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

本研究关注的是真实图像中二维和三维形状的恢复、表示和识别问题。基于先前由NSF资助的研究结果，对分割形状的表示进行了研究，该研究对视觉场景的变化具有鲁棒性，目前的工作重点是直接从相当复杂的真实图像中提取这种表示，包括部分遮挡、间隙、虚假边缘和噪声。提出了两种关键的互补方法。第一种方法依赖于变形和激波形成的局部公式，通过直接从边缘元素传播局部标记波，检测、分类、分组和标记形成的奇点（激波），从部分轮廓段中恢复部分激波段，在分割之前对灰度图像中的形状进行基于激波的分割，并完成缺失的轮廓。提出了二次（互穿）波和一组激波变换来处理由于部分遮挡、间隙和虚假边缘元素造成的变化。第二种方法是对第一种方法的补充，并通过随机初始化对象假设作为四阶冲击（种子）来捕获区域连续性，然后根据低级过程的输出增长。该研究的动机是三维分割和配准问题，并将集中在两个关键领域：1)三维冲击分类的形式化，冲击语法的发展，以及对其检测的鲁棒数值方案的实施；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pde耦合系统集的可视化建模，这是一种允许边界和区域过程同时交互以及自下而上/自上而下通信的范式。

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.