ROTATION, SCALE AND TRANSLATION-INVARIANT SEGMENTATION-FREE SHAPE RECOGNITION Hae Yong Kim and Sidnei Alves de Araújo Escola Politécnica, Universidade de São Paulo, Brazil {hae,saraujo}@lps.usp.br ABSTRACT In this paper, we propose a RST-invariant (Rotation, Scale, Trans- lation) segmentation-free shape recognition method. Most of the existing shape recognition techniques require segmentation before extracting shape features and recognizing it. Unfortunately, seg- mentation is usually prone to error and segmentation errors pro- duce recognition errors. The proposed technique is based on circu- lar and radial sampling spaces, two 3D spaces built by projecting the analyzed image on circles and radial lines. First, we demon- strate the robustness of the technique in one-scale RT-invariant shape recognition for noisy binary images. We also show that the technique can categorize similar shapes into classes. Then, we make the technique to become invariant to scale. Finally, we dem- onstrate how the technique can recognize shapes in noisy grayscale images with inconstant background. We demonstrate that, under certain assumptions, the technique is 100% accurate. 1. INTRODUCTION This paper considers RST-invariant (Rotation, Scale, Translation), segmentation-free shape recognition in both binary and grayscale images. This problem occurs naturally in computer vision applica- tions: the vision algorithm must search a noisy image with incon- stant background for a query shape that can be darker or lighter than the background, and that can be in any location, any angle and within some range of scales. The “brute force” solution of this problem would be to perform a series of correlations (or template matchings) between the analyzed image and the query shape ro- tated by every possible angle, scaled by every possible factor (within the scale range) and translated to every possible position. Clearly, this takes too long to be practical. We propose a technique to substantially accelerate this searching, without compromising the accuracy. To escape from the brute force algorithm, a typical shape rec- ognition algorithm first separates the shape from the background, then extracts some RST-invariant features and compares them with the features of the sample shapes. In the literature, there are many papers on RST-invariant shape descriptors. One of the most impor- tant is a set of moments introduced in 1962 by Hu [1]. In recent years, many other techniques that use invariant moments have This work was supported by CNPq, process numbers 475155/2004-1 and 307193/2006-3. The authors thank prof. Farzin Mokhtarian for permitting us to use the SQUID image database. been developed [2, 3]. There are other approaches for the shape recognition, for example the curvature scale space proposed by Mokhtarian [4] was adopted by MPEG-7 as standard shape de- scriptor. Other approaches use circular or radial masks [5, 6]. These techniques are not segmentation-free. Segmentation is usu- ally prone to error, and segmentation error causes recognition er- ror. A segmentation-free RT-invariant system was proposed in [7], but it is not S-invariant and can distinguish only simple shapes. A segmentation-free character recognition technique was proposed in [8], but it is not RS-invariant. This paper proposes a solution to this problem. It is based on Circular Sampling Space (CiSS) and Radial Sampling Space (RaSS), two 3D spaces built by projecting the analyzed image on circles or radial lines. We show that, under some assumptions, the proposed technique can be as accurate as the brute force algorithm. 2. CIRCULAR AND RADIAL SAMPLING SPACES In this paper, a shape is a binary image defined inside a circle. That is, a query shape Q is a function } 1 , 0 { : → D Q , where the domain D is a circle (figure 1). A shape may be disconnected (fig- ure 1a) or present holes (figure 1c). The aim of this paper is to search an analyzed image A (binary or grayscale) for a query shape Q. The shape can appear anywhere inside A and it can be rotated and possibly also scaled. As the shape recognition will search only for the shape inside the domain circle, the center of the domain and its radius may be modified to specify which subpart of the pattern is to be searched for (figures 1a and 1b). Given a 2D image ｧ ｧ → 2 : A to be analyzed, its circular sampling space (CiSS) is a function ｧ ｧ ｧ → × + 2 : A C defined: ∫ π θ θ + θ + = 2 0 d ) sin , cos ( ) , , ( r y r x A r y x C A Intuitively, ) , , ( r y x C A is the average grayscale of the pixels of image A situated at distance r from pixel ) , ( y x . A computer graphics algorithm for drawing circles, as [9], can be used to find efficiently all the pixels that belong to a specific circle. (a) (b) (c) (d) Fig. 1: Examples of shapes. Figure (d) depicts CiSS in green and RaSS in blue.