3D Skeletonization as an Optimization Problem

Abstract

A skeleton refers to a significant shape which is used to capture some important topologies of an object in both two and three dimensions. A curve-skeleton of 3D object is a centerline representation or a stick-like figure of that object that can be implemented in a number of applications including animation and virtual colonoscopy. In this paper, a novel approach is represented to illustrate 1D curve-skeletonization of 3D objects. In order to analyze and compare several 1D skeletons of the same 3D object. This report will further discuss a specific implementation of this concept and show different experiment results.

3D Skeletonization as an Optimization Problem

Introduction

With the emerging modern imaging techniques, the generation of large 3D volume data sets are allowed to capture at high resolution, like CT and MRI data. It is important to find new ways in order to maximize the information that is acquired from data sets and at the same time reducing the cost of interacting with it. Skeletonization of such a 3D volume is considered as a significant preprocessing step for extracting object features in order to perform complicated classification methods. Skeleton basically represents the original object in its thin version but its original shape and properties. In 3D, the skeleton is referred to both line-like representation and a medial-surface while in 2D, the term skeleton is only refers to as medial-axis. The skeleton in the grass-fire analogy is comprised of some specific points on which different fire fronts intersect each other.

Problem Statement

The problem statement of this report is the reduction of the skeletonization process to a numerical optimization problem to compare and evaluate several 1D skeletons belonging to the same 3D object.

According to Attene and Biscotti (2003), an evaluation of the quality of the skeleton can be performed by the calculations of the similarities among the skeleton's silhouette and the original shape. So the problem of skeletonization can be converted into a numerical optimization problem. To create a skeleton this concept has to be implemented.

Discussion

A lot of work has been done on studying the 3D skeltonization. According to Bae and Kim, (2012), a skeleton is actually the name given to a graphical representation which is used to capture some of the major metrical and topological properties of the object. It is the 1D thin version of the object's original shape. Skeletons play a very significant role in computer vision as it is a very simple and easy task to acquire features of any shape from a graphical representation instead of its boundary description. A 2D shape skeleton can be defined as a shape's medial axis. Cornea and Silver (2007), further says that this medial axis represents set of all different points that is comprised of two or more closest points on the shape's boundary. The medial axis of a 2D shape is can be computed efficiently as it is always a 1D set. A curve-skeleton of a 3D shape is a 1D skeleton which is considered as an ill-defined ...