A Novel Approach for Coin Identification using Eigenvalues of Covariance Matrix, Hough Transform and Raster Scan Algorithms

Authors: J. Prakash, K. Rajesh

Abstract:

In this paper we present a new method for coin identification. The proposed method adopts a hybrid scheme using Eigenvalues of covariance matrix, Circular Hough Transform (CHT) and Bresenham-s circle algorithm. The statistical and geometrical properties of the small and large Eigenvalues of the covariance matrix of a set of edge pixels over a connected region of support are explored for the purpose of circular object detection. Sparse matrix technique is used to perform CHT. Since sparse matrices squeeze zero elements and contain only a small number of non-zero elements, they provide an advantage of matrix storage space and computational time. Neighborhood suppression scheme is used to find the valid Hough peaks. The accurate position of the circumference pixels is identified using Raster scan algorithm which uses geometrical symmetry property. After finding circular objects, the proposed method uses the texture on the surface of the coins called texton, which are unique properties of coins, refers to the fundamental micro structure in generic natural images. This method has been tested on several real world images including coin and non-coin images. The performance is also evaluated based on the noise withstanding capability.

Keywords: Circular Hough Transform, Coin detection, Covariance matrix, Eigenvalues, Raster scan Algorithm, Texton.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1059459

References:

[1] P.V.C Hough, "Methods and means for recognizing complex pattern," U.S. Patent No.3069654.
[2] J. Illingworth and J. Kittler, "A survey of the Hough transforms," Computer vision, Graphics and Image processing 44, pp. 87-116, 1988.
[3] R.O. Duda and P.E. Hart, "Use of the Hough transform to detect lines and curves in pictures," CACM 15, No. 1, pp. 11-15, 1972.
[4] S. Tsuji, F. Matsumoto, "Detection of circles/ellipses by a modified Hough transforms," IEEE Trans. Computers., 27(8), pp. 777-781, 1978.
[5] D. H. Ballard, "Generalizing the Hough transforms to detect arbitrary shapes," Pattern Recogn., 13(2), pp. 111-122, 1981.
[6] D.H Ballard, C. Kimme and J. Sklansky, "Finding circles by an array of accumulators," Commun, ACM, 18(2), pp. 120-122, 1975.
[7] J. Illingworth and J. Kittler, "The adaptive Hough Transform," IEEE Trans, PAMI-9(5), pp 690-697, 1987.
[8] E. R. Davis, "A modified Hough scheme for general circle location,," Pattern Recogn,7(1), pp. 37-44, 1988.
[9] Michele Ceccarelli, "Alfredo Petrosino and Giuliano, Circle detection based on orientation matching," IEEE trans. PAMI Vol 20, pp. 119-124, 2001.
[10] J. Illingworth, J. Kittler and H.K Yuen, "Comparative study of Hough Transform methods for circle detection," Image vision, Comput. 8(1), pp 71-77, 1990.
[11] G. Gerig and F. Klein, "Fast contour identification through efficient Hough Transform and simplest interpretation strategy," Proceedings of 8th international conference on pattern recognition, 1986, pp. 498-500.
[12] Chun-Ta Ho and Ling-Hwei Che, "A fast ellipse/circle detector using geometric symmetry," Pattern Recognition Vol. 28, No. 1, 1995, 117- 124
[13] Peng-Yeng Yin, "A new circle/ellipse detector using genetic algorithms," Pattern Recognition Letters 20, pp. 731-740, 1999.
[14] Du-Ming Tsai, H. T. Hou, H.J. Su, "Boundary based corner detection using Eigen values of covariance matrices", Pattern. Recogn. 20, pp. 31- 40, 1998.
[15] D. S. Guru B, H. Shekar, P. Nagabhushan, "A simple and robust line detection algorithm based on small Eigen value analysis", Pattern Recogn. 25, pp. 1-13, 2003.
[16] J. Prakash and K. Rajesh, "A Novel and Accurate method for Circular object identification - combined approach of Hough transform, Eigenvalues and Raster scan algorithms," IEEE International conference on Signal and Image processing,Vol.2, 2006, pp. 815-820.
[17] J. Prakash, K. Rajesh, "Extracting geometric primitives: Combined approach of Hough transform, Eigenvalues and Raster scan algorithms," International Journal of systemics, Cybernetics and Informatics (IJSCI), pp. 48-55, 2007.
[18] Rafael C. Gonzalez, Richard E. Woods, "Digital Image processing " (5th edition), Addison Wesley, 2000
[19] Donald Hearn, M. Pauline Baker, "Computer graphics" (2nd edition), Pearson Education,2003
[20] S.C. Zhu, C. Guo, Y. Wu and Y.Wang, "What are Textons?", ECCV, pp. 793-807, Springer Verlag, 2002
[21] T. Leung and J.Malik, "Representing and recognizing the visual appearance of materials using three dimensional textons," IJCV, 1999.
[22] R.M Haralick and L.G. Shapiro, "Survey-Image segmentation techniques," Computer Vision Graphics and Image processing, vol.29, pp. 100-132, 1985.
[23] M.K. Ng, "A note on K-means algorithm," Pattern Recognition, vol.33, pp. 515-519, 2000.