Journal of Computer Applications, Vol – II, No.2, April-June 2009 Page No. 27 REGION REPRESENTATION USING ENHANCED DISCRETE CYLINDRICAL ALGEBRAIC DECOMPOSITION (EDCAD) TO PRESERVE THE SHAPE AND SIZE OF THE CONNECTED REGIONS IN BINARY IMAGES B. Rajesh Kanna St. Joseph’s College of Engineering, Chennai, India, rajesh@stjosephs.ac.in C. Aravindan S.S.N College of Engineering, Chennai, India, AravindanC@ssn.edu.in K. Kannan SASTRA University, Thanjavur, India, kkannan@maths.sastra.edu M. Krishna Priya St. Joseph’s College of Engineering, India, Chennai, krishnapriyamurugan@gmail.com Abstract In this paper we proposed a syntactic approach to represent any connected region taken from the binary digital image. The proposed method is an enhancement of DCAD algorithm and it provides alphanumeric string to represent the connected region, which preserves the shape and size. In enhanced DCAD we introduced two variables to differentiate the left and right bends to avoid the shape anomaly and we also computed the cylinder width and height relative to Region Of Interest’s (ROI) width and height to preserve the dimension during the reconstruction of ROI. To evaluate our method we have created a database of connected regions in binary format and the regenerated connected region from our resultant alphanumeric string is compared with the actual one and found to be similar. The purpose of this EDCAD is to overcome the anomalies of size and orientation found in the original DCAD. This can be potentially used in applications like pattern recognition, pattern matching and retrieval, machine learning etc. Keywords Region representation, Connected regions, Decomposition and Shape and size. 1. Introductions and Motivation More and more images have been generated in digital form around the world and there is a growing need to find images from large collection of databases. In order to find an image efficiently from the database, the image has to be represented by certain features. The region representation plays an important role in systems for object recognition and classification, shape matching and retrieval, machine learning and in image synthesis for graphics applications. For example in a trademark registry application [1], the new trademark can be ensured to be distinct from the existing marks by searching the database. Dengsheng Zhang et.al [2] has classified the shape representation into two categories: boundary- based (also called as contour-based) methods and region-based methods. The following are some of the contour-based methods: Chain codes [3], Polygonal approximation [4] [5], Scale space method [6], Shape invariants [7] [8] [9] [10], etc. The disadvantage of contour-based method is that they can be applied only to simply connected region and not to multiply connected region. This limitation is can be overcome by using region-based methods. The following are some of the region-based methods: Algebraic moment invariants [11] [12], Orthogonal moments [13], Fourier descriptors [14], Grid based method [15], etc. The region-based method deals with connected regions. But the region-based methods are highly complex and it requires more memory space as image size increases. EDCAD takes the advantages of both contour-based and region-based methods. EDCAD decomposes the connected regions using DCAD and represent each decomposed binary component using syntactic method (a contour-based method). Usually syntactic method uses predefined primitives to describe the orientation of the connected region but we have included dynamic primitive in EDCAD, which describes both the orientation and size of the connected region. The rest of the paper is organized as follows. The Section 2 reviews connected regions, CAD, and DCAD. In Section 3, we described the shape and size anomalies of the existing DCAD. The steps undertaken to overcome the problems of existing DCAD and the algorithms to implement EDCAD are discussed in Section 4. The Section 5 shows the experimental work and the discussion of the result. We conclude the paper in Section 6 by discussing possible extension of the work. 2. Background Definition 1: (Binary image, Binary component [16]) A binary image D is a subset of the digital plane given by : Z 2 : D ={(i, j, g) | 1 ≤ i ≤ N, 1 ≤ j ≤ M, g∈{0,1}} Each element x∈D is called pixel; gx denotes its intensity; the pair (ix, jx) indicates its position. A binary component of D is a subset of D whose pixel-values are 1. Definition 2 : (Connected, Region [17]) A non-empty subset of Rj is called connected, if it is connected in a topological sense with respect to the topology induced on Rj by the Euclidean metric. We call a connected subset a region.