A Practical Approach of Selecting the Edge Detector Parameters to Achieve a Good Edge Map of the Gray Image

Transcription

1 Journal of Computer Science 5 (5): , 2009 ISSN Science Publications A Practical Approac of Selecting te Edge Detector Parameters to Acieve a Good Edge Map of te Gray Image 1 Akram A. Moustafa and 2 Ziad A. Alqadi 1 Department of Computer Science, Al Al-Bayt University, P.O. Box , Mafraq, Jordan Faculty of Engineering, Al-Balqa Applied University, Amman, Jordan Abstract: Problem statement: practical approac of detecting edge map was proposed. Approac: Te metodology of tis approac was presented and tested in order to select te best value of te operator, used to smoot and get te gradient, and te tresold value used to convert te gray gradient to binary edge map, so a practical value of te tresold and edge operator coefficient was investigated, tese values used to calculate te gradient in order to get a better edge-map. Results: Wile increasing te value of C (constant C te first parameter in our practical approac of detecting te edge), we narrow te range of t and at te same time te value of te suitable t will be increased toward 1. Conclusion: Tis approac can be used to get te best edge map and to get a clear edge map, wic can be used later in image segmentation and object extraction. Keywords: Gradient, detecting, edge detection metodology, original image, edge direction, pixels INTRODUCTION As we a gray image is a set of pixels wic are arranged in a 2D matrix, te intersection of a certain row and column defines te x and y coordinates of a certain pixel and te corresponding value of te pixel reflects te intensity value of te point wic ranges from te minimum gray level (0) to te maximum gray level (for example 255) [1]. Edge detection is point processing metod used to segment te image and to separate te image into different discontinuous objects wic can be used for farter image processing operation [2]. Edge detection tecniques are based [3-7] on te Properties of te gradient wic includes: Te magnitude of gradient provides information about te strengt of te edge. Te direction of gradient is always perpendicular to te direction of te edge as sown in Fig. 1 So te main idea of getting te gradient at eac point is to: Compute derivatives in x and y directions Find gradient magnitude Tresold gradient magnitude ( + ) ( ) f f x, y f x, y lim x 0 ( + ) ( ) f f x, y f x, y lim y 0 Setting to 1 we can obtain: ( + ) ( ) f f x x,y f x,y x y ( ) ( ) ( ) f x + 1, y f x, y, 1 ( + y ) ( ) f f x, y f x, y y y ( ) ( ) ( y ) f x, y + 1 f x, y, 1 x (1) (2) (3) (4) Tus we can estimate te gradient wit finite differences: Fig. 1: Point gradient Corresponding Autor: Akram A. Moustafa, Department of Computer Science, Al Al-Bayt University, P.O. Box , Mafraq, Jordan

2 Fig. 2: Pixel coordinates Using pixel-coordinate notation (j corresponds to te x direction and i to te negative y direction) as sown in Fig. 2. Let us now Consider te arrangement of pixels about te pixel (i, j) as follows: a0 a1 a 2 a 7 a[ i, j] a 3 a6 a5 a 4 Te partial derivatives can be computed by: ( ) ( ) M a + ca + a a + ca + a (5) x ( ) ( ) M a + ca + a a + ca + a (6) y We call te constant C te first parameter in our practical approac of detecting te edge. By setting C to 1 we can obtain te Prewitt operator [3-7] : MX MY And by setting C to 2 we can get te Sobel operator [3-7] : MX MY MATERIALS AND METHODS We proposed te following steps in order to get te edge map of te original gray image: J. Computer Sci., 5 (5): , Get te original gray image Select X and Y gradient operators by setting C to a defined number Smoot te gray image and get te smooted X and Y gradients by performing te following 2 steps: Correlate te original image wit X operator to get te X gradient Correlate te original image wit Y operator to get te Y gradient Compute te total gradient Convert te total gray gradient to binary in order to get te edge map by tresold te gray gradient using a tresold value t( t is a second operator in our practical approac of detecting te edge map) Let us illustrates tese steps by example using mat lab Get te original image: a Imread ('rice.png') In Fig. 3, imsow(a); title 'Original image' Select te gradient operators(let C 1): x [; ; ] x >> y x' y Get a smooted X gradient by correlating te original image wit X operator: Gx filter2(x, a) Get a smooted Y gradient by correlating te original image wit Y operator: Gy filter2(y, a) Compute te total gray gradient: G sqrt(gx.*gx+gy.*gy) Select te tresold value and convert te gray gradient to binary in order to get te edge map: t 0.3 e_map im2bw(g/255,t) In Fig. 4, imsow(e_map), title 'Edge Map'.

3 Fig. 3: Original image Fig. 6: Values of t 0.1 Fig. 4: Edge Map: Fig. 7: Values of t 0.2 Fig. 5: Original gray image Fig. 8: Values of t 0.3 RESULTS Now we will try to use various values of te operator C and for eac value of C we will select different values of t, ten we apply te metodology of detecting te edge map. Te obtained results will be analyzed in order to get te exact rang of t values wic can be used as a best results to get te best clear edge map. Here are some practical results (Fig. 5-45). Fig. 9: Values of t 0.4 C 1(Prewitt detector) gx >> gy gx' gy 357 Fig. 10 Values of t 0.5

4 Fig. 11: Values of t 0.6 Fig. 15: Values of t 1 Fig. 12: Values of t 0.7 Fig. 16: Edge wit t 0.1 Fig. 13: Values of t 0.8 Fig. 17: Edge wit of t 0.2 Fig. 18: Edge wit t 0.3 Good for 0.4 < t < 0.9 C 2 (Sobel detector) gx gy Fig. 14: Values of t 0.9 Good for 0.4 < t < 0.8 C 3 gxz >> gyz gxz' gyz

5 Fig. 19: Edge wit of t 0.4 Fig. 23: Edge wit of t 0.8 Fig. 20: Edge wit t 0.5 Fig. 24: Edge wit t 0.9 Fig. 21: Edge wit of t 0.6 Fig. 25: Edge wit of t 1 Good for 0.6< t < 0.9 C 4 gx Fig. 22: Edge wit t 0.7 >> gy gx' gy Fig. 26: Values of t 0.1 Fig. 27: Values of t 0.2

6 Fig. 28: Values of t 0.3 Fig. 32: Values of t 0.7 Fig. 29: Values of t 0.4 Fig. 33: Values of t 0.8 Fig. 30: Values of t 0.5 Fig. 34: Values of t 0.9 Good for 0.8 < t < 1 C 5 gx Fig. 31: Values of t 0.6 >> gy gx' gy Good for 0.9 < t < Fig. 35: Values of t 1

7 Fig. 36: Values of t 0.1 Fig. 41: Values of t 0.6 Fig. 37 Values of t 0.2 Fig. 42: Values of t 0.7 Fig. 38: Values of t 0.3 Fig. 43: values of t 0.8 Fig. 39: Values of t 0.4 Fig. 44: Values of t 0.9 Fig. 40: Values of t Fig. 45: Values of t 1

8 DISCUSSION As we see from te results wile increasing te value of C we narrow te range of t and at te same time te value of te suitable t will be increased toward 1. CONCLUSION In order to get a clear edge map we ave to select te C parameter wic is to be used as a constant to define te X and Y operators to get te X and Y gradients. Increasing of C value leads to narrow te range of t, tus we ave to select a ig value of t wic is closed to 1. REFERENCES 1. Canny, J., A computational approac to edge detection. IEEE Trans. Patt. Anal. Mac. Intell., 8: ttp://portal.acm.org/citation.cfm?id Derice, R., Using Canny's criteria to derive an optimal edge detector recursively implemented. Int. J. Comput. Vis., 1: DOI: /BF Lindeberg, T., Edge detection and ridge detection wit automatic scale selection Int. J. Comput. Vis., 30: ttp://portal.acm.org/citation.cfm?id Lindeberg, T., Scale-Space Teory in Computer Vision. Kluwer Academic Publisers, USA., ISBN: , pp: Pategama, M. and Ö. Göl, Edge-end pixel extraction for edge-based image segmentation. Proceedings of te World Academy of Science, Engineering and Tecnology, Jan. 2005, pp: ttp:// 6. Zang, W. and F. Bergolm, Multi-scale blur estimation and edge type classification for scene analysis. Int. J. Comput. Vis., 24: ttp://portal.acm.org/citation.cfm?id Ziou, D. and S. Tabbone, Edge detection tecniques an overview. Int. J. Patt. Recog. Image Anal., 8: ttp://en.scientificcommons.org/