Topology-Varying 3D Shape Creation via Structural Blending

We introduce an algorithm for generating novel 3D models via topology-varying shape blending. Given a source and a target shape, our method blends them topologically and geometrically, producing continuous series of in-betweens as new shape creations. The blending operations are defined on a spatio-structural graph composed of medial curves and sheets. Such a shape abstraction is structure-oriented, part-aware, and facilitates topology manipulations.

Bilateral Maps for Partial Matching

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.

Co-Hierarchical Analysis of Shape Structures

We introduce an unsupervised co-hierarchical analysis of a set of shapes, aimed at discovering their hierarchical part structures and revealing relations between geometrically dissimilar yet functionally equivalent shape parts across the set. The core problem is that of representative co-selection. For each shape in the set, one representative hierarchy (tree) is selected from among many possible interpretations of the hierarchical structure of the shape. Collectively, the selected tree representatives maximize the within-cluster structural similarity among them.

Active Co-Analysis of a Set of Shapes

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.

Optimization in High-D

We present an approach to optimizing a high-dimensional scalar function that systematically explores the parameter space. Our core idea is the following two-stage technique: We start with a sparse sampling of the parameter space and apply a statistical model to estimate the response of the segmentation algorithm. The statistical model incorporates a model of uncertainty of the estimation which we use in conjunction with the actual estimate in (visually) guiding the user towards areas that need refinement by placing additional sample points.

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

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.

Prior Knowledge for Part Correspondence

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.