Ridges And Valleys Extraction On Meshes

Ridges and valleys are powerful shape descriptors. They reflect the basic shape and obvious feature on meshes and are the essential curves while rendering the objects. Ridges and valleys also play important roles in mesh simplification, segmentation and texture synthesis, etc. This paper study on ridges and valleys extraction on meshes.We define the ridge and valley point as the extremes of the principal curvatures along their normal sections. Ridges and valleys are the loci of ridge and valley points. According to this definition, we can find the ridge and valley points through discrete method. As three and four order derivatives are required to calculate ridge and valley point, we propose another new method based on local polynomial fitting. The experimental results show that both methods can locate obvious feature on meshes effectively.In order to obtain ridges and valleys, we need to estimate the principal curvature and direction on mesh vertices. We propose a new intuitive method to estimate curvature based on Weingarten map. The experimental results have proved its feasibility and reliability.After having found the ridge and valley points, we traced them to generate ridges and valleys. It's necessary to set up threshold to filter out short and fairy lines caused by computational errors and characteristic of models. Some smooth methods should also be used to obtain desired result.