Recovery, Representation, and Recognition of Two and Three-Dimensional Shape from Real Images

这 研究涉及从真实的图像恢复、表示和识别二维和三维形状的问题。基于先前NSF资助的研究结果，导出对视觉场景变化具有鲁棒性的分段形状表示，当前的努力集中在导出这样的表示 直接从真实的 图像 相当复杂，涉及 部分遮挡、间隙、虚假边缘和噪声。提出了两个关键的互补办法。第一种依赖于变形和冲击形成的局部公式化，其通过直接从边缘元素传播局部标记的波并且检测、分类、分组和标记所形成的奇点（冲击）以从部分轮廓段恢复部分冲击段，在分割之前对灰度图像中的形状进行基于冲击的分割，和缺失轮廓的完成。 二次（互穿）波和一组冲击变换，提出了处理由于部分闭塞，间隙和虚假的边缘元素的改变。第二种方法是第一种方法的补充，通过随机初始化对象假设作为四阶冲击（种子），然后根据低级别过程的输出增长，从而捕获区域连续性。 该研究的动机是在3D分割和配准问题，将集中在两个关键领域：1）形式化的分类的3D冲击，冲击文法的发展，并实施强大的数值计划，他们的检测; 2）通过设计扩散的表面演化方案，发展了三维尺度的几何概念，从而将反应扩散空间推广到三维。 整体方法反映了可视化建模的耦合系统的偏微分方程，一个范例，允许同时互动的边界和区域的过程，以及自下而上/自上而下的通信。

This research is concerned with the problem of recovery, representation, and recognition of two and three-dimensional shape from real images. Building on the results of previous NSF- funded research on deriving a representation for segmented shape that is robust to variations in the visual scene, the current effort focuses on deriving such representations directly from real images of appreciable complexity, involving partial occlusion, gaps, spurious edges, and noise. Two key complementary approaches are proposed. The first relies on a local formulation of deformation and shock formation by propagating local, labeled waves directly from edge elements and detecting, classifying, grouping, and labeling the formed singularities (shocks) to recover partial shock segments from partial contour segments, shock-based partitioning of shapes in grey-scale images prior to segmentation, and completion of missing contours. Secondary (interpenetrating) waves and a set of shock transformations are proposed to deal with alterations due to partial occlusion, gaps, and spurious edge elements. The second approach is complementary to the first and captures regional continuity by randomly initializing object hypotheses as fourth-order shocks (seeds), which then grow based on the output of low-level processes. The research is motivated by segmentation and registration problems in 3D and will focus on two key areas: 1) the formalization of a classification of 3D shocks, the development of a shock grammar, and the implementation of robust numerical schemes for their detection; and 2) the development of a geometric notion of scale in 3D by devising a surface evolution scheme of diffusion, thus generalizing the reaction-diffusion space to 3D. The overall approach reflects visual modeling by sets of coupled systems of PDEs, a paradigm which allows for simultaneous interaction of boundary and regio n processes as well as bottom-up/top-down communication.