Multiscale Shape Processing

headed by Prof. Dr. Alexandru C. Telea

Shapes come in a variety of flavors: 2D images or countours, 3D surfaces or volumes, and can also carry data attributes, such as normals, textures, vectors, scalars, or tensors. Multiscale shape processing refers to a wide class of operations performed on such shapes at different levels-of-detail. A list of such shape processing operations which relate to currently active research topics includes

• feature-preserving smoothing: eliminating the small-scale details of a shape (e.g. noise) while keeping its sailent features (e.g. edges)
• shape classification: partitioning a shape into regions having different properties, e.g. corners, edges, convex, concave, and flat regions
• shape segmentation: decomposing a shape into regions perceived as its different parts, e.g. finding the limbs, torso and head of a human silhouette
• shape matching: given two or more shape, find their similar components
• shape simplification: given a shape, produce a simpler shape (e.g. less polygons) which looks similar

To address these goals, we use two specific classes of techniques:

• skeletonization: computing the so-called skeleton, or medial axis, a thin structure centered within a 2D or 3D shape
• partial differential equations: represent the shape modification as a differential operator, and the processing as the operator's application

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