v : erosion h : erosion H : dilation V : dilation s : erosion r : erosion R : dilation S : dilation

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1 AUTOMATIC GENERATION OF DIRECTIONAL EROSION AND DILATION SEQUENCE BY GENETIC ALGORITHMS Ikushi Yoda Image Understanding Section Machine Understanding Division Electrotechnical Laboratory Umezono, Tsukuba, 305 Japan Abstract This paper presents a method to obtain an image processing sequence by showing an original image and a goal image. Even if some object shapes and sizes are changed, this method can obtain a suitable sequence by showing two binary images. There are some works concerns with automatic generation of image processing sequences in the lowest level. In this approach, it uses eight directional erosion and dilation operations. This method uses the genetic algorithms to search sequences. Utilizing a global searching function of the genetic algorithms, it searches a sequence of mathematical morphology. 1 Introduction In this paper, the method focuses on the lowest level of image processing operation in a binary image. It uses directional erosion and dilation as the four fundamental rules of arithmetic in image processing. The purpose is an automatic generation of an image processing sequence by presenting an original image and a goal image. The earliest work in low level image processing was done by Gillies at Michigan University [1]. Its automatic construction of extracting features by sampling a shape was related to the project of the Cytocomputer. It was an image processing computer employing logical neighborhood operations. When this Cytocomputer was presented with an image containing some shapes, it produced a procedure of the Cytocomputer operations that generated a shape. However, this system used only the dilation operations and generated its sequence to make a presented convexity. Therefore, it could not be used to extract the presented shape. In this paper, the author is proposing an automatic generation method by using not only dilation operations but also erosion operations to extract a presented shape. Joo, Haralick and Shapiro also worked on an automatic generation of mathematical morphology procedures [2]. They replaced mathematical morphology operations [3] with predicate logic for automatic generations. The substitution between mathematical morphology and predicate logic was only demonstrated, but the automatic construction was not realized by using a computer. Its realization is dicult. Because how to combine image processing operations depends on a shape and a size of its target, a exible correspondence is needed for its changes at the same time. In this paper, the author uses eight directional basic operations, and propose an automatic generation of an image processing sequence by a simple presented shape. 2 Directional erosion and dilation operations The directional erosion and dilation operations are taken as basic operations for constructing image processing sequences. The directional two-neighbor operations of erosion and dilation are expressed as follows (gure 1). v : erosion V : dilation r : erosion R : dilation h : erosion H : dilation s : erosion S : dilation Figure 1: Directional operations of two-neighbor erosion and dilation.

2 original image automatic generation of procedure vvhhrrss? (each operation is practiced from left side) goal image (made by user s hand) Figure 2: An original image and a goal image. 1. Produce an initial population. Generate rst 100 chromosomes made from eight genes at random. Their lengths are 4 through Loop until the terminated condition. (50th generation) (1) Image processing by each chromosome. (2) The evaluation of tness. The evaluation is done by using similarity (0 S 1 : a normalized correlation coecient) between a goal and a processed image. Here, an original binary image and a goal image are presented in gure 2. The goal image is made manually by deleting unnecessary pixels of original image. The objective here is to construct a sequence automatically that transforms the original image into the goal image by using the directional operations of erosion and dilation. Similarity : S = (f 1 f) 1 1 N 1 N i=1 (f 1 g) 1 1 N 1 N i=1 (f 1 g) p (f 1 f) p (g 1 g) f (i; j) 1 f(i; j) j=1 f (i; j) 1 g(i; j) j=1 (1) 3 Genetic algorithms for searching sequences This method uses the genetic algorithms(ga) [4] to search for an optimal sequence that satises this objective. GA is an algorithm that is based on biological evolution. It is a parallel searching method for probabilistic searching, learning and optimization. For using this algorithm, the method assumes that the eight directional operations are genes in GA, and that their image processing sequence is a chromosome. 1 2 (1) start produce initial chromosomes image processing unit (3) The selection. Select their 35 pairs by using roulette rule based on their tness and keep best 30 chromosomes. (4) The crossover. Two-point crossover in random place. (5) The mutation. One gene is changed in one chromosome at random. Iterating this loop practices over 50 generations. The loop indicates this process in gure 3. This is the fundamental method for generating a sequence to extract a similar image to the goal image from the original image. Each parameter of GA is obtained through rst experiment in the section 4. 4 Generations of image processing sequences for basic examples First, the method makes experiments with four simple rectangles. Second, it treats some simple shapes of a sheet of music. (2) evaluation of similarity 4.1 Experiments in four rectangles (3) (4) 50th generation? N selection two-point crossover Y end The gure 4(a) is an original image and includes four congruent rectangles. It is a binary image and its size is pixels. The gure 4(b), (c), (d) and (e) are goal images to the gure 4(a). By showing each set of two images, a result of the table 1 is obtained. It indicates the sequences, their (5) mutation Figure 3: The frame of searching by the genetic algorithms. The method uses a process of GA, and searches a sequence as follows (gure 3). 1 RrvhvvvhHVVVvVS hvhhhhhhvh shrrrrrrsrsrrsvs HVssssrHrsrvSSSss SRSRrVvSSSR Table 1: The obtained sequences of each goal. length, tness and their obtained number of generation.

3 4.2 Experiments on a sheet of music The method deals with a music score. The gure 5(a) is an original image and a part of a sheet of music. It is a binary image and its size is pixels. The gure 5(b), (c), (d) and (e) are goal images to the gure 5(a). These goal images are made by a user's hand. It is hoped that the system automatically obtains a sequence that extracts each shape. Each sequence is practiced from left side. The gure 4(f), (g), (h) and (i) are result images by them. The 1st goal and the 3rd goal image obtain their optimal sequences. The 2nd goal and the 4th goal do not obtain their optimal sequences. There is no guarantee that this method obtains an optimal sequence, but it obtained an approximate sequence within only 50 generations. heads rvrsrvrvsrrvss hook rvhhvvsvrrsvrrvs sta hvhhhhhhhhhhhhhlines hhhhhhhhhhhhh HHHHHHhHHHv stems Hrvvvv Table 2: The obtained sequences of the parts of triplet. Table 2 indicates each obtained sequence, its length, tness and its obtained number of generation. The gure 5(f), (g), (h) and (i) are result images by them. In this case, a rate of mutations is 2% (two genes are changed in two chromosomes), and the length of rst chromosomes is 4 through 30. The gure 6(a) is the whole music score ( pixels). The gure 5(a) is a part of this gure. These sequences practice this original gure, and the gure 6(b)-(e) are obtained as results. However there are some remnants of other shapes, all heads, hooks, sta lines and stems are extracted in each result. (a)original image (b)goal image (c)result image Figure 7: The other heads of dierent resolution. heads rshrv Table 3: The obtained sequences of the other heads. The gure 7(a) is a part of another sheet of music. Because the resolution of this gure is low, the sizes of four heads are smaller than the three heads of the gure 5(a). By showing it and a goal image (gure 7(b)), a suitable sequence is generated automatically in this case too. Figure 7(c) is a result image by it. The table 3 shows a sequence, its length, tness and its obtained number of generation. In all experiments, the searching process nished within 2 minutes on IRIS INDIGO 2. (The size of images are pixels. The number of generation is 50.) 5 Conclusion This paper proposes an automatic generation of a combination that consists of image processing operations. Their eight operations are directional erosion and dilation. If some wide, length and size of an object are changed, users can obtain a suitable sequence only by showing an original image and a goal image. This function contributes to an automation of extracting some details. There is no guarantee to obtain an optimal solution by using the genetic algorithms, but the author uses GA as a method of optimization for the automatic acquisition of image processing. Because GA is a global searching method, it obtains an approximate sequence in this case. In this paper, the method is only applied to extract the rectangle and some basic shapes from the music scores. Some results are good, and the other are not satised. The author will try to extend to a repertory of fundamental operations and advance an additional learning problem by using some results. References [1] Andrew M. Gillies, \ An Image Processing Computer which Learns by Example," SPIE, Vol.155, Image Understanding Systems & Industrial Applications, [2] Hyonam Joo, Robert M. Haralick, and Linda G. Shapiro, \Toward the Automatic Generation of Mathematical Morphology Procedures Using Predicate Logic", Proceeding of the Third International Conference on Computer Vision, pp , Osaka, Japan, [3] R. M. Haralick, S. R. Sternberg, and X. Zhuang, \Image analysis using mathematical morphology", IEEE Trans. patt. Anal. Machine Intell., Vol.PAMI- 9, no.4, pp , [4] Holland, J., Adaptation in Natural and Articial Systems, The University of Michigan Press, 1975., and MIT Press, Considering these results, there is a possibility of obtaining a better sequence by selecting suitable scene.

4 (a)original image (b)1st goal (c)2nd goal (d)3rd goal (e)4th goal (f)1st result (g)2nd result (h)3rd result (i)4th result Figure 4: The original image, four goal images and their results. (a)original image (b)heads (c)hook (d)sta lines (e)stems (f)result of heads (g)result of hook (h)result of lines (i)result of stems Figure 5: The original image of a triplet, four goal images and their results.

5 (a)whole musuic score (b)extracted heads (c)extracted hooks (d)extracted sta lines (e)extracted stems Figure 6: The whole music score and the results by each obtained sequence.