A robust approach for constructing a graph representation of articulated and tubular-like objects from 3D scattered data

Abstract

This paper describes an approach for constructing a graph representation of 3D objects and more particularly of articulated and tubular-like objects. For objects without cavities, this representation is a tree structure that encodes the object template while being invariant to global and local rigid transformation. The approach described in this paper has some interesting aspects: (1) It operates on raw 3D scattered data points, without any pre-processing stage. (2) It has low computational cost. (3) It is robust against irregular data point distribution and data deficiencies. This graph representation can be used in various applications such as object coding, recognition, and segmentation.

Introduction

3D object shape abstraction and encoding has been receiving an increasing attention in the recent years. It is fuelled by the advances in 3D shape imaging technologies and the proliferation of 3D object model databases, where 3D shape representation plays a fundamental role in model retrieval and shape matching. In the literature (Tangelder and Veltkamp, 2004) shape representation can be broadly categorized in three categories, namely, feature based representations, graph based representations, and other representations. Feature based representations encompass only pure geometry information of the object. In contrast, graph based representations, which use a graph showing how shape components are linked together, embed in addition to some geometric information, topological and structural meanings that are quite suitable for high level processing. Graph based representations include three families, namely, model graph, skeletons, and Reeb-graph. Model graph representations are especially suitable for man-made objects (i.e. CAD/CAM models) and are generally difficult to apply for models of natural shape. Skeletons can be applied to wider shapes including animal and human shapes. Skeleton constructions have been approached using the medial axis model (Chuang et al., 2000, Näf et al., 1996, Siddiqi et al., 2002, Bouix et al., 2005) and the distance transform (Gavani and Silver, 1999, Sanniti di Baja and Svensson, 2002, Svensson and Sanniti di Baja, 2002).

Reeb-graph, introduced by Reeb (1946), is a particular skeleton determined using a continuous scalar function defined on an object surface. The main characteristics of a Reeb-graph are (1) one-dimensional graph structure and (2) invariance to both global and local geometric transformations. These characteristics make it suitable for articulated objects. Reeb-graph has been used in many applications such as shape coding (Tai et al., 1998), shape matching (Hilaga et al., 2001), surface compression (Biasotti et al., 2002), and human-body scan segmentation (Xiao et al., 2003a, Xiao et al., 2003b, Xiao et al., 2004). In this paper we propose a method for constructing and visualizing a Reeb-graph of a 3D object. Compared to previous methods, our method is characterized by the following features: (1) It operates on raw 3D data, i.e. cloud of scattered data points (in contrast to methods that require mesh-model data). (2) It is robust against data deficiencies such as irregular distribution reflected by gaps and holes. (3) It has low computational costs. The approach targets objects having tubular-like shapes or a blending of generalized cylinder shapes and assumes that the surface of the object is topologically continuous.

The rest of the paper is organized as follows: Section 2 gives an overview of the approach. Sections 3 Computation of the level-sets, 4 Construction of a connectivity graph, 5 Extraction of joint nodes and branches, 6 Visualization describe the different stages of the approach. Experimental results are discussed in Section 7. Finally, in Section 8, conclusions are drawn and further research work is suggested.