Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, June 02, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Bálint Miklós (Applied Geometry Group)

The Scale Axis Transform

We introduce the scale axis transform, a new skeletal shape representation for bounded open sets O -> R^d. The scale axis transform induces a family of skeletons that captures the important features of a shape in a scale-adaptive way and yields a hierarchy of successively simplified skeletons. Its definition is based on the medial axis transform and the simplification of the shape under multiplicative scaling: the s-scaled shape O_s is the union of the medial balls of O with radii scaled by a factor of s. The s-scale axis transform of O is the medial axis transform of O_s, with radii scaled back by a factor of 1/s. We prove topological properties of the scale axis transform and we describe the evolution s -> O_s by defining the multiplicative distance function to the shape and studying properties of the corresponding steepest ascent flow. All our theoretical results hold for any dimension. In addition, using a discrete approximation, we present several examples of two-dimensional scale axis transforms that illustrate the practical relevance of our new framework.

Joint work with Joachim Giesen, Mark Pauly and Camille Wormser.

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