We present a shape segmentation method for complete and incomplete shapes. The key idea is to directly optimize the decomposition based on a characterization of the expected geometry of a part in a shape. Rather than setting the number of parts in advance, we search for the smallest number of parts that admit the geometric characterization of the parts. The segmentation is based on an intermediate-level analysis, where first the shape is decomposed into approximate convex components, which are then merged into consistent parts based on a nonlocal geometric signature. Our method is designed to handle incomplete shapes, represented by point clouds. We show segmentation results on shapes acquired by a range scanner, and an analysis of the robustness of our method to missing regions. Moreover, our method yields results that are comparable to state-of-the-art techniques evaluated on complete shapes.

In this paper, we introduce a new approach to constrained clustering which treats the constraints as features. Our method augments the original feature space with additional dimensions, each of which derived from a given Cannot-link constraints. The specified Cannot-link pair gets extreme coordinates values, and the rest of the points get coordinate values that express their spatial influence from the specified constrained pair. After augmenting all the new features, a standard unconstrained clustering algorithm can be performed, like k-means or spectral clustering. We demonstrate the efficacy of our method for active semi-supervised learning applied to image segmentation and compare it to alternative methods. We also evaluate the performance of our method on the four most commonly evaluated datasets from the UCI machine learning repository.

Abstract We define the convexity rank of a set of points to be the portion of mutually visible pairs of points out of the total number of pairs. Based on this definition of weak convexity, we introduce a spectral method that decomposes a given shape into weakly convex regions. The decomposition is applied without explicitly measuring the convexity rank. The method merely amounts to a spectral clustering of a matrix representing the all‐pairs line of sight. Our method can be directly applied on an oriented point cloud and does not require any topological information, nor explicit concavity or convexity measures. We demonstrate the efficiency of our algorithm on a large number of examples and compare them qualitatively with competitive approaches.