User-Steered Methods for Extracting Geometric Features in 3D Meshes

Woosuk University, jsha@woosuk.ac. kr ABSTRACT In order to extract geometric features in 3D meshes with effective interactions according to user-steering, we generalize the 2D algorithms of snapping and wrapping that, respectively, move a cursor to a nearby feature and construct feature boundaries in images. First, we define two numerical values measuring the geometric characteristics of meshes: approximate curvatures and cost functions. By exploiting the defined measuring values, the techniques of geometric snapping and geometric wrapping in 3D meshes are developed and implemented. We also visualize the results obtained from applying the techniques to extracting geometric features in the general meshes modeled for human faces, cows, and single teeth. Keywords: geometric snapping, geometric wrapping, geometric features, user-steered methods, 3D mesh. 1. INTRODUCTION In CAD and graphics systems, diverse 3D models are represented with 3D meshes in order to be effectively processed. One of the most important functions in mesh applications is to detect geometric features representing their principal boundaries appearing in the meshes. Similarly to edges in images, geometric features are crucial for deciding which parts of the meshes have to be processed or to be preserved in many applications such as simplification, compression, editing, morphing, and deformation of the meshes. In mesh simplification and compression, the geometric features have to be maximally preserved. Mesh editing usually tends to process the parts appearing as geometric features in a mesh, and mesh morphing can also be performed by morphing the corresponding geometric features between two meshes. Meshes can be deformed by manipulating their parts appearing as the geometric features. In this paper, we consider user-steered methods for extracting geometric features from a given mesh with effective interactions. Many researches [5-6][12-13][15] for extracting edges in 2D images have been reported for the last decade. Recently, 2D image snake technique [13] was extended to extracting geometric features in 3D meshes, which is called the geometric snake [14]. The concept of the geometric snake is to lock up geometric features with curves after mapping some parts of a given 3D mesh into the plane [7]. Initial curves are drawn for approximating the boundary of user-steered features, and then final curves are determined by changing the initial curves to minimize their energy functions. Since the geometric snake is dependent on only automatic boundary extraction after the initial curves are drawn, it often has difficulty in interactively extracting boundary shape. In this paper, we propose methods for extracting geometric features in 3D meshes according to user-steering by importing powerful interaction techniques, which are called the user-steered geometric feature extraction . The user-steered feature extraction is composed of two important steps snapping and wrapping; a user moves a cursor to locate a sequence of seed points, and then boundary paths connecting the seed points are automatically constructed to form an entire boundary. These two steps can be iterated by moving or deleting some seed points, and by inserting more seed points to the sequence of seed points. In order to exactly move the cursor position to an intended point, a technique called the snapping is used, which moves the cursor to a nearby feature. The process of constructing the boundary paths enclosing geometric features after snapping the seed points is called the wrapping . 2D image snapping [9-10] is an evolution of the cursor snapping [2-3][18]. A few of practical methods have been presented for image wrapping: intelligent scissors [15], livewire and livelane [5], livewire on the fly [6], and enhanced lane [12]. In this paper, we propose two steps of geometric snapping and geometric wrapping for the user-