On the Use of the Tree Structure of Depth Levels for Comparing 3D Object Views

Today the simple availability of 3D sensory data, the evolution of 3D representations, and their application to object recognition and scene analysis tasks promise to improve autonomy and flexibility of robots in several domains. However, there has been little research into what can be gained through the explicit inclusion of the structural relations between parts of objects when quantifying similarity of their shape, and hence for shape-based object category recognition. We propose a Mathematical Morphology inspired hierarchical decomposition of 3D object views into peak components at evenly spaced depth levels, casting the 3D shape similarity problem to a tree of more elementary similarity problems. The matching of these trees of peak components is here compared to matching the individual components through optimal and greedy assignment in a simple feature space, trying to find the maximum-weight-maximal-match assignments. The matching thus achieved provides a metric of total shape similarity between object views. The three matching strategies are evaluated and compared through the category recognition accuracy on objects from a public set of 3D models. It turns out that all three methods yield similar accuracy on the simple features we used, while the greedy method is fastest.