# Detection and classification of topological evolution for linear metamorphosis

This source preferred by Alexander Pasko

**Authors: **Nieda, T., Pasko, A. and Kunii, T.L.

http://www.springerlink.com/content/100388/

**Journal:** The Visual Computer

**Volume:** 22

**Pages:** 346-356

**ISSN:** 0178-2789

**DOI:** 10.1007/s00371-006-0011-9

The advantage of function-based methods for shape metamorphosis is the automatic generation of intermediate shapes possibly between the key shapes of different topology types. However, the functional methods have a serious problem: shape interpolation is applied without topological information and thereby the time values of topological changes are not known. Thus, it is difficult to identify the time intervals for key frames of shape metamorphosis animation that faithfully visualizes the topological evolution. Moreover, the information on the types of the topological changes is missing. To overcome the problem, we apply topological analysis to functional linear shape metamorphosis and classify the type of topological evolution by using Hessian matrix. Our method is based on the Morse theory and analyzes how the critical points appear. We classify the detected critical points into maximum point, minimum point, and saddle point types. Using the types of critical points, we can define the topological information for shape metamorphosis. We illustrate these methods using shape metamorphosis in 2D and 3D spaces.

This data was imported from Scopus:

**Authors: **Nieda, T., Pasko, A. and Kunii, T.L.

**Journal:** Visual Computer

**Volume:** 22

**Issue:** 5

**Pages:** 346-356

**ISSN:** 0178-2789

**DOI:** 10.1007/s00371-006-0011-9

The advantage of functional methods for shape metamorphosis is the automatic generation of intermediate shapes possible between the key shapes of different topology types. However, functional methods have a serious problem: shape interpolation is applied without topological information and thereby the time values of topological changes are not known. Thus, it is difficult to identify the time intervals for key frames of shape metamorphosis animation that faithfully visualize the topological evolution. Moreover, information on the types of topological changes is missing. To overcome the problem, we apply topological analysis to functional linear shape metamorphosis and classify the type of topological evolution by using a Hessian matrix. Our method is based on Morse theory and analyzes how the critical points appear. We classify the detected critical points into maximum point, minimum point, and saddle point types. Using the types of critical points, we can define the topological information for shape metamorphosis. We illustrate these methods using shape metamorphosis in 2D and 3D spaces.

This data was imported from Web of Science (Lite):

**Authors: **Nieda, T., Pasko, A. and Kunii, T.L.

**Journal:** VISUAL COMPUTER

**Volume:** 22

**Issue:** 5

**Pages:** 346-356

**eISSN:** 1432-2315

**ISSN:** 0178-2789

**DOI:** 10.1007/s00371-006-0011-9