Artificial intelligence for sustainability: Challenges, opportunities, and a research agenda[J]. International Journal of Information Management,2020,53.[69]Hoang Nguyen,Xuan-Nam Bui. Soft computing models for predicting blast-induced air over-pressure: A novel artificial intelligence approach[J]. Applied Soft Computing Journal,2020,92.[70]Benjamin S. Hopkins,Aditya Mazmudar,Conor Driscoll,Mark Svet,Jack Goergen,Max Kelsten,Nathan A. 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A Discriminatively Trained,Multiscale,Deformable Part ModelPedro Felzenszwalb University of Chicago pff@David McAllesterToyota Technological Institute at Chicagomcallester@Deva RamananUC Irvinedramanan@AbstractThis paper describes a discriminatively trained,multi-scale,deformable part model for object detection.Our sys-tem achieves a two-fold improvement in average precision over the best performance in the2006PASCAL person de-tection challenge.It also outperforms the best results in the 2007challenge in ten out of twenty categories.The system relies heavily on deformable parts.While deformable part models have become quite popular,their value had not been demonstrated on difficult benchmarks such as the PASCAL challenge.Our system also relies heavily on new methods for discriminative training.We combine a margin-sensitive approach for data mining hard negative examples with a formalism we call latent SVM.A latent SVM,like a hid-den CRF,leads to a non-convex training problem.How-ever,a latent SVM is semi-convex and the training prob-lem becomes convex once latent information is specified for the positive examples.We believe that our training meth-ods will eventually make possible the effective use of more latent information such as hierarchical(grammar)models and models involving latent three dimensional pose.1.IntroductionWe consider the problem of detecting and localizing ob-jects of a generic category,such as people or cars,in static images.We have developed a new multiscale deformable part model for solving this problem.The models are trained using a discriminative procedure that only requires bound-ing box labels for the positive ing these mod-els we implemented a detection system that is both highly efficient and accurate,processing an image in about2sec-onds and achieving recognition rates that are significantly better than previous systems.Our system achieves a two-fold improvement in average precision over the winning system[5]in the2006PASCAL person detection challenge.The system also outperforms the best results in the2007challenge in ten out of twenty This material is based upon work supported by the National Science Foundation under Grant No.0534820and0535174.Figure1.Example detection obtained with the person model.The model is defined by a coarse template,several higher resolution part templates and a spatial model for the location of each part. object categories.Figure1shows an example detection ob-tained with our person model.The notion that objects can be modeled by parts in a de-formable configuration provides an elegant framework for representing object categories[1–3,6,10,12,13,15,16,22]. While these models are appealing from a conceptual point of view,it has been difficult to establish their value in prac-tice.On difficult datasets,deformable models are often out-performed by“conceptually weaker”models such as rigid templates[5]or bag-of-features[23].One of our main goals is to address this performance gap.Our models include both a coarse global template cov-ering an entire object and higher resolution part templates. The templates represent histogram of gradient features[5]. As in[14,19,21],we train models discriminatively.How-ever,our system is semi-supervised,trained with a max-margin framework,and does not rely on feature detection. We also describe a simple and effective strategy for learn-ing parts from weakly-labeled data.In contrast to computa-tionally demanding approaches such as[4],we can learn a model in3hours on a single CPU.Another contribution of our work is a new methodology for discriminative training.We generalize SVMs for han-dling latent variables such as part positions,and introduce a new method for data mining“hard negative”examples dur-ing training.We believe that handling partially labeled data is a significant issue in machine learning for computer vi-sion.For example,the PASCAL dataset only specifies abounding box for each positive example of an object.We treat the position of each object part as a latent variable.We also treat the exact location of the object as a latent vari-able,requiring only that our classifier select a window that has large overlap with the labeled bounding box.A latent SVM,like a hidden CRF[19],leads to a non-convex training problem.However,unlike a hidden CRF, a latent SVM is semi-convex and the training problem be-comes convex once latent information is specified for thepositive training examples.This leads to a general coordi-nate descent algorithm for latent SVMs.System Overview Our system uses a scanning window approach.A model for an object consists of a global“root”filter and several part models.Each part model specifies a spatial model and a partfilter.The spatial model defines a set of allowed placements for a part relative to a detection window,and a deformation cost for each placement.The score of a detection window is the score of the root filter on the window plus the sum over parts,of the maxi-mum over placements of that part,of the partfilter score on the resulting subwindow minus the deformation cost.This is similar to classical part-based models[10,13].Both root and partfilters are scored by computing the dot product be-tween a set of weights and histogram of gradient(HOG) features within a window.The rootfilter is equivalent to a Dalal-Triggs model[5].The features for the partfilters are computed at twice the spatial resolution of the rootfilter. Our model is defined at afixed scale,and we detect objects by searching over an image pyramid.In training we are given a set of images annotated with bounding boxes around each instance of an object.We re-duce the detection problem to a binary classification prob-lem.Each example x is scored by a function of the form, fβ(x)=max zβ·Φ(x,z).Hereβis a vector of model pa-rameters and z are latent values(e.g.the part placements). To learn a model we define a generalization of SVMs that we call latent variable SVM(LSVM).An important prop-erty of LSVMs is that the training problem becomes convex if wefix the latent values for positive examples.This can be used in a coordinate descent algorithm.In practice we iteratively apply classical SVM training to triples( x1,z1,y1 ,..., x n,z n,y n )where z i is selected to be the best scoring latent label for x i under the model learned in the previous iteration.An initial rootfilter is generated from the bounding boxes in the PASCAL dataset. The parts are initialized from this rootfilter.2.ModelThe underlying building blocks for our models are the Histogram of Oriented Gradient(HOG)features from[5]. We represent HOG features at two different scales.Coarse features are captured by a rigid template covering anentireImage pyramidFigure2.The HOG feature pyramid and an object hypothesis de-fined in terms of a placement of the rootfilter(near the top of the pyramid)and the partfilters(near the bottom of the pyramid). detection window.Finer scale features are captured by part templates that can be moved with respect to the detection window.The spatial model for the part locations is equiv-alent to a star graph or1-fan[3]where the coarse template serves as a reference position.2.1.HOG RepresentationWe follow the construction in[5]to define a dense repre-sentation of an image at a particular resolution.The image isfirst divided into8x8non-overlapping pixel regions,or cells.For each cell we accumulate a1D histogram of gra-dient orientations over pixels in that cell.These histograms capture local shape properties but are also somewhat invari-ant to small deformations.The gradient at each pixel is discretized into one of nine orientation bins,and each pixel“votes”for the orientation of its gradient,with a strength that depends on the gradient magnitude.For color images,we compute the gradient of each color channel and pick the channel with highest gradi-ent magnitude at each pixel.Finally,the histogram of each cell is normalized with respect to the gradient energy in a neighborhood around it.We look at the four2×2blocks of cells that contain a particular cell and normalize the his-togram of the given cell with respect to the total energy in each of these blocks.This leads to a vector of length9×4 representing the local gradient information inside a cell.We define a HOG feature pyramid by computing HOG features of each level of a standard image pyramid(see Fig-ure2).Features at the top of this pyramid capture coarse gradients histogrammed over fairly large areas of the input image while features at the bottom of the pyramid capture finer gradients histogrammed over small areas.2.2.FiltersFilters are rectangular templates specifying weights for subwindows of a HOG pyramid.A w by hfilter F is a vector with w×h×9×4weights.The score of afilter is defined by taking the dot product of the weight vector and the features in a w×h subwindow of a HOG pyramid.The system in[5]uses a singlefilter to define an object model.That system detects objects from a particular class by scoring every w×h subwindow of a HOG pyramid and thresholding the scores.Let H be a HOG pyramid and p=(x,y,l)be a cell in the l-th level of the pyramid.Letφ(H,p,w,h)denote the vector obtained by concatenating the HOG features in the w×h subwindow of H with top-left corner at p.The score of F on this detection window is F·φ(H,p,w,h).Below we useφ(H,p)to denoteφ(H,p,w,h)when the dimensions are clear from context.2.3.Deformable PartsHere we consider models defined by a coarse rootfilter that covers the entire object and higher resolution partfilters covering smaller parts of the object.Figure2illustrates a placement of such a model in a HOG pyramid.The rootfil-ter location defines the detection window(the pixels inside the cells covered by thefilter).The partfilters are placed several levels down in the pyramid,so the HOG cells at that level have half the size of cells in the rootfilter level.We have found that using higher resolution features for defining partfilters is essential for obtaining high recogni-tion performance.With this approach the partfilters repre-sentfiner resolution edges that are localized to greater ac-curacy when compared to the edges represented in the root filter.For example,consider building a model for a face. The rootfilter could capture coarse resolution edges such as the face boundary while the partfilters could capture details such as eyes,nose and mouth.The model for an object with n parts is formally defined by a rootfilter F0and a set of part models(P1,...,P n) where P i=(F i,v i,s i,a i,b i).Here F i is afilter for the i-th part,v i is a two-dimensional vector specifying the center for a box of possible positions for part i relative to the root po-sition,s i gives the size of this box,while a i and b i are two-dimensional vectors specifying coefficients of a quadratic function measuring a score for each possible placement of the i-th part.Figure1illustrates a person model.A placement of a model in a HOG pyramid is given by z=(p0,...,p n),where p i=(x i,y i,l i)is the location of the rootfilter when i=0and the location of the i-th part when i>0.We assume the level of each part is such that a HOG cell at that level has half the size of a HOG cell at the root level.The score of a placement is given by the scores of eachfilter(the data term)plus a score of the placement of each part relative to the root(the spatial term), ni=0F i·φ(H,p i)+ni=1a i·(˜x i,˜y i)+b i·(˜x2i,˜y2i),(1)where(˜x i,˜y i)=((x i,y i)−2(x,y)+v i)/s i gives the lo-cation of the i-th part relative to the root location.Both˜x i and˜y i should be between−1and1.There is a large(exponential)number of placements for a model in a HOG pyramid.We use dynamic programming and distance transforms techniques[9,10]to compute the best location for the parts of a model as a function of the root location.This takes O(nk)time,where n is the number of parts in the model and k is the number of cells in the HOG pyramid.To detect objects in an image we score root locations according to the best possible placement of the parts and threshold this score.The score of a placement z can be expressed in terms of the dot product,β·ψ(H,z),between a vector of model parametersβand a vectorψ(H,z),β=(F0,...,F n,a1,b1...,a n,b n).ψ(H,z)=(φ(H,p0),φ(H,p1),...φ(H,p n),˜x1,˜y1,˜x21,˜y21,...,˜x n,˜y n,˜x2n,˜y2n,). We use this representation for learning the model parame-ters as it makes a connection between our deformable mod-els and linear classifiers.On interesting aspect of the spatial models defined here is that we allow for the coefficients(a i,b i)to be negative. This is more general than the quadratic“spring”cost that has been used in previous work.3.LearningThe PASCAL training data consists of a large set of im-ages with bounding boxes around each instance of an ob-ject.We reduce the problem of learning a deformable part model with this data to a binary classification problem.Let D=( x1,y1 ,..., x n,y n )be a set of labeled exam-ples where y i∈{−1,1}and x i specifies a HOG pyramid, H(x i),together with a range,Z(x i),of valid placements for the root and partfilters.We construct a positive exam-ple from each bounding box in the training set.For these ex-amples we define Z(x i)so the rootfilter must be placed to overlap the bounding box by at least50%.Negative exam-ples come from images that do not contain the target object. Each placement of the rootfilter in such an image yields a negative training example.Note that for the positive examples we treat both the part locations and the exact location of the rootfilter as latent variables.We have found that allowing uncertainty in the root location during training significantly improves the per-formance of the system(see Section4).tent SVMsA latent SVM is defined as follows.We assume that each example x is scored by a function of the form,fβ(x)=maxz∈Z(x)β·Φ(x,z),(2)whereβis a vector of model parameters and z is a set of latent values.For our deformable models we define Φ(x,z)=ψ(H(x),z)so thatβ·Φ(x,z)is the score of placing the model according to z.In analogy to classical SVMs we would like to trainβfrom labeled examples D=( x1,y1 ,..., x n,y n )by optimizing the following objective function,β∗(D)=argminβλ||β||2+ni=1max(0,1−y i fβ(x i)).(3)By restricting the latent domains Z(x i)to a single choice, fβbecomes linear inβ,and we obtain linear SVMs as a special case of latent tent SVMs are instances of the general class of energy-based models[18].3.2.Semi-ConvexityNote that fβ(x)as defined in(2)is a maximum of func-tions each of which is linear inβ.Hence fβ(x)is convex inβ.This implies that the hinge loss max(0,1−y i fβ(x i)) is convex inβwhen y i=−1.That is,the loss function is convex inβfor negative examples.We call this property of the loss function semi-convexity.Consider an LSVM where the latent domains Z(x i)for the positive examples are restricted to a single choice.The loss due to each positive example is now bined with the semi-convexity property,(3)becomes convex inβ.If the labels for the positive examples are notfixed we can compute a local optimum of(3)using a coordinate de-scent algorithm:1.Holdingβfixed,optimize the latent values for the pos-itive examples z i=argmax z∈Z(xi )β·Φ(x,z).2.Holding{z i}fixed for positive examples,optimizeβby solving the convex problem defined above.It can be shown that both steps always improve or maintain the value of the objective function in(3).If both steps main-tain the value we have a strong local optimum of(3),in the sense that Step1searches over an exponentially large space of latent labels for positive examples while Step2simulta-neously searches over weight vectors and an exponentially large space of latent labels for negative examples.3.3.Data Mining Hard NegativesIn object detection the vast majority of training exam-ples are negative.This makes it infeasible to consider all negative examples at a time.Instead,it is common to con-struct training data consisting of the positive instances and “hard negative”instances,where the hard negatives are data mined from the very large set of possible negative examples.Here we describe a general method for data mining ex-amples for SVMs and latent SVMs.The method iteratively solves subproblems using only hard instances.The innova-tion of our approach is a theoretical guarantee that it leads to the exact solution of the training problem defined using the complete training set.Our results require the use of a margin-sensitive definition of hard examples.The results described here apply both to classical SVMs and to the problem defined by Step2of the coordinate de-scent algorithm for latent SVMs.We omit the proofs of the theorems due to lack of space.These results are related to working set methods[17].We define the hard instances of D relative toβas,M(β,D)={ x,y ∈D|yfβ(x)≤1}.(4)That is,M(β,D)are training examples that are incorrectly classified or near the margin of the classifier defined byβ. We can show thatβ∗(D)only depends on hard instances. Theorem1.Let C be a subset of the examples in D.If M(β∗(D),D)⊆C thenβ∗(C)=β∗(D).This implies that in principle we could train a model us-ing a small set of examples.However,this set is defined in terms of the optimal modelβ∗(D).Given afixedβwe can use M(β,D)to approximate M(β∗(D),D).This suggests an iterative algorithm where we repeatedly compute a model from the hard instances de-fined by the model from the last iteration.This is further justified by the followingfixed-point theorem.Theorem2.Ifβ∗(M(β,D))=βthenβ=β∗(D).Let C be an initial“cache”of examples.In practice we can take the positive examples together with random nega-tive examples.Consider the following iterative algorithm: 1.Letβ:=β∗(C).2.Shrink C by letting C:=M(β,C).3.Grow C by adding examples from M(β,D)up to amemory limit L.Theorem3.If|C|<L after each iteration of Step2,the algorithm will converge toβ=β∗(D)infinite time.3.4.Implementation detailsMany of the ideas discussed here are only approximately implemented in our current system.In practice,when train-ing a latent SVM we iteratively apply classical SVM train-ing to triples x1,z1,y1 ,..., x n,z n,y n where z i is se-lected to be the best scoring latent label for x i under themodel trained in the previous iteration.Each of these triples leads to an example Φ(x i,z i),y i for training a linear clas-sifier.This allows us to use a highly optimized SVM pack-age(SVMLight[17]).On a single CPU,the entire training process takes3to4hours per object class in the PASCAL datasets,including initialization of the parts.Root Filter Initialization:For each category,we auto-matically select the dimensions of the rootfilter by looking at statistics of the bounding boxes in the training data.1We train an initial rootfilter F0using an SVM with no latent variables.The positive examples are constructed from the unoccluded training examples(as labeled in the PASCAL data).These examples are anisotropically scaled to the size and aspect ratio of thefilter.We use random subwindows from negative images to generate negative examples.Root Filter Update:Given the initial rootfilter trained as above,for each bounding box in the training set wefind the best-scoring placement for thefilter that significantly overlaps with the bounding box.We do this using the orig-inal,un-scaled images.We retrain F0with the new positive set and the original random negative set,iterating twice.Part Initialization:We employ a simple heuristic to ini-tialize six parts from the rootfilter trained above.First,we select an area a such that6a equals80%of the area of the rootfilter.We greedily select the rectangular region of area a from the rootfilter that has the most positive energy.We zero out the weights in this region and repeat until six parts are selected.The partfilters are initialized from the rootfil-ter values in the subwindow selected for the part,butfilled in to handle the higher spatial resolution of the part.The initial deformation costs measure the squared norm of a dis-placement with a i=(0,0)and b i=−(1,1).Model Update:To update a model we construct new training data triples.For each positive bounding box in the training data,we apply the existing detector at all positions and scales with at least a50%overlap with the given bound-ing box.Among these we select the highest scoring place-ment as the positive example corresponding to this training bounding box(Figure3).Negative examples are selected byfinding high scoring detections in images not containing the target object.We add negative examples to a cache un-til we encounterfile size limits.A new model is trained by running SVMLight on the positive and negative examples, each labeled with part placements.We update the model10 times using the cache scheme described above.In each it-eration we keep the hard instances from the previous cache and add as many new hard instances as possible within the memory limit.Toward thefinal iterations,we are able to include all hard instances,M(β,D),in the cache.1We picked a simple heuristic by cross-validating over5object classes. We set the model aspect to be the most common(mode)aspect in the data. We set the model size to be the largest size not larger than80%of thedata.Figure3.The image on the left shows the optimization of the la-tent variables for a positive example.The dotted box is the bound-ing box label provided in the PASCAL training set.The large solid box shows the placement of the detection window while the smaller solid boxes show the placements of the parts.The image on the right shows a hard-negative example.4.ResultsWe evaluated our system using the PASCAL VOC2006 and2007comp3challenge datasets and protocol.We refer to[7,8]for details,but emphasize that both challenges are widely acknowledged as difficult testbeds for object detec-tion.Each dataset contains several thousand images of real-world scenes.The datasets specify ground-truth bounding boxes for several object classes,and a detection is consid-ered correct when it overlaps more than50%with a ground-truth bounding box.One scores a system by the average precision(AP)of its precision-recall curve across a testset.Recent work in pedestrian detection has tended to report detection rates versus false positives per window,measured with cropped positive examples and negative images with-out objects of interest.These scores are tied to the reso-lution of the scanning window search and ignore effects of non-maximum suppression,making it difficult to compare different systems.We believe the PASCAL scoring method gives a more reliable measure of performance.The2007challenge has20object categories.We entered a preliminary version of our system in the official competi-tion,and obtained the best score in6categories.Our current system obtains the highest score in10categories,and the second highest score in6categories.Table1summarizes the results.Our system performs well on rigid objects such as cars and sofas as well as highly deformable objects such as per-sons and horses.We also note that our system is successful when given a large or small amount of training data.There are roughly4700positive training examples in the person category but only250in the sofa category.Figure4shows some of the models we learned.Figure5shows some ex-ample detections.We evaluated different components of our system on the longer-established2006person dataset.The top AP scoreaero bike bird boat bottle bus car cat chair cow table dog horse mbike person plant sheep sofa train tvOur rank 31211224111422112141Our score .180.411.092.098.249.349.396.110.155.165.110.062.301.337.267.140.141.156.206.336Darmstadt .301INRIA Normal .092.246.012.002.068.197.265.018.097.039.017.016.225.153.121.093.002.102.157.242INRIA Plus.136.287.041.025.077.279.294.132.106.127.067.071.335.249.092.072.011.092.242.275IRISA .281.318.026.097.119.289.227.221.175.253MPI Center .060.110.028.031.000.164.172.208.002.044.049.141.198.170.091.004.091.034.237.051MPI ESSOL.152.157.098.016.001.186.120.240.007.061.098.162.034.208.117.002.046.147.110.054Oxford .262.409.393.432.375.334TKK .186.078.043.072.002.116.184.050.028.100.086.126.186.135.061.019.036.058.067.090Table 1.PASCAL VOC 2007results.Average precision scores of our system and other systems that entered the competition [7].Empty boxes indicate that a method was not tested in the corresponding class.The best score in each class is shown in bold.Our current system ranks first in 10out of 20classes.A preliminary version of our system ranked first in 6classes in the official competition.BottleCarBicycleSofaFigure 4.Some models learned from the PASCAL VOC 2007dataset.We show the total energy in each orientation of the HOG cells in the root and part filters,with the part filters placed at the center of the allowable displacements.We also show the spatial model for each part,where bright values represent “cheap”placements,and dark values represent “expensive”placements.in the PASCAL competition was .16,obtained using a rigid template model of HOG features [5].The best previous re-sult of.19adds a segmentation-based verification step [20].Figure 6summarizes the performance of several models we trained.Our root-only model is equivalent to the model from [5]and it scores slightly higher at .18.Performance jumps to .24when the model is trained with a LSVM that selects a latent position and scale for each positive example.This suggests LSVMs are useful even for rigid templates because they allow for self-adjustment of the detection win-dow in the training examples.Adding deformable parts in-creases performance to .34AP —a factor of two above the best previous score.Finally,we trained a model with partsbut no root filter and obtained .29AP.This illustrates the advantage of using a multiscale representation.We also investigated the effect of the spatial model and allowable deformations on the 2006person dataset.Recall that s i is the allowable displacement of a part,measured in HOG cells.We trained a rigid model with high-resolution parts by setting s i to 0.This model outperforms the root-only system by .27to .24.If we increase the amount of allowable displacements without using a deformation cost,we start to approach a bag-of-features.Performance peaks at s i =1,suggesting it is useful to constrain the part dis-placements.The optimal strategy allows for larger displace-ments while using an explicit deformation cost.The follow-Figure 5.Some results from the PASCAL 2007dataset.Each row shows detections using a model for a specific class (Person,Bottle,Car,Sofa,Bicycle,Horse).The first three columns show correct detections while the last column shows false positives.Our system is able to detect objects over a wide range of scales (such as the cars)and poses (such as the horses).The system can also detect partially occluded objects such as a person behind a bush.Note how the false detections are often quite reasonable,for example detecting a bus with the car model,a bicycle sign with the bicycle model,or a dog with the horse model.In general the part filters represent meaningful object parts that are well localized in each detection such as the head in the person model.Figure6.Evaluation of our system on the PASCAL VOC2006 person dataset.Root uses only a rootfilter and no latent place-ment of the detection windows on positive examples.Root+Latent uses a rootfilter with latent placement of the detection windows. Parts+Latent is a part-based system with latent detection windows but no rootfilter.Root+Parts+Latent includes both root and part filters,and latent placement of the detection windows.ing table shows AP as a function of freely allowable defor-mation in thefirst three columns.The last column gives the performance when using a quadratic deformation cost and an allowable displacement of2HOG cells.s i01232+quadratic costAP.27.33.31.31.345.DiscussionWe introduced a general framework for training SVMs with latent structure.We used it to build a recognition sys-tem based on multiscale,deformable models.Experimental results on difficult benchmark data suggests our system is the current state-of-the-art in object detection.LSVMs allow for exploration of additional latent struc-ture for recognition.One can consider deeper part hierar-chies(parts with parts),mixture models(frontal vs.side cars),and three-dimensional pose.We would like to train and detect multiple classes together using a shared vocab-ulary of parts(perhaps visual words).We also plan to use A*search[11]to efficiently search over latent parameters during detection.References[1]Y.Amit and A.Trouve.POP:Patchwork of parts models forobject recognition.IJCV,75(2):267–282,November2007.[2]M.Burl,M.Weber,and P.Perona.A probabilistic approachto object recognition using local photometry and global ge-ometry.In ECCV,pages II:628–641,1998.[3] D.Crandall,P.Felzenszwalb,and D.Huttenlocher.Spatialpriors for part-based recognition using statistical models.In CVPR,pages10–17,2005.[4] D.Crandall and D.Huttenlocher.Weakly supervised learn-ing of part-based spatial models for visual object recognition.In ECCV,pages I:16–29,2006.[5]N.Dalal and B.Triggs.Histograms of oriented gradients forhuman detection.In CVPR,pages I:886–893,2005.[6] B.Epshtein and S.Ullman.Semantic hierarchies for recog-nizing objects and parts.In CVPR,2007.[7]M.Everingham,L.Van Gool,C.K.I.Williams,J.Winn,and A.Zisserman.The PASCAL Visual Object Classes Challenge2007(VOC2007)Results./challenges/VOC/voc2007/workshop.[8]M.Everingham, A.Zisserman, C.K.I.Williams,andL.Van Gool.The PASCAL Visual Object Classes Challenge2006(VOC2006)Results./challenges/VOC/voc2006/results.pdf.[9]P.Felzenszwalb and D.Huttenlocher.Distance transformsof sampled functions.Cornell Computing and Information Science Technical Report TR2004-1963,September2004.[10]P.Felzenszwalb and D.Huttenlocher.Pictorial structures forobject recognition.IJCV,61(1),2005.[11]P.Felzenszwalb and D.McAllester.The generalized A*ar-chitecture.JAIR,29:153–190,2007.[12]R.Fergus,P.Perona,and A.Zisserman.Object class recog-nition by unsupervised scale-invariant learning.In CVPR, 2003.[13]M.Fischler and R.Elschlager.The representation andmatching of pictorial structures.IEEE Transactions on Com-puter,22(1):67–92,January1973.[14] A.Holub and P.Perona.A discriminative framework formodelling object classes.In CVPR,pages I:664–671,2005.[15]S.Ioffe and D.Forsyth.Probabilistic methods forfindingpeople.IJCV,43(1):45–68,June2001.[16]Y.Jin and S.Geman.Context and hierarchy in a probabilisticimage model.In CVPR,pages II:2145–2152,2006.[17]T.Joachims.Making large-scale svm learning practical.InB.Sch¨o lkopf,C.Burges,and A.Smola,editors,Advances inKernel Methods-Support Vector Learning.MIT Press,1999.[18]Y.LeCun,S.Chopra,R.Hadsell,R.Marc’Aurelio,andF.Huang.A tutorial on energy-based learning.InG.Bakir,T.Hofman,B.Sch¨o lkopf,A.Smola,and B.Taskar,editors, Predicting Structured Data.MIT Press,2006.[19] A.Quattoni,S.Wang,L.Morency,M.Collins,and T.Dar-rell.Hidden conditional randomfields.PAMI,29(10):1848–1852,October2007.[20] ing segmentation to verify object hypothe-ses.In CVPR,pages1–8,2007.[21] D.Ramanan and C.Sminchisescu.Training deformablemodels for localization.In CVPR,pages I:206–213,2006.[22]H.Schneiderman and T.Kanade.Object detection using thestatistics of parts.IJCV,56(3):151–177,February2004. 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