전역 및 국부 기하 특성을 반영한 메쉬 분할
A Mesh Segmentation Reflecting Global and Local Geometric Characteristics
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초록
본 논문에서는 3D 메쉬 모델의 텍스쳐 매핑, 단순화, 모핑, 압축, 형상정합 등 다양한 분야에 응용될 수 있는 메쉬분할 문제를 다룬다. 메쉬분할은 주어진 메쉬를 서로 떨어진 집합(disjoint sets)으로 나누는 과정으로서, 본 논문에서는 메쉬의 전역적 및 국부적 기하 특성을 동시에 반영하여 메쉬를 분할하는 방법을 제시하고자 한다. 먼저 주어진 메쉬의 국부적 기하 특성인 곡률 정보와 전역적 기하 특성인 볼록성을 이용하여 메쉬 정점들 중 첨예정점(sharp vertex)을 추출하고, 모든 첨예정점들 간의 유클리디언 거리에 기반한 -평균군집화 기법[26]을 적용하여 첨예정점들을 분할한다. 분할된 첨예정점에 속하지 않는 나머지 정점들에 대해서는 유클리디언 거리상 가까운 군집으로 병합하여 최종적인 메쉬분할이 이루어진다. 또한 본 논문에서 제안한 메쉬분할 방법을 구현하여 여러 메쉬 모델에 대해 실험 결과를 보여준다.
Abstract
This paper is concerned with the mesh segmentation problem that can be applied to diverse applications such as texture mapping, simplification, morphing, compression, and shape matching for 3D mesh models. The mesh segmentation is the process of dividing a given mesh into the disjoint set of sub-meshes. We propose a method for segmenting meshes by simultaneously reflecting global and local geometric characteristics of the meshes. First, we extract sharp vertices over mesh vertices by interpreting the curvatures and convexity of a given mesh, which are respectively contained in the local and global geometric characteristics of the mesh. Next, we partition the sharp vertices into the number of clusters by adopting the -means clustering method [29] based on the Euclidean distances between all pairs of the sharp vertices. Other vertices excluding the sharp vertices are merged into the nearest clusters by Euclidean distances. Also we implement the proposed method and visualize its experimental results on several 3D mesh models.
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