Shape Matching and Object Recognition

Shape Matching and Object Recognition by Alexander Christiansen Berg Doctor of Philosophy in Computer Science University of California, Berkeley Professor Jitendra Malik, Chair We address comparing related, but not identical shapes in images following a deformable template strategy. At the heart of this is the notion of an alignment between the shapes to be matched. The transformation necessary for alignment and the remaining differences after alignment are then used to make a comparison. A model determines what kind of deformations or alignments are acceptable, and what variation in appearance should remain after alignment. This ties strongly with the idea that the difference in shape is the residual difference, after some family of transformations has been applied for alignment. Finding an alignment of a model to a novel object involves search through the space of possible alignments. In many settings this search is quite difficult. This work shows that the search can be approximated by an easier discrete matching problem between key points on a model and a novel object. This is a departure from traditional approaches to deformable template matching that concentrate on analyzing differential models. This thesis presents theories and experiments on searching for, identifying, and using alignments found via discrete matchings. In particular we present a mathematical and ecological motivation for a medium scale descriptor of shape, geometric blur. Geometric blur is an average over transfor-