Research in Shape Modeling

This is a new edited volume on shape analysis presenting results in shape modeling and computational geometry from the 2013 Association for Women in Mathematics (AWM) symposium held at UCLA's Institute for Pure and Applied Mathematics (IPAM). In-depth discussion of shape modeling techniques is supplemented by full-color illustrations demonstrating the results of workshop-developed shape modeling algorithms. It will be the first volume in Springer's AWM series.

Demonstrates the latest techniques in analysis of shapes and shape metrics, providing a resource for further research in the growing field of mathematical shape modeling First volume in Springer's new Association for Women in Mathematics Series Features preliminary results and collaborations from the international participants of the Women in Shape Modeling (WiSh) Conference 2013 Includes supplementary material: sn.pub/extras

Autorentext
Kathryn Leonard Department of Mathematics California State University, Channel Islands One University Drive Camarillo, CA, USA 93012 Sibel Tari Department of Computer Engineering Middle East Technical University Universiteler Mah. Dumlupinar Blv. No: 1 06800 Ankara, Turkey.

Klappentext

Presenting the latest research from the growing field of mathematical shape analysis, this volume is comprised of the collaborations of participants of the Women in Shape Modeling (WiSh) workshop, held at UCLA's Institute for Pure and Applied Mathematics in July 2013. Topics include:

• Simultaneous spectral and spatial analysis of shape
• Dimensionality reduction and visualization of data in tree-spaces, such as classes of anatomical trees like airways and blood vessels
• Geometric shape segmentation, exploring shape segmentation from a Gestalt perspective, using information from the Blum medial axis of edge fragments in an image

• Representing and editing self-similar details on 3D shapes, studying shape deformation and editing techniques Several chapters in the book directly address the problem of continuous measures of context-dependent nearness and right shape models. Medical and biological applications have been a major source of motivation in shape research, and key topics are examined here in detail. All together, the chapters in the book cover an entire spectrum in shape analysis starting from raw images and ending with shape-related decisions.

  Inhalt
  Automatic prior shape selection for image segmentation.- A scalable fluctuating distance field: an application to tumor shape analysis.- Part-aware distance fields for easy inbetweening in arbitrary dimensions.- A biomechanical model of cortical folding.- Quantification and visualization of variation in anatomical trees.- Skeleton-based recognition of shapes in images via longest path matching.- Revisiting skeletons from natural images.-Towards automated filtering or the medial axis using the scale axis transform.- Identifying perceptually salient features on 2D shapes.