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Deformable Fourier models for surface finding in 3D images

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2. RELATED WORK IN BOUNDARY FINDING
Local edge detectors applied to real images produce spurious edges and gaps. These problems can only be overcome by the incorporation of information from higher scale organization of the image and models of the objects sought. Contextual information has been used for boundary determination via grouping [1], relaxation labeling [2] and scale-space methods [3] . These methods, by themselves, will not necessarily find complete boundaries. Pixel search methods associate edge elements by finding an optimal path through a twodimensional image, based on criteria designed to find boundaries. The typical objective function combines
overall.
90 ISPIE Vol. 1808 Visualization in Biomedical Computing 1992
0-8194-1008-X/92/$4.00
A powerful prn object from its surroundings in an image is overall or global shape. In order to take full advantage of shape, the problem of object identification is approached as a process of boundary finding or delineation using a boundary measure and incorporating global shape information.
1. INTRODUCTION
This work is aimed at extracting the surfaces of structures found in three-dimensional images. Threedimensional images are available from the medical imaging modalities: magnetic resonance imaging (MRI), computed tomography (CT) , single photon emission computed tomography (SPECT) and positron emission tomography (PET) . Confocal microscopy is also a growing source of three-dimensional images. Segmentation in three-dimensional images is a crucial step for visualization either to strip away obscuring structures or to render the surface of the structure delineated. The problems of manual segmentation in two-dimensional images are exacerbated in three-dimensional images when it is done slice by slice. In addition, surfaces formed slice by slice either manually or automatically are likely to contain inconsistencies that will tend to corrupt the rendering.
Smoothly deformable objects do not necessarily have an obvious decomposition that can be exploited. A uniform shape representation that describes the entire shape is therefore needed and it should describe a relatively broad class of shapes. Representations for objects are needed in order to characterize and understand shape. A great deal of research has been done in the area of shape representation. For a representation to be useful for modeling it should be concise. Methods based on explicitly listing points or patches on the surface are verbose because of the implicit redundancy. Parametric representations capture the overall shape in a small number of parameters. This means that the optimization of a match measure between data and a model can occur in a lower dimensional space. Boundary finding using only local information has often been frustrated by poor-contrast boundary regions due to occluding and occluded objects, adverse viewing conditions and noise. A model-free interpretation is doomed by the underconstrained nature of the problem. Imperfect image data can be augmented with the extrinsic information that a geometric shape model provides. In order to exploit model-based information to the fullest extent, it should be incorporated explicitly, specifically, and early in the analysis. In addition, the boundary can be profitably considered as a whole because it tends to result in a more consistent solution
boundary strength and low overall curvature [4] . Pixel search does not generalize obviously to three dimensions because there is no natural ordering of voxels in a surface.
bridges gaps and results in overall consistency. Terzopoulos et al. [5] used energy-minimizing meshes that are attracted to image features such as lines and edges while internal spline forces impose a smoothness constraint. The goal was to find surfaces implied by silhouettes in two-dimensional images. This idea has also been used for finding symmetry surfaces from scale space stacks of two-dimensional images [6] , surfaces in range images [7, 8] and surfaces in three-dimensional images [9, 10].
Deformable Fourier models for surface finding in 3D images
Lawrence H. Staibt and James S. Duncant,*
Departments of tDiagnostic Radiology and *Electrical Engineering Yale University, New Haven, CT 06510, U.S.A.
ABSTRACT
This paper describes a new global shape parametrization for smoothly deformable three-dimensional objects, such as those found in biomedical images, whose diversity and irregularity make them difficult to represent in terms of fixed features or parts. This representation is used for geometric surface matching to three-dimensional image data. The parametrization decomposes the surface into sinusoidal basis functions. Four types of surfaces are modeled: tori, open surfaces, closed surfaces and tubes. This parametrization allows a wide variety of smooth surfaces to be described with a small number of parameters. Surface finding is formulated as an optimization problem. Results of the method applied to synthetic and medical threedimensional images are presented.

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DEFORM基本操作指南

DEFORM基本操作指南


沿X轴旋转 沿Z轴旋转 XY 平面视图 XZ 平面视图
1.5 点和面的选取
1．点或面的选取工具 点击工具栏上的 按钮，在显示窗口可以选择 物体的任意一节点或面 2．标尺工具 点击工具栏上的 按钮，点击物体上的任意一个 节点，并按住鼠标不放，再选择另一个节点，然后 松开鼠标。连接这两点的一条线段和该线段的长度 值就会显示在在显示窗口中，直到用户点击Refresh 按钮
2.8 设置模拟参数
1．在前处理控制窗口的右上角选择按钮 进入Simulation Control窗口 2．选择左侧第二个选项Step进行模拟步数和步长的设定。 3．设置Number of Simulation Steps:20；除非模拟意外终止，否则程序将 运行至20步。设置 Set the Step Increment to Save: 2．这里的意思是每2 步保存一次，这是避免每步都保存，造成数据文件过大． 4．前面设置了20步，但每一步的含义还没有明确，在下面设置With Constant Die Displacement为0.13. 这个数值是根据变形体单元长度的1/3 来估算的。一般模拟都用这个比例，比较容易收敛而且又不会浪费时间。 这样上模将向下(- Z)运动1.6in 5. OK关闭该窗口
2.6 改动物体的空间位置
在DEFORM中，虽然不可以直接 进行几何造型，但是可以通过旋 转(Rotation)平移(Translation)修 改物体的空间位置。 点击按钮 ，就可以进入到 Object Positioning窗口中，进行 操作，本例中不涉及改变物体的 空间位置，在这里不赘述，用户 感兴趣可以操作，与其他CAD软 件相似，比较容易操作。
在上个练习中施加对称边界条件的对称面均落在坐标面上即xy面yz面及xz面但在很多场合如本例中的正方环对称面并不落在坐标面上而仅仅是任意平面对于这类问题就不能用练习04中的方法本例中将通过引入一个刚体平面作为辅助面来实现对称边界条件的施加
deforamble-detr公式

deforamble-detr公式

一、背景介绍随着深度学习技术的不断发展和应用，目标检测技术作为计算机视觉领域的重要研究内容，也在不断取得突破。

传统的目标检测方法主要包括基于候选区域的方法和基于密集预测的方法，但这些方法在速度和准确性上都存在一定的局限性。

为了解决这些问题，最近提出了一种名为Deformable DETR（Deformable Deformable Transformer）的目标检测方法，该方法结合了自注意力机制和可变形卷积，取得了很好的效果。

二、Deformable DETR的原理Deformable DETR方法采用了Transformer网络结构，将目标检测问题转化为图像像素到预测类别和位置的全局优化问题。

与传统的目标检测方法不同，Deformable DETR取消了锚框和NMS等设计，使用了位置编码和注意力机制来实现目标的检测定位。

Deformable DETR引入了可变形卷积，允许每个像素点对应的感受野在空间上有一定的变换，从而提高了模型对于目标的识别和定位能力。

三、Deformable DETR的优势1. 更好的全局编码能力：Deformable DETR基于Transformer网络结构，能够更好地实现全局感知和编码，从而降低了目标漏检和重复检测的问题。

2. 强大的位置感知能力：通过可变形卷积模块，Deformable DETR 实现了对目标位置的自适应感知和编码，更好地适应了目标的形变和遮挡情况。

3. 高效的训练和推理速度：相比传统的目标检测方法，Deformable DETR在准确性和速度上都取得了显著的提升，能够快速高效地完成大规模图像数据中的目标检测任务。

四、Deformable DETR的应用前景作为一种全新的目标检测方法，Deformable DETR已经在各种计算机视觉领域得到了广泛的应用。

在无人驾驶、智能监控、工业生产等场景中，Deformable DETR都能够发挥出良好的效果，为实际应用带来了便利和安全保障。

EN 10025-3

EN 10025-3

欧洲标准存在三种正式版本（英语，法语，德语）。由CEN成员国家负责翻译成本国语言的任何其它版本并通知 管理中心，享有与正式版本相同的地位。 CEN members are the national standards bodies of Austria, Belgium, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg,
English version
Hot rolled products of structural steels
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structural steels
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第3部分：DIN EN 10025-2标准可焊接细晶粒结构钢热轧产品技术 交付条件
Produits lamines a chaud en aciers de construction - Partie 3: Conditions techniques de livraison pour les aciers de construction soudable a grains fins a t'etat normalise/laminage normalise
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The European Standards exist in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the Management Centre has the same status as the official versions.
Surfaces in ${mathbb R}^{N^2-1}$ based on harmonic maps $S^2to CP^{N-1}$

Surfaces in ${mathbb R}^{N^2-1}$ based on harmonic maps $S^2to CP^{N-1}$


Surfaces in RN
2
−1
based on harmonic maps S 2 → CP N −1
2
1. Introduction A few years ago, Konopelchenko et al [1, 2] initiated a construction of surfaces immersed in multidimensional spaces basing their discussion on the Weierstrass procedure generalised to higher dimensional spaces. This has led to further studies [3] and to relating the surfaces to the solutions of the CP N −1 model[4]. Recently, together with Grundland [5], we have presented a general procedure for the construction of surfaces from the harmonic CP N −1 maps. This approach involved writing the equation for the harmonic map as a conservation law and then observing that the coordinates of the surfaces can be constructed out of the components of the special operator which appears in the conservation law. Our procedure has then been generalised to the supersymmetric case [6]. At this stage it has become clear that, in the holomorphic case, the projector in question is proportional to the fundamental projector of the holomorphic map. This observation has suggested to us to look at other projectors that arise in the description of harmonic maps and to use them to construct further surfaces. In the next section we recall the general construction of S 2 → CP N −1 harmonic 2 maps and then use them to construct surfaces in RN −1 . In the following section we look, in detail, at the case of CP 2 and show that, in contradistinction to the CP 1 case, its surfaces do not have to be of constant curvature. We calculate this curvature for two classes of such harmonic maps. Finally, we look at the Veronese sequence and show that in this case all surfaces are of constant curvature. We finish the paper with a few comments about the generality of our results. 2. Harmonic maps S 2 → CP N −1 [7] The S 2 → CP N −1 harmonic maps involve maps into CP N −1 , i.e. C ∋ ζ = ζ1 + iζ2 → z = (z 1 , ...., z N ) ∈ C N ,