2D object recognition based on curvature functions obtained from local histograms of the contour chain code 1 A. Bandera * , C. Urdiales, F. Arrebola, F. Sandoval Dpto. Tecnologõa Electr onica, E.T.S.I. Telecomunicaci on, Universidad de M alaga, Campus de Teatinos, 29071 M alaga, Spain Received 8 December 1997; received in revised form 16 September 1998 Abstract In this paper a real time 2D object recognition algorithm is proposed. Contours are represented by their curvature functions, decomposed in the Fourier domain as linear combination of a set of representative objects. Finally, objects are identi®ed by multilevel clustering. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: 2D object recognition; Clustering algorithm; Chain code local histograms; Curvature function; Hierarchical classi®cation architecture 1. Introduction The recognition of 2D objects is a very impor- tant issue in computer vision that can be divided into three stages (Friedland and Rosenfeld, 1997): (i) delineation, consisting of representing the ob- ject; (ii) representation, consisting of extracting features of the delineation stage output to create the following stage input vector; and (iii) classi®- cation, giving information about the nature of the object. The delineation stage yields several problems, especially if working in hard conditions. First, transformations can occur, the most common ones being: geometric transformations (e.g., rotations, translations and scaling), and noise distortion. This problem can be solved by including prepro- cessing algorithms at this stage (Shrikantan et al., 1996; Hsu and Hwang, 1997), though they increase its complexity and computational time. The im- plementation of a feature extractor as independent as possible to distortions is also feasible, but dif- ®cult. A second problem is that patterns for dis- torted versions of the same object must be related at the classi®cation stage. A learning process to relate those versions could solve it, but this would lead to massive stored information (Cyganski et al., 1987). Problems related to the representation stage are basically two: the determination of which features to include and the need of a reduced number of elements per vector to ease its classi®cation. Many solutions have been proposed, their most common disadvantages being: (i) too large vectors (Shri- kantan et al., 1996; Campbell et al., 1997; Romero et al., 1997), (ii) the need of expert systems for feature extraction requiring a deep study of sam- ples and restricted to very specialised ®elds of ap- plication (Cao et al., 1997; Romero et al., 1997; Pattern Recognition Letters 20 (1999) 49±55 * Corresponding author. E-mail: bandera@dte.uma.es. 1 Electronic annexes available. See http://www.elsevier.nl/ locate/patrec. 0167-8655/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 8 6 5 5 ( 9 8 ) 0 0 1 2 3 - 8