# Multiscale Data and Shape Analysis

*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. 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

*Data* from measurements or scientific simulations also comes in many flavors: multivariate tables, graphs, having quantitative, ordinal, categorical, or relational values. Multiscale data processing refers to operations performed to represent, analyze, and understand such data at different level-of-detail. Example operations in this area include

*graph analysis:*given a large and complex graph, produce a simplified view thereof that highlights the main patterns;*multidimensional analysis:*given a table-like dataset having thousands of points, each with hundreds of dimensions (or more), identify and depict the main correlations, outliers, groups, trends in the data;

To address these goals, we use several classes of techniques:

*image-based techniques:*represent, process, and interact with the data in terms of (continuous) images, thereby leveraging many existing image-processing techniques to assist complex data-centric tasks;*multidimensional projections:*given a high-dimensional dataset, construct a low-dimensional (2D or 3D) representation thereof that allows users to spot patterns of interest easily and reliably;*graph bundling:*given a large relational dataset, construct a visually simple 2D embedding thereof which emphasizes main connectivity and/or data-related patterns between groups of related nodes;*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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