A Study on Segmentation of Artificial Grayscale Image for Vector Conversion

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1 A31 TV A Study on Segmentation of Artificial Grayscale Image for Vector Conversion Kei KAWAMURA, Daisuke ISHII, and Hiroshi WATANABE Graduate School of Global Information and Telecommunication Studies, Waseda University, A31, 111 Nishi-Tomida, Honjo-shi, Saitama , Japan. kawamura@suou.waseda.jp Abstract Object oriented coding segment an image into regions, which characteristics are coherent. Vector representation is suitable to describe contours of regions in object oriented coding. On the other hand, we have proposed border extraction using sub pixel binarization for the low resolution grayscale image. This image which is originally binary image is obtained as grayscale image by a scanner. In this paper, a target is an image which originally consists of homogeneous regions is obtained as grayscale image containing anti aliasing. This image is named the artificial image. The research object is the image coding based on vector representation. We propose the segmentation method considering characteristics of the artificial image. An inverse norm is introduced to achieve the segmentation. Then the segmentation problem is converted to the minimization problem of an object function with the inverse norm. An algorithm to solve the minimization problem is designed. Total variation image decomposition is recently remarkable technique as preprocess of segmentation. The validity of the proposed method is confirmed by comparative experiments, which are proposed method and total variation. Key words coding. Image segmentation, homogeneous region, anti aliasing, vector representation, image - 1 -

2 1. MRC JPEG DCT Discrete Cosine Transform JPEG DWT Discrete Wavelet Transform H DCT SIC SIC MRC SIC [1] []. SIC Segmented Image Coding MRC Mixed Raster Content [] MPEG 4 Part 3 MRC Mixed Raster Content Compound Image [3] JPEG Part 6 [7] TV. 1 MRC [4 7] Ricardo [3] {x n(i, j)} {m n(i, j)} CG 64 [] J n = R n + λd n (1) JPEG λ - -

3 SSE Sum of Squared Error SSE m n (i, j) = u(t n x n (i, j) 1) () SSE SSE t n u(k) k < = Edgmentation [11] 64 Edgmentation [9] 4 MRC Steepest Path Growing Algorithm [7]. SIC SIC Segmented Image Coding RSST Recursive Shortest Spanning Tree [1] Edgmentation [11] Edgmentation [] SIC Christlpoulos 5%. 4 Edgmentation [] Edgmentation [] CF (i, j) CF (i, j) j i SIC G(i, j) S(j) CF (i, j) = D(i, j) (3) L(i, j) L(i, j) G(i, j) i j.. 1 RSST [1] L(i, j) i j RSST S(j) j D(i, j) 4 i j RSST SSE - 3 -

4 Edgmentation. 5 Total Variation Chambolle Total Variation Minimization [1] 3. N N X R N N I(u) = X ( u) i,j 1 (9) u X u ( u) i,j = `( u) 1 i,j, ( u) i,j < u ( u) 1 i+1,j u i,j (i < N), i,j = (i = N), < u ( u) i,j+1 u i,j (i < N), i,j = (i = N) i, j = 1,..., N (4) (5) (6) u Total Variation J(u) = X ( u) i,j (7) 1< = i,j< = N 1< = i,j< = N < 1/ p y y 1 1 = + y = y 1, y, Other y = p y1 + y u g min + J(u) () u X λ < g + (g g s) k g g s > th, ROF g X < λ usm(g) = (1) g Other X Total Variation u u g «min min u usm(g)), + I(u)(13) u X λ λ g s X g k th u SIC (1) u g min + I(u) (11) u X λ g X < λ λ - 4 -

5 SIC 4. QVGA λ = 64 λ = th = λ/16 k = 4/λ 1 1 [1] F. Marques, A. Gasull, T.R. Reed, M. Kunt, Coding-Oriented Segmentation based on Gibbs- Markov Random Fields and Human Visual System Knowledge, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICCASP- 91) Apr [] C.A. Christopoulos, W. Philips, A.N. Skodras, and J. Cornelis, Segmented image coding Techniques and experimental results, Signal Processing Image Communication 11, pp.63, [3] R.L. de Queiroz, Compressing Compound Documents, in The Document and Image Compression Handbook, edited by M. Barni, Marcel-Dekker, 5. Total Variation ROF [4] K. Kawamura, H. Watanabe, and H. Tominaga, Vector representation of binary images containing ROF halftone dots, 4 IEEE ICME Proceedings., Jun [5] ROF FIT6 J 3 Sep. 6 [6] 6 AVM 54 no.6 Sep. 6 [7] 7 6 Lenna 1 AVM 56 no.11 Mar. 6 ROF [] 4 4 [9] R. de Queiroz, Z. Fan, and T. Tran, Optimizing - 5 -

6 Cost I(u) D(u) Cost I(u) D(u) Iterations [times] Iterations [times] 1 1 Fig. 1 Transition of object function and norm (Image 1). Fig. Transition of object function and norm Fig. 3 A relation of row 16 in Image 1. 4 Fig. 4 A relation of row 4 in Image Lenna 1 Fig. 5 A part of the relation of row 16 in Image 1. Fig. 6 A relation of row 1 in Lenna. block-thresholding segmentation for multi-layer compression of compound images, IEEE Trans. on Image Processing, Vol. 9, pp , Oct.. [1] M.J. Biggar, O.J. Morris, A.G. Constantinides, Segmented image coding performance comparison with the discrete cosine transform, Radar and Signal Processing, IEE Proceeding F, Vol. 135, Issue, pp.11 13, Apr. 19. [11] J. Cornelis, J.D. Becker, M. Bister, C. Vanhove, G. Demonceau, and A. Cornelis, Techniques for Cardiac Image Segmentation, IEEE International Conference of Engineering in Medicine and Biology Society, 199. [1] A. Chambolle, An Algorithm for Total Variation Minimization and Applications. Journal of Mathematical Imaging and Vision 9-97, E