Non-parametric planar shape representation based on adaptive curvature functions
Introduction
The increasing number of applications relying on multimedia databases has motivated research in object representation. Particularly, shapes have received much attention as a powerful tool to represent planar objects. The goal of representation procedures is to extract a feature vector from segmented raw images.
In order to grant fast and efficient storage and retrieval of objects from a database, feature vectors must fulfill the following requirements: (i) they must be unique for each object; (ii) they must be resistant to distortions and noise; (iii) they must be as short as possible in order to minimise storage requirements and to ease classification; (iv) they must not be specific for a given type of object; and (v) they must be fast and easy to obtain.
In this paper, a new method to represent planar shapes by means of a short feature vector is depicted. Since the method is boundary-based, objects must be correctly segmented from the background and no occlusions are allowed. A brief review of shape representation methods is presented in Section 2. Initially, the shape of the object is represented by means of an adaptively built curvature function, as described in Section 3. This curvature function is very robust against noise, scale and rotations, although its main advantage is that it provides a good quantization of angles, corners and curves. In Section 4, a procedure to build a very short feature vector is presented. The procedure does not depend on shape parameters and it is quite robust against several distortions such as blurring, sharpening, softening, and even against minor perspective changes. An unsupervised classifier is introduced in Section 5 to test the quality of the representation algorithm. The classification has no rejection rate and classes can be unsupervisedly added at any time. Section 6 portrays several experiments using different image databases and new objects, which do not belong to any previously known type. Finally, Section 7 presents conclusions and future work.
Section snippets
Earlier work
Shape descriptors can be roughly divided into scalar transform methods and space domain methods. The first ones generate descriptors which are mathematically derived from the shape, whereas the second ones express structural and relational properties on the shape.
Scalar transform methods present the advantage of not requiring comprehension of the shape to be used, but only mathematical operations. The most representative scalar methods are simple escalar techniques, Fourier shape descriptors
Shape representation by means of a curvature function
Curvature functions, easily extracted from the contour chain code of a shape, basically describe how much a curve bends at each point. The peaks of a curvature function correspond to the corners of the represented object and their height depends on the angle at these corners. Flat segments whose average value is larger than zero are related to curves and those whose average value is equal to zero are related to straight lines. Fig. 1a presents a shape yielding two corners (points 2 and 3) and a
Calculation of a short sized feature vector
Curvature functions do represent a shape, but they are usually too large for efficient storage. The most reliable approach to compare these functions is correlation, which is a computationally heavy process when a high number of comparisons is required [17]. This section proposes a method to reduce the size of the feature vector which is based on spectral properties of the curvature function. The system does not require any shape parameter calculation and resulting vectors are quite resistant
Classification of feature vectors
In order to recognise a given object, its feature vector must be classified according to certain rules. It is usually easier and more precise to establish a certain number of classes beforehand. Then, the input vector is compared to all available prototypes and it is included into the most suitable class. However, it is preferable not to establish any class a priori, but to create them on-line, so that objects can be classified despite their being equal to any known prototype.
We propose a
Experiments and results
The proposed system has been implemented in C on a Pentium PC 166 MHz, 32 Mb RAM. The system was fed with raw binarised images extracted from random databases. Images may present rotations, translations, scaling, high random or uniform noise levels, blurring, sharpening, dilating, eroding and minor perspective changes. Examples of these distortions may be observed in Fig. 5, Fig. 7, Fig. 8, Fig. 9, Fig. 10. All tests consisted of classifying sets of 1000 random shapes, where each object could
Conclusions and future work
This paper has depicted a non-parametric method to represent planar shapes by means of a very short sized feature vector. No previous knowledge about the objects to be represented is required. The proposed method is fast and computationally cheap. In exchange, it yields a small representation error, but it only affects shapes allowing a very similar curvature.
The resulting vectors are very small and, therefore, suitable for massive storage in database applications. They are also quite resistant
Summary
This paper presents a non-parametric method to extract a very short feature vector from the curvature function of a planar shape. First, the curvature function of the shape is calculated by means of a new procedure that removes as much noise as possible from the contour of the shape without missing relevant points. The procedure consists of evaluating the slope at each pixel of the contour according to the distance between possible relevant points. In order to obtain a feature vector, the
Acknowledgements
This work has been partially supported by the Spanish Comisión Interministerial de Ciencia y Tecnologı́a (CICYT), project No. TIC098-0562.
About the Author—CRISTINA URDIALES was born in Spain in 1971. She received her title of Telecommunication Engineering from the Technical University of Madrid, Spain, in 1995 and her Ph.D. degree from the University of Malaga, Spain, in 1999. From 1996 to the present day she has worked as Assistant Professor in the Department of Tecnologı́a Electrónica of the University of Malaga. Her research is focused on robotics and artificial vision.
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About the Author—CRISTINA URDIALES was born in Spain in 1971. She received her title of Telecommunication Engineering from the Technical University of Madrid, Spain, in 1995 and her Ph.D. degree from the University of Malaga, Spain, in 1999. From 1996 to the present day she has worked as Assistant Professor in the Department of Tecnologı́a Electrónica of the University of Malaga. Her research is focused on robotics and artificial vision.
About the Author—ANTONIO BANDERA was born in Spain in 1971. He received his title of Telecommunication Engineering and Ph.D. degree from the University of Malaga, Spain, in 1995 and 2000, respectively. During 1996 he worked in a research project under a grant by the spanish CYCIT. From 1997 to the present day he has worked as Assistant Professor in the Department of Tecnologı́a Electrónica of the University of Malaga. His research is focused on robotics and artificial vision.
About the Author—FRANCISCO SANDOVAL was born in Spain in 1947. He received the title of Telecommunication Engineering and Ph.D. degree from the Technical University of Madrid, Spain, in 1972 and 1980, respectively. From 1972 to 1989 he was engaged in teaching and research in the fields of opto-electronics and integrated circuits in the Universidad Politécnica de Madrid (UPM) as an Assistant Professor and a Lecturer successively. In 1990 he joined the University of Málaga as Full Professor in the Department of Tecnologı́a Electrónica, starting his research on Artificial Neural Networks (ANN). He is currently involved in autonomous systems and foveal vision, and application of ANN to Energy Management Systems and Broad Band Communication.