Use of medial axis transforms for computing normals at boundary points J. Mukherjee a, * , M. Aswatha Kumar b,1 , P.P. Das a,2 , B.N. Chatterji c a Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur 721 302, India b Department of Electronics and Communication Engineering, BDT College of Engineering, Dawangere 577 002 Karnataka, India c Department of Electronics and ECE, I.I.T, Kharagpur 721 302, India Received 9 April 2001; received in revised form 6 December 2001 Abstract Medial axis transform (MAT) is well known for object representation. It is interesting to explore its use in different kinds of computations. In this paper an algorithm has been proposed for computation of normals at the boundaries of two-dimensional objects based on their MATs. In this technique, there is no requirement of linking boundary points during the computation compared to other existing techniques. The added advantage in the computation is that the computation can be restricted purely in the integer domain. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Medial axis transform; Octagonal distance; Medial disks; Normals of digital curves 1. Introduction Medial axis transform (MAT) for two-dimen- sional (2D) and three-dimensional (3D) binary images have been introduced by Rosenfeld and Pfaltz (1968). It may be noted however that before this work, H. Blum first introduced medial axis function (MAF) in one of his work (Blum, 1967). The maximal blocks of MAT are also termed as ‘disks’ in 2D and ‘balls’ in 3D. It has been shown that using generalized octagonal distances (Das and Chatterji, 1990) in MATs, good approxima- tions to Euclidean circles (for the medial disks) can be obtained for binary images. The representation is found to be useful for the computation of linear geometric transformations like translation, rota- tion and scaling (Aswatha Kumar et al., 1996) and computation of cross-sections for 3D objects (Mukherjee et al., 2000). Interestingly, such com- putations are difficult to perform using hierarchi- cal schemes like quad-tree or octree which are other popular alternatives for representing binary data. MATs have also been used in discrete Pattern Recognition Letters 23 (2002) 1649–1656 www.elsevier.com/locate/patrec * Corresponding author. Tel.: +91-3222-83484; fax: +91- 3222-55303. E-mail address: jay@cse.iitkgp.ernet.in (J. Mukherjee). 1 Present address: Department of Computer Science and Engineering, J.N.N. College of Engineering, Shimoga 577204, India. 2 Present address: EDA Soft (India) Pvt. Ltd., Kolkata 700091, India. 0167-8655/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S0167-8655(02)00128-9