Symmetry Map and Symmetry Transforms for Shape Recovery and Object Recognition

该项目涉及图像中形状的恢复、表示和识别问题。PI建议使用对称映射，即边缘映射的激波图，作为2D形状的中级表示。然后，形状的变形被表示为一系列对称变换，这些对称变换对应于骨架固有的不稳定性(激波转变)。使用编辑距离方法找到两个形状之间的最佳变形路径，以找到冲击图上最小的变换或编辑动作序列。该路径的成本被用作索引到图像数据库中的相异度量。该方法还允许形状建模和设计、变形序列的构造和可变形模板。在3D中，PI建议将三维骨架简化为由一维空间曲线组成的冲击支架，在该支架上可以分析地构建3D骨架，从而大大节省了复杂形状的恢复和存储，例如米开朗基罗的Pieta、人类肺部等。这项研究是通用的，可能会对许多工业和医疗应用产生重大影响，包括基于形状的检索和计算地图集的构建。

This project is concerned with the problem of recovery, representation, and recognition of shapes in images. The PI proposes to use the symmetry map, the shock graph of an edge map, as an intermediate-level representation for 2D shape. Deformations of shape are then expressed as a sequence of symmetry transforms which correspond to the inherent instabilities of skeletons (shock transitions). The optimal deformation path between two shapes is found using an edit distance approach to finding the least action sequence of transforms, or edits, on the shock graph. The cost of this path is used as a dissimilarity measure for indexing into image databases. This approach also allows for shape modeling and design, the construction of morphing sequences, and deformable templates. In 3D, The PI proposes to reduce the three-dimensional skeleton to a shock scaffold consisting of 1D space curves on which the 3D skeleton can be analytically constructed, leading to significant savings in recovery and storage of complex shapes, e.g., Michelangelo's Pieta, human lungs, etc. The research is generic and can potentially significantly impact a number of industrial and medical applications, including shape-based retrieval and construction of computational atlases.