Orientation and Spatial Occupancy Representations in Shape Analysis

In this paper we propose representations of two-dimensional curves that capture curve orientation and spatial occupancy, and show how they can be used in isolation or jointly to address problems in dynamic shape analysis and model-based matching of occluded objects. To explicitly represent curve orientation, we generalize the notion of extended circular image to a non-convex curve, by representing it as a sequence of extended circular images of its convex and concave parts. Evaluating the similarity of two curves can then be reduced to evaluating the similarity of corresponding segments by directly correlating their extended circular images. To explicitly represent spatial occupancy in a manner that can be used in shape matching, we blur the two-dimensional binary image obtained from the curve. Two curves that are similar in both shape and size and optimally aligned with respect to each other in both position and orientation will then result in a value close to one of the correlation coefficient obtained from the respective binary images. In dynamic shape analysis we use the orientation-based representation alone, while in the model-based matching of occluded objects we use orientation for generating hypotheses and spatial occupancy for selecting the correct ones.