Multi-objective shape segmentation

The users of shape segmentation algorithms possess a wealth of knowledge about the objects they wish to segment. Current automatic segmentation approaches, however, apply a fixed objective uniformly to all parts and limit their input to the number of segments desired and a small set of parameter values. In this paper, we propose the concept of multi-objective shape segmentation. This model allows for the incorporation of domain specific knowledge by means of competing objectives that can selectively refer to one or more segmentation labels or to the segmentation as a whole. The segmentation problem is thus cast as the optimization of an aggregate objective function which is a combination of these heterogeneous competing objectives. We introduce the use of multiplicatively weighted Voronoi partitioning as a means to parameterize segmentations and present algorithms for coarse center placement, segmentation labeling as a function of objectives, and center refinement. We then show how our approach can accommodate symmetry constraints, which ensure desired segmentation properties and effectively reduce the dimensionality of the optimization domain when prior knowledge of the shape is available. Finally, we show how even shapes under complicated articulation can be handled by our approach by using multi-dimensional scaling.