We introduce the bilateral map, a local shape descriptor whose region of interest is defined by two feature points. Compared to the classical descriptor definition using a single point, the bilateral approach exploits the use of a second point to place more constraints on the selection of the spatial context for feature analysis. This leads to a descriptor where the shape of the region of interest is anisotropic and adapts to the context of the two points, making it more refined for shape analysis, in particular, partial matching.
Unsupervised co-analysis of a set of shapes is a difficult problem since the geometry of the shapes alone cannot always fully describe the semantics of parts. In this paper, we consider the use of a semi-supervised learning method where the user actively assists in the co-analysis by iteratively providing input that progressively constrains the system. We introduce a novel constrained clustering method based on a spring system which embeds elements to better respect their inter-distances in feature space together with the user given set of constraints.
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.
Classical approaches to shape correspondence base their computation purely on the properties, in particular geometric similarity, of the shapes in question. Their performance still falls far short of that of humans in challenging cases where corresponding shape parts may differ significantly in geometry or even topology. We stipulate that in these cases, shape correspondence by humans involves recognition of the shape parts where prior knowledge on the parts would play a more dominant role than geometric similarity.
We have developed the first Ant Colony Optimization algorithm specifically aimed at solving the Quadratic Assignment Problem for establishing shape-correspondence, with proximity information incorporated.
We consider the problem of shape correspondence and retrieval. Although our focus is on articulated shapes, the methods developed are applicable to any shape specified as a contour, in the 2D case, or a surface mesh, in 3D. We propose separate methods for2D and 3D shape correspondence and retrieval, but the basic idea for both is to characterize shapes using intrinsic measures, defined by geodesic distances between points, to achieve robustness against bending in articulated shapes.