Free Form Shape Representation Using NURBS Modeling

Kim Meng Liang¹, Mandava Rajeswari², Bee Ee Khoo³

School of Industrial Technology

University Science Malaysia

11800 Minden Penang

Malaysia

e-mail: liangkm@hotmail.com¹, mandava@usm.my², bekhoo@usm.my³

ABSTRACT

The representation, matching and analysis of objects of interest are of prime importance in shape-based retrieval systems. Considering that these systems involve analysis of various complex shapes, an accurate representation of free form shape is required. A simple and accurate shape representation procedure would ensure meaningful results from the shape-based retrieval systems. Motivated by this factor, this paper presents a free form shape representation technique using Non-Uniform Rational B-Spline (NURBS) modelling. The free form shapes are modelled using control points and weights. NURBS posses attractive properties such as spatial uniqueness, bounded and continuous, local shape controllability and shape invariance under transformation. Furthermore, NURBS based shape descriptor allows accurate reconstruction of the shape boundary from the NURBS features used to describe it. This paper presents the details of deriving a set of NURBS features using the boundary of the object. The accuracy and data reduction properties using NURBS are examined by carrying out an experiment on two sets of images: geometric and free form. Accuracy of the representation is evaluated by using centroid-radii error function, which computes the cumulative distance between the intersection points by radii lines on the boundary of the original image and the reconstructed image. The data reduction property is shown by the ratio computation between the number of control points and the boundary points. The overall experiment results show that NURBS is an accurate shape descriptor and a potential candidate for use in shape-based image retrieval systems.

Keywords: Shape Representation, NURBS, Shape-Based Image Retrieval