Joint shape and texture analysis of objects boundaries in images using a Riemannian approach

In order to detect, track and recognize objects in images, one has to develop statistical models for features representing those objects. Shapes and textures are two main features that are used for this purpose. While past research has developed separate techniques for analyzing these for these two features, our goal is to study them together. We represent the 2D coordinates of the boundary and the texture function along that boundary as a composite parameterized curve in a high-dimensional Euclidean space. Then, we define equivalence relations on these representations to obtain the desired invariances. The shape component is made invariant to rigid motions, global scalings and re-parameterizations, while the texture component is made invariant only to the last two. Using a Riemannian structure on the resulting quotient space, we compute geodesic paths between shape-texture functions to compare different objects. In addition to optimal deformations of one object into another, this method provides a cohesive registration of points across objects using both shape and texture information. We will demonstrate this framework using examples of objects in artificial and real images.