A VARIATIONAL APPROACH FOR DETECTING FEATURE LINES ON MESHES

Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using F-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polyno- mials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.

A Spectral Segmentation Method for Large Meshes

Mesh segmentation is a fundamental and critical task in mesh processing,and it has been studied extensively in computer graphics and geometric modeling communities.However,current methods are not well suited for segmenting large meshes which are now common in many applications.This paper proposes a new spectral segmentation method specifically designed for large meshes inspired by multi-resolution representations.Building on edge collapse operators and progressive mesh representations,we first devise a feature-aware simplification algorithm that can generate a coarse mesh which keeps the same topology as the input mesh and preserves as many features of the input mesh as possible.Then,using the spectral segmentation method proposed in Tong et al.(IEEE Trans Vis Comput Graph 26(4):1807–1820,2020),we perform partition on the coarse mesh to obtain a coarse segmentation which mimics closely the desired segmentation of the input mesh.By reversing the simplification process through vertex split operators,we present a fast algorithm which maps the coarse segmentation to the input mesh and therefore obtain an initial segmentation of the input mesh.Finally,to smooth some jaggy boundaries between adjacent parts of the initial segmentation or align with the desired boundaries,we propose an efficient method to evolve those boundaries driven by geodesic curvature flows.As demonstrated by experimental results on a variety of large meshes,our method outperforms the state-of-the-art segmentation method in terms of not only speed but also usability.