Simplification and multi-resolution representations

Abstract

© The Author(s) 2014. Simplification of Morse and Morse-Smale complexes is an important issue to eliminate noise and reduce over-segmentation. Moreover, different users may have different requirements in terms of degree of simplification, which usually vary over time and location within the field domain. Thus, a multi-resolution representation of morphology is critical for interactive analysis and exploration of data. In this chapter, we first describe and compare simplification operators on Morse functions and Morse and Morse-Smale complexes (Sect. 6.1). We then present multi-resolution models for the morphology of scalar fields (Sect. 6.2), and we specify two models in more detail: the first one providing a multi-resolution description of the combinatorial structure of Morse and Morse Smale complexes in arbitrary dimensions, and the second one addressing the problem of coupling a multi-resolution representation of geometry and of morphology in 2D.