An Image Segmentation Technique based on Edge-preserving smoothing filter and Anisotropic Diffusion Tuan DANG Email: [email protected] http://www.multimania.com/dangt

Abstract: An efficient and simple segmentation algorithm is presented which is based on a good edge-preserving smoothing filter and a fast anisotropic diffusion technique. A number of examples are shown to demonstrate the capabilities of this algorithm. Key Words: Image segmentation, Contrast enhancement, Smoothing filters, anisotropic diffusion.

1. Introduction A fundamental step in most of vision systems is to generate a compact description of an image, which is easier to be interpreted than a set of pixels. In order to achieve this, a wide variety of methods have been proposed for image segmentation. Among these techniques, one could find out mainly two approaches: 1) contours segmentation (edge detection plus contours tracing) and 2) region segmentation (grouping of connected pixels into regions of uniform properties). In this paper we propose a fast and simple region segmentation algorithm based on an edgepreserving smoothing filter, the symmetric nearest neighbor mean [1] and a fast anisotropic diffusion [2] which is followed by a region growing technique and a merging scheme. The details of the algorithm are discussed in Section 2. A number of examples demonstrating the capabilities of this technique are shown in Section 3.

2. Segmentation based on edgepreserving smoothing filter and anisotropic diffusion

2.1 Edge-preserving smoothing filters

Edge-preserving smoothing filters designate a class of edge-preserving noisecleaning filters. Many comparative studies of various edge-preserving noise smoothing techniques [1] [3] indicate that the Symmetric Nearest Neighbor (SNN) filters give the best results in both smoothing and preserving edges. So the SNN filters have often been used as an image enhancement technique. Westman et al [4] have used a SNN filter to preprocess color images before segmenting them. The principle of the SNN filters is described below. The SNN filters make use of both the spatial and gray value information in the neighborhood of a pixel to be processed. In a square window, half the number of pixels is selected by choosing one pixel nearest in gray value to the center pixel from each pair of pixels located symmetrically opposite the center. Only the selected pixels are used to compute a new value for the center pixel. 2.2 Anisotropic diffusion

Anisotropic diffusion is a technique proposed by Perona and Malik [6] to selectively enhance contrast by using a modified heat diffusion equation. The technique is basically a discontinuitypreserving smoothing approach and closely related to the adaptive smoothing proposed

by Chen et al [7]. The idea of adaptive smoothing is that a pixel should become the weighted average of its neighbors. The weights correspond to the continuity measure of these pixels. The continuity is a function of a gradient value at each pixel and a scale factor. Adaptive smoothing is an iterative implementation of anisotropic diffusion [8] in which the undesired edges will disappear along the iteration. To avoid the slowness of such scheme, we use the Toboggan contrast enhancement proposed by Fairfield [2]. One may consider that Toboggan enhancement is another way to implement anisotropic diffusion. Indeed, Toboggan enhancement consists of "sliding downhill" on the discontinuity surface until a minimum in discontinuity is reached, then the gray value of the pixel representing the minimum is spread along the visited pixels. The following figure (figure 1) illustrates this technique in one dimensional signal:

Fairfield's diffusion algorithm [2] less sensitive to the noises, we use the CannyDeriche detector [5] to compute the image gradient. The following figure (figure 2) illustrates our algorithm:

Figure 2

The region growing procedure is a simple, recursive grouping of connected pixels. A pixel p is grouped into a region R if: gray( p) − median( R) < T1 T1 is a threshold. A first merging procedure is used to recursively group two regions R1 and R2 if: Figure 1

median( R1 ) − median( R2 ) < T2

2.3 Applying Edge-preserving smoothing and Anisotropic diffusion to the Segmentation of images

T2 is another threshold. Finally, a second merging procedure is used to eliminate small regions. A region R1 is merged with an adjacent region R2 if:

SNN filters are very good for cleaning noises and preserving edges, however they can't make potential regions uniform. Whereas anisotropic diffusion is suitable for making potential regions uniform, but it is sensitive to the noises because it makes use of the detection of discontinuities in gray values. So in this paper, we propose to use both techniques in a cooperative way to enhance an image before segmenting it by a region growing process. In order to make

Card ( R1 ) < T3 , and R2 = arg{ min median( Rj ) − median( R1 )} R j ∈N ( R1 )

T3 is a threshold, N(R1) designates all the neighboring regions of R1. The merging procedure stops when there is no more region smaller than T3. 3. Examples

Figure 3: House image (256x256)

Figure 4: House image segmented (α=2.0, T1=10, T2=10, T3=100)

Figure 5: Aerial image (400x400)

Figure 6: Aerial image segmented (α=2.0, T1=10, T2=10, T3=150)

Figure 4 shows a segmentation result for the image of the figure 3. α is an adjustable parameter in the Canny-Deriche gradient (Decreasing α will lower the edge localization, but yield better signal to noise and vice versa).

Figure 6 represents a segmentation of the image in the figure 5.

Figure 10: segmentation of figure 9 Figure 7: Aerial image (350x350)

The figure 8 shows a segmentation of the image in the figure 7 (α=2.0, T1=5, T2=10, T3=200). The segmentation of the figure 9 was obtained with α=2.0, T1=5, T2=5 and T3=150. 4. Conclusion

Figure 8: Segmentation of figure 7

We have shown a simple image segmentation algorithm which uses edgepreserving smoothing filter and anisotropic diffusion as a preprocessing step. Both the techniques are fast and simple. The examples demonstrates the capabilities of this algorithm to give comparable results to more sophisticated methods. In fact, in using the Canny-Deriche edge detector, we have implicitly combined the contours segmentation approach with the region one. References

Figure 9: Rings image (256x256)

[1] D. Harwood, M. Subbarao, H. Hakalahti and L.S. Davis, "A new class of edgepreserving smoothing filters", Pattern Recognitions Letters, No. 6, pp. 155-162, August 1987. [2] J. Fairfield, "Toboggan Contrast Enhancement for Contrast Segmentation", 10th ICPR, June 1990, Atlantic City. [3] W.Y. Wu, M.J. Wang and C. Liu, "Performance Evaluation of Some Noise Reduction Methods", CVGIP, Vol. 54, No. 2, pp. 134-146, March 1992. [4] T. Westman, D. Harwood, T. Laitinen and M. Pietikaninen, "Color Segmentation by

[5]

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hierarchical connected components analysis with image enhancement by Symmetric Neighborhood Filters", 10th ICPR, June 1990, Atlantic City. R. Deriche, "Using Canny's criteria to derive a recursively implemented optimal edge detector", International Journal of Computer Vision, May 1987. P. Perona and J. Malik, "Scale space and edge detection using anisotropic diffusion", IEEE Workshop on Computer Vision, pp. 16-22, Miami, 1987. J.S. Chen, P. Saint-Marc and G. Medioni, "Adaptive Smoothing: A General Tool for Early Vision", Proceeding of IEEE Conference on Computer Vision and Pattern Recognition, pp. 618-624, San Diego, 1989. J.S. Chen, "Accurate Edge Detection for Multiple Scale Processing", Ph.D dissertation, Institute for Robotics and Intelligent Systems, University of Southern California, December 1989.