Unsupervised two-color ELISPOT image segmentation based on k-means clustering

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1 Unsupervised two-color ELISPOT image segmentation based on k-means clustering Wojciech Bieniecki, Michał Krupiński, Szymon Grabowski, Katarzyna Kościelska-Kasprzak, Dominika Drulis-Fajdasz, Oktawia Mazanowska, Marian Klinger Abstract An algorithm for color microscope image segmentation is presented. The aim of the segmentation is to extract two types of color spots in a viewing area. The algorithm, based on k-means clustering, with a known number of spot types, automatically selects the color ranges for each type of spot and carries out the pixel classification. Keywords Color image segmentation, clustering I. INTRODUCTION Segmentation is a fundamental image processing task aiming to partition the image area into disjoint regions corresponding to real-world objects. In many cases, it is enough to assign pixels to one of a few predefined classes (e.g., the thresholding problem). An example of such an approach is clustering. Clustering [1] is a technique which requires defining a feature space and mapping the image pixels to vectors in this space. With use of statistical methods the feature space is split into connected regions (clusters) which implies grouping the pixels of similar color to some classes. One of the most common used clustering algorithms is k- means [2]. The most important parameter for this algorithm is k, the number of clusters in a feature space (here: color space) to be found. A fixed value of k may be a drawback of the algorithm if the predicted number of classes is unknown. The algorithm must start from initializing k centers of the clusters the initial values may be set manually or chosen randomly. In each iteration each point is attracted to the nearest centroid and the centroids are updated (as a mean value of all points belonging to one class). The algorithm presented below uses clustering and thresholding techniques. It is a part of the computer vision system SpotView [3], built for the research project run by Computer Engineering Department of Technical University of Lodz, and Department of Nephrology and Transplantation Medicine of the Wroclaw Medical University. The project is focused on the optimization of the method based on the ELISPOT approach for determination of alloreactivity of renal transplant recipient in clinical practice. The goal is to obtain a non-invasive diagnostic tool for prediction of long Wojciech Bieniecki PhD, Szymon Grabowski PhD, Michał Krupiński MSc: Computer Engineering Dept., al. Politechniki 11, Lodz, Poland, tel , wbieniec@kis.p.lodz.pl. Katarzyna Kościelska-Kasprzak, PhD, Dominika Drulis- Fajdasz PhD, Oktawia Mazanowska Ph D, Marian Klinger DSc: Dept. of Nephrology and Transplantation Medicine, Wroclaw Medical University, ul. Traugutta 7/9, Wrocław, tel term renal allograft function and early detection of markers of chronic graft rejection process [4, ]. II THE IMAGES Our current research has focused on the simultaneous enumeration of the recipient peripheral blood lymphocytes that are able to produce two different cytokines in response to stimulation with renal allograft donor antigens. The ELISPOT experiment (Fig. 1) is performed in membrane bottomed 96- well plates with each well bottom (6 mm diameter) coated with antibodies specific against each of the cytokines analyzed. During the co-incubation of recipient and donor cells, any secreted cytokine of the analyzed type is bound around the secreting cell by the specific antibody. During the experiment the known number of the analyzed recipient lymphocytes is incubated with or without donor lymphocytes to observe the donor specific immunological responses. Fig. 1 ELISPOT procedure and image acquisition When the cells are removed the still attached cytokines are detected with the use of two parallel immunoenzymatic procedures. Both of them result in the production of insoluble colored (red or blue) product, with its color indicating the presence of the given cytokine. In the case of our experiments the red spots are the result of the interleukin-2 production, and the blue ones of interferon gamma. When the cell secreted both of the analyzed cytokines the spot is purple The microscope head or camera is moved over the plate and the

2 photo of each well is taken (Fig. 2). In our case DS-M Nikon camera equipped with AF micro Nikkor 60 mm lenses is used for image acquisition. The subject of the image analysis is to extract the spots from the viewing area and evaluate their morphological parameters as well as the type of the cytokine secreted through spot color determination. The spot morphology is the result of actual cytokine productivity, lateral diffusion and dissociation of the immunocomplexes. Fig. 3 The masks for segmentation algorithm In the next, teaching phase, the gravity centers for each class are initialized and pixels are initially classified. Those centers are generated on the basis of one of three methods: global gray-, global feature, local feature. Global gray is the method, where the centers are initialized basing on the maximum and minimum s found in the whole region of interest (Table 1). Fig. 2. ELISPOT microscopic image III. THE ALGORITHM The algorithm works in four phases: (Fig. 4), teaching, grouping and finalization. The image to process is divided into square regions using specified masks (Fig. 3). This helps to cope with uneven lighting and varying focal conditions in the whole image. The mask for teaching phase is bigger. The phases of teaching and grouping work separately on the square regions. 1. Get segmentation params and the coordinates of ROI 2. Initialize the class matrix for image pixels 3. Load the image 4. Set the ROI Fig. 4 The phase The following parameters are set by the user at the start: - the number of classes, diameters of scanning masks (separately for teaching and grouping phases), - the gray- thresholds (the of homogeneity which controls the algorithm s sensitivity and the of spot which affects the spot sharpness), - the method of centroids, - optionally post segmentation median filtering. In this stage a class matrix for the image pixels is allocated. TABLE 1 CENTROID INITIALIZATION GLOBAL GRAY LEVEL 0 maxgray maxgray maxgray 1 maxgray mingray mingray 2 mingray mingray maxgray 3 mingray maxgray mingray 4 maxgray maxgray mingray mingray maxgray maxgray 6 maxgray mingray maxgray The global feature method (Table 2) is assumes that the initial positions of centroids are constructed of feature values (R, G, B) of pixel with is darkest (min) and brightest (max) within the region of interest. The last variant, local feature (Table 3), works analogically as in the previous case, but the values are evaluated individually for each square region. TABLE 2 CENTROID INITIALIZATION GLOBAL FEATURE LEVEL 0 max max max 1 max min min 2 min min max 3 min max min 4 max max min min max max 6 max min max

3 TABLE 3 CENTROID INITIALIZATION LOCAL FEATURE LEVEL 0 maxr maxg maxb 1 maxr ming minb 2 minr ming maxb 3 minr maxg minb 4 maxr maxg minb minr maxg maxb 6 maxr ming maxb The thresholds: homogeneity and spot are used as follows. Homogeneity (hl) is a factor used in the expression of homogeneity of the analyzed square: ( ay localmingray) > ( Maxgray Mingray) hl localmaxgr (1) where Maxgray and Mingray are the s defined in Table 1 and localmaxgray and localmingray are minimum and maximum pixel s within the individual quare. The spot (sl) is a factor in the decision rule if the pixel is assigned as a spot pixel. The rule is: pixelgray > MinGray + MaxGray MinGray sl 0.01 (2) As a result of the teaching phase the matrix of pixel classes is filled. The algorithm is presented in Fig.. 1. Initialize the matrix of gravity centers (for each mask region) 2. If the region is homogenous (homogeneity is not achieved) set all region pixel class as background and proceed to the next region. Otherwise, go to Get the next pixel in the region. 4. If the gray- is less than the spot, set the pixel class as background, otherwise assign the pixel class to the nearest class and go to.. If all region pixels are set, go to 6 else go to Update the matrix of gravity centers. 7. if the gravity center matrix has been changed go to step 3, else proceed to the next region. Fig. The teaching phase In the grouping phase the region of interest is split using a mask with smaller diameter. This is the final step of pixel classification; all pixels are assigned to some class. For each mask region: 1. Initialize the gravity center matrix based on the class matrix. 2. Evaluate the mean gray- in the region. 3. Get the next pixel. 4. If the gray of the pixel is less than the mean value, assign the pixel as a background and go to 6 else assign it to the nearest class and go to.. If all pixels are classified go to 6 else go to Update the gravity center matrix. 7. Once again assign all pixels to nearest centers. Fig. 6 The grouping phase In the last finalization phase, the image of classes is generated. The part which is not in the Region of Interest is painted gray, the background pixels are painted white, and the other pixels have the color compatible to the adequate gravity center value. If the median filter option is on, a filtering procedure to remove the image artifacts and smooth the ragged object edges is carried out. IV. THE RESULTS The algorithm has been tested to prove reliability and high performance of the segmentation. The test system was: - a PC computer: Gigabyte K8 Triton motherboard, AMD Sempron GHz CPU and 768 MB of RAM, - Windows XP PE (SP2) with Visual Studio 98 IDE. All the images were two-color ELISPOT images prepared, acquired and provided by Wroclaw Medical University. The tests enclosed: - the impact of the number of gravity centers upon the algorithm s convergence (Tables 4 7), - the impact of masks sizes upon the speed and quality of the segmentation (Table 8), - the impact of homogeneity and sensitivity thresholds upon the segmentation accuracy (Table 9). The results shown in Tables 4 7 indicate that the global gray approach is most convergent and the initial positions of centroids correspond to the colors: red, green, blue, cyan, magenta, yellow and white. Other methods require more iterations to achieve the final positions but the initial position is set better, which may be an advantage, when the maximum number of iterations is limited. All three methods are convergent to the same centroid positions. TABLE 4 METHODS (PART 1) Iteration 0 s coordinates The distance from Global gray Local feature

4 TABLE METHODS (PART 2) Iteration 1 s coordinates The distance from Global gray Local feature TABLE 6 METHODS (PART 3) Iteration 2 s coordinates The distance from Global gray Local feature TABLE 7 CONV. TESTS FOR VARIOUS CENTROID INIT METHODS (PART 4) method Global gray Local feature Last iteration s Number of coordinates iterations R G B TABLE 8 SEGMENTATION QUALITY FOR VARIOUS SEGMENT. MASK SIZES method Global gray Local feature Teaching phase Mask size Grouping phase Time Fract. of properly detect. spots [ms] [%]

5 Mask size adjustments affect the algorithm speed and the segmentation quality. The experiments carried out on the images showed that the mask in teaching phase should be less than in the grouping with the ratio about 1:3. The suggested mask sizes for processed resolution are for teaching and for grouping. Too small masks defect the weak fuzzy spot detection and too large dramatically increase the computation time. TABLE 9 SEGMENTATION QUALITY AS A FUNCTION OD THRESHOLDING FACTORS hl sl Time method [%] [%] [ms] Global gray Local feature Spot count False spot count * * * * * 2719 * * * * * means very poor segmentation The homogeneity and spot s have a very high impact on the quality of the segmentation. The values must be adjusted experimentally and may differ in case of replacing the camera or changing the reagents. CONCLUSIONS The experiments showed that proper adjustment of the segmentation parameters enables segmentation of all tested ELISPOT images. The method with local feature s offers the highest segmentation quality. Despite its worst convergence, it is also the fastest one because the segmentation mask may be relatively small. Its drawback is high sensitivity to threshold factors adjustment, which is important weakness for unattended processing. The global feature method gives a high quality segmentation without excessive care for the parameters but it requires big segmentation masks which increases the computation cost. The method of global gray gives stable results without modifying the clustering parameters, but during the segmentation the weakest and smallest spots are often omitted. ACKNOWLEDGEMENTS This work was supported by the Polish Ministry of Science and Higher Education grant 3T11E REFERENCES [1] Hanson A. R., Riseman E. R. (1978): Segmentation of natural scenes. In Hanson and Riseman, editors, Computer Vision Systems, pp , Academic Press, NJ. [2] MacQueen J. (1967): Some methods for classification and analysis of multivariate observations. th Berkeley Symposium on Mathematics, Statistics and Probability, University of California Press, Berkeley, CA, USA, Vol. 1, pp [3] Bieniecki W., Grabowski Sz., Sankowski D., Kościelska- Kasprzak K., Berna B., Klinger M. (): An Efficient Processing and Analysis Algorithm for Images Obtained from Immunoenzymatic Visualization of Secretory Activity. Proceedings of the 8th. International IEEE Conference CADSM, Lviv-Polyana, Ukraine, pp [4] Gebauer B. S., Hricik D.E., Atallah A., Bryan K., Riley J., Tary-Lehmann M., Greenspan N. S., Dejelo C., Boehm B. O., Hering B. J., Heeger P. S. (2): Evolution of the enzyme-linked immunosorbent spot assay for posttransplant alloreactivity as a potentially useful immune monitoring tool. Am. J. Transplant. vol. 2, pp [] Hricik D. E., Rodriguez V., Riley J., Bryan K., Tary- Lehmann M., Greenspan N., Dejelo C., Schulak J. A., Heeger P. S. (3): Enzyme linked immunosorbent spot (ELISPOT) assay for interferon-gamma independently predicts renal function in kidney transplant recipients. Am. J. Transplant. vol. 3, pp