Improved Watershed Algorithm for Cell Image Segmentation Yu Zhang1,a, Duanquan Xu1,b 1
Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan, China a
[email protected],
[email protected]
Keywords: Watershed, Gradient Transformation, Segmentation.
Transformation,
Open-Close
Reconstruction,
Distance
Abstract.Watershed is an image segmentation algorithm based on mathematical morphology, which can determine the boundary of connected section efficiently and effectively. But the traditional watershed algorithm is sensitive to noise. To overcome the weakness of classical watershed, this paper presents an improved watershed algorithm based on gradient transform, openclose reconstruction and distance transform. The experiment result shows that application of this improved watershed algorithm in cell image segmentation has a good performance. Introduction Watershed is an image segmentation algorithm based on mathematical morphology [1]. But the classical watershed algorithm is sensitive to noise, which can cause serious over-segmentation [2]. Basing on gradient transform, open-close reconstruction and distance transform, this paper proposes an improved watershed algorithm, which inherits the advantage of classical watershed algorithm and improves the noise immunity of classical watershed algorithm. This algorithm not only overcome the over-segmentation, but also has an apparently better performance than the approach of employing watershed simply based on open-close operation and distance transformation [3]. Image segmentation is one of the fundamental and important tasks in medical image analysis since only on the basis of a successful segmentation can meaningful cell feature be extracted. The cell has a round shape which is fit for distance transformation and watershed transformation. And considering the high speed and accuracy of Watershed Algorithm in solving connected region segmentation, we apply our improved watershed algorithm in cell image segmentation to solve the adhesion cell segmentation [4]. Fundamentals A. Morphological Reconstruction Morphological reconstruction can be thought of conceptually as repeated dilations of an image, called the marker image, until the contour of the marker image fits under a second image, called the mask image. In morphological reconstruction, the peaks in the marker image "spread out," or dilate [5].
Figure 1 Processing of Reconstruction in 1-Dimension
Fig 1 illustrates this processing in 1-Dimension. Each successive dilation is constrained to lie underneath the mask. When further dilation ceases to change the image, the processing stops. The final dilation is the reconstructed image. The figure shows the successive dilations of the marker. B. Gradient Transform To simplify the discussion follows, we use the notation in fig 2 to denote image points in a 3x3 region. For example,
Figure 2 Example for 3x3 region
the center point z5 denotes f(x,y), and z1 denotes f(x-1,y-1). Denote the cross differences [6]: Then we compute the gradient as
C. OTSU Method Otsu method is firstly proposed by Nobuyuki Otsu [7] in 1979, which is an adaptive method of determining the threshold. Divide the image into background and objective by its gray scale feature. The greater the between-class variance between background and objective, the greater difference between the two parts of the image will have. When some of the objectives are classified wrong into background or some of the background is classified wrong into objectives, the difference between these two parts will decrease. Thus, the Otsu method can make the probability of wrong division the least.
D. Distance Transform Assume the input image is BW, and the output image is D. Gradient Transform computes the Euclidean distance transform of the binary image BW. For each pixel in BW, the distance transform assigns a number that is the distance between that pixel and the nearest nonzero pixel of BW. BW can have any dimension. D is the same size as BW [8]. E. Median Filter Median filter replaces the value of a pixel by the median of the gray levels in the neighborhood of that pixel (the original value of the pixel is included in the computation of the median). Median filters are particularly effective in the presence of impulse noise, also called salt-and- pepper noise because of its appearance as white and black dots superimposed on an image [9]. Assume the input matrix is A, and the dimension of its neighborhood is m-by-n. In this paper, we performs median filtering of the matrix A in two dimensions. Each output pixel contains the median value in the m-by-n neighborhood around the corresponding pixel in the input image. This paper pads the image with 0s on the edges, so the median values for the points within [m n]/2 of the edges might appear distorted. F. Watershed Algorithm [10] Suppose that a hole is punched in each regional minimum and that the entire topography is flooded from below by letting water rise through the holes at a uniform rate. When the rising water in distinct catchment basins is about to merge, a dam is built to prevent the merging. The flooding will eventually reach a stage when only the tops of the dams are visible above the water line. These dam boundaries correspond to the divide lines of the watersheds. Therefore, they are the continuous boundaries extracted by a watershed segmentation algorithm. Cell Image Segmentation Method We use the improved watershed algorithm to segment cell image, and this algorithm follows these steps: Step 1: Apply open-reconstruction and close-reconstruction to the gray scale cell image Through applying the open-reconstruction and close-reconstruction filtering to gray scale cell image, we eliminate the burrs in the cell, isolate the small adhesions between cells, fill the small holes in cells and smooth the cell boundaries, meanwhile, do not change the size and shape of the cell images. This pretreatment makes it easier to segment the cell image. Step 2: Calculate the gradient image of the filtered image Apply the gradient transform to the image got in step 1. In the gradient image, the gradients of the boundaries between cells and background in original cell image are much larger than that of region in cells. Step 3: Use the OTSU algorithm to get the binary image of the gradient image Transform the gradient image got in step 2 to binary image using OTSU algorithm. OTSU algorithm is an adaptive algorithm which can find the best binary threshold. The threshold determined by OTSU is objective and reasonable, which can lead to a good binarization performance. After binarization, the boundaries between cells and background can be detected. Step 4: Fill the cell areas After detecting the cell boundaries, we fill the cell areas to accomplish the extraction of the cells in image [11]. Then we segment the adhesion cells. Step 5: Apply open operation to the filled cell image Open operation can eliminate the region smaller than structure element and cut off slender connection. In order to prevent from segmenting non-existent cells, use the open operation to eliminate the small false cell areas.
Step 6: Apply the distance transform to filled cell image Apply distance transform to the image got in step 5 to get a gray scale image. Get the complement image as a new distance image and use median filter method to eliminate the noise in image. In the new distance image, the values of pixel increase from the inner cell to outer cell. The value of innermost pixel in cell is the smallest, and the value of outermost pixel in cell is the largest. And the value of the background pixel is 255. Step 7: Apply Watershed Transform to gray scale distance image Find the local minimum point in each cell in the distance image, which is the center of each cell. We use the minimum points to mark each cell area and use the pixel of value 255 to mark the background. Then apply the watershed algorithm to the distance image to segment the adhesion cells and mark the cell regions with different colors. Step 8: Add the segmentation result to the original image Add the segmentation result to the original image to show the final result. Experiment and Results We use the staining liquid based cell microscopic image as sample image to test the performance of the presented algorithm. And the results of each step are shown in Figure 3. Fig 3(a) is the original cell image. The algorithm is illustrated from fig 3(b) to fig 3(i), where fig(b) is the image after open-reconstruction filtering, fig(c) is the image after close-reconstruction filtering, fig(d) is the distance transformed image of (d), fig(e) is the binary image of (d), fig(f) is the filled image of (e), fig(g) is the image after open operation filtering, fig(h) is the distance transformed image of (g) and fig(i) is the watershed transformed image of (h). Fig 3(j) is the final segmentation result. From fig 3(j), we can find that the result is satisfactory and precisely divide the cell and background in this image with no over-segmentation.
Figure 3 Improved watershed segmentation for cell image
Conclusions This paper presents an improved watershed algorithm based on open-close reconstruction, gradient transformation, median filter and distance transformation. This improved watershed algorithm overcomes the weakness of classical watershed while inherits the advantage of classical
watershed. Through the experiment, we can conclude that this algorithm has a good performance in cell image segmentation. The experiment result is satisfactory and successfully segments the adhesion cells, providing convenience for the further medical processing. Acknowledgment This work is supported by Hubei Provincial Natural Science Foundation of China under Grant No. 2009CDB296 and National University Innovative Foundation of China under Grant No. 091048709. References [1] Luc Vincent and Pierre soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, Vol.13, No.6, pp.583-598. [2] Huang Qi-kun and Zhou Yun-cai, “A method based on watershed algorithm for core particles image segmentation,” Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on, 2010, vol.3, pp.408-410. [3] Yuqian Zhao, Jianxin Liu, Huifen Li and Guiyuan Li, “Improved watershed algorithm for dowels image segmentation,” Proceedings of the 7th world congress on intelligent control and automation, June 25-27, 2008, Chongqing, China, pp.7644-7648 [4] Yu Zhang and Duanquan Xu, “Improvement on Watershed algorithm of OpenCV and its application in cell image segmentation,” unpublished. [5] Vincent, L., "Morphological Grayscale Reconstruction in Image Analysis: Applications and Efficient Algorithms," IEEE Transactions on Image Processing, Vol. 2, No. 2, April, 1993, pp. 176-201. [6] Rafael C. Gonzalez and Richard E. Woods, Digital Image Processing, 2nd ed, Prentice Hall, 2002, pp.134-137. [7] Otsu, N., "A Threshold Selection Method from Gray-Level Histograms," IEEE Transactions on Systems, Man, and Cybernetics, Vol. 9, No. 1, 1979, pp. 62-66. [8] Maurer, Calvin, Rensheng Qi, and Vijay Raghavan, "A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 25, No. 2, February 2003, pp. 265-270. [9] Rafael C. Gonzalez and Richard E. Woods, Digital Image Processing, 2nd ed, Prentice Hall, 2002, pp.123-124. [10] Meyer, Fernand, "Topographic distance and watershed lines," Signal Processing , Vol. 38, July 1994, pp. 113-125. [11] Soille, P., Morphological Image Analysis: Principles and Applications, Springer-Verlag, 1999, pp. 173-174.
