Consistent segmentation projects: Supervised Part Correspondence, Unsupervised Co-Segmentation

Unsupervised Co-Segmentation of a Set of Shapes via Descriptor-Space Spectral Clustering

Oana Sidi1, Oliver van Kaick2, Yanir Kleiman1, Hao Zhang2, Daniel Cohen-Or1,
1Tel Aviv University 2Simon Fraser University
SIGGRAPH Asia 2011
Cosegmentation on a set of liquid containers

Figure: Unsupervised co-segmentation of a highly varied set of container objects using our algorithm. Corresponding parts differ significantly in their shape, pose, position, and cardinality.


We introduce an algorithm for unsupervised co-segmentation of a set of shapes so as to reveal the semantic shape parts and establish their correspondence across the set. The input set may exhibit significant shape variability where the shapes do not admit proper spatial alignment and the corresponding parts in any pair of shapes may be geometrically dissimilar. Our algorithm can handle such challenging input sets since, first, we perform co-analysis in a descriptor space, where a combination of shape descriptors relates the parts independently of their pose, location, and cardinality. Secondly, we exploit a key enabling feature of the input set, namely, dissimilar parts may be ``linked'' through third-parties present in the set. The links are derived from the pairwise similarities between the parts' descriptors. To reveal such linkages which may manifest themselves as anisotropic and non-linear structures in the descriptor space, we perform spectral clustering with the aid of diffusion maps. We show that with our approach, we are able to co-segment sets of shapes that possess significant variability, achieving results that are close to those of a supervised approach.


Results 1 Results 2 Results 3
Results 4 Results 5 Results 6

Figure: Results of our co-segmentation on a variety of shapes. Corresponding segments in each class are shown with the same color. Notice how the segmentation and labeling is coherent for many of the parts in each set.


PDF (12MB)
Supplementary material (14MB)

BibTex Reference

    author = {Oana Sidi and Oliver van Kaick and Yanir Kleiman and Hao Zhang and Daniel Cohen-Or},
    title = {Unsupervised Co-Segmentation of a Set of Shapes via Descriptor-Space Spectral Clustering},
    journal = {ACM Trans. on Graphics (Proc. SIGGRAPH Asia)},
    volume = {30},
    number = {6},
    pages = {126:1--126:10},
    year = 2011,

Presentation slides



The dataset can now be found here.


We thank the anonymous reviewers for their valuable comments and suggestions. Thanks also go to Aleksey Golovinskiy and Thomas Funkhouser for providing their consistent segmentation code, to Evangelos Kalogerakis and collaborators for providing their dataset of labeled shapes and evaluating their supervised method on our dataset, to Xiaobai Chen for the segmentation benchmark, and to Lior Shapira for the SDF code. This research is supported in part by the Israel Science Foundation and the Natural Sciences and Engineering Research Council of Canada (Grant no. 611370 for Hao Zhang and 611393 for Ghassan Hamarneh).


GrUVi Project Page
Related project: Prior Knowledge for Part Correspondence
A recent related project: Active Co-Analysis of a Set of Shapes