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

本文研究的是从真实图像中恢复、表示和识别二维和三维形状的问题。基于先前由美国国家科学基金会资助的研究结果，即为分段形状导出对视觉场景中的变化具有健壮性的表示，当前的工作集中于直接从可感知的复杂性的真实图像中导出此类表示，涉及部分遮挡、间隙、伪边和噪声。提出了两种关键的互补方法。第一种方法依赖于变形和冲击形成的局部公式，方法是直接从边缘元素传播局部标记波，并对形成的奇点(冲击)进行检测、分类、分组和标记，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，以及完成缺失的轮廓。提出了二次(互穿)波和一组激波变换，以处理由于部分遮挡、缝隙和虚假边缘元素而引起的变化。第二种方法是对第一种方法的补充，通过将对象假设随机初始化为四阶激波(种子)，然后根据低层过程的输出进行生长，从而获得区域连续性。这项研究的动机是3D中的分割和配准问题，并将集中在两个关键领域：1)3D冲击分类的形式化，冲击语法的发展，以及用于检测3D冲击的稳健数值方案的实现；2)通过设计扩散的表面演化方案，发展3D中的几何尺度概念，从而将反应-扩散空间推广到3D。总体方法反映了通过一组耦合的PDE系统进行可视化建模，这是一种允许边界和区域进程同时交互以及自下而上/自上而下沟通的范例。

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.