Проанализированы алгоритмы сегментации изображений, их преимущества и недостатки, а также объективные и субъективные критерии качества сегментации. При исследовании алгоритмов сегментации выполнены компьютерные эксперименты с использованием базы данных биомедицинских (гистологических) изображений рака молочной железы.
Проаналізовано алгоритми сегментації зображень, їх переваги та недоліки, а також об’єктивні та суб’єктивні критерії якості сегментації. При дослідженні алгоритмів сегментації виконано комп’ютерні експерименти з використанням бази даних біомедичних (гістологічних) зображень раку молочної залози.
Introduction. Color image segmentation is a process of image division into one or more regions based on a certain criterion of homogeneity. The following major classes of segmentation algorithms are presented: the threshold segmentation algorithms, the morphological segmentation algorithms, the region growing algorithms, the algorithms based on a cluster analysis. Today there is no single universal algorithm for image segmentation. The most common specialized algorithms are used for a certain class of tasks. The quality of image segmentation can be defined as for subjective and objective levels. Subjective criteria are the criteria of a visual perception that are received from the experts. Objective criteria are the criteria resulting from the comparison of the quantitative features of segmented and standard images. All known quantitative assessment criteria can be divided into two groups: non supervisory criteria and supervisory criteria. Non supervisory criteria are based on the calculation of various statistics and applied in the absence of priori information about the segmented image. Supervisory criteria are based on calculating of the distance measure results of segmented and standard images. Purpose. The purpose of the article is to develop algorithms of quantified quality of image segmentation on the basis of metrics. Methods. The image is presented with union contour and internal region. The original image is segmented by an expert and therefore a set of segments is received. In turn, segments are presented with sets of contours and regions. Similarly, after each segmentation the algorithms are obtained by sets of images contours and regions. The Frechet metric is used to evaluate the similarity of images contours. The discrete Frechet distance is used in the paper. Contour curves are approximated by polygonal curves. Two arrays of vertices coordinates are obtained from the polygonal contours curves. The array of connection pair’s points between the vertices coordinates of two contours is formed on the basis of the previous arrays. The maximum distance to the nodes of the second contour is calculated for each node of the first contour. Thus, the array of the longest distances is formed from each node of the first contour with the nodes of the second contour. The minimum value, equal to the discrete Frechet distance, is calculated for this array. The computational complexity of the discrete Freshet distance algorithm is equal to the product of the line segments number of two polygonal contours. The article also describes the use of the Hausdorff metric. The regions are presented by vertices arrays of arcwise segments of the external boundary. Projections of the first region vertices to the second region are calculated. The maximum value distance is formed from this array. Similarly, the projections of the second region vertices on the first region are found and the maximum value of these distances is calculated. Then, the Hausdorff distance between regions is equal to the maximum of two maximums. The complexity of the Hausdorff distance algorithm is equal to the sum of the number of arcwise segments of two polygonal regions. The Gromov – Hausdorff metric is used for calculation of the shortest distance between regions images. This metric performs isometric transformations (parallel transfer, rotation) of the two given regions for obtaining their maximum superposition. The work discusses the isometric transformation algorithm as well as superposes the mass centers of two regions. The next step is calculating and superposition of two maximum chords regions. Тhе Gromov – Fresh metric calculates the minimum distance between the contours. The shortest distance between two given images is equal to the smallest sum of distances between contours and regions with given weight ratios. Results. The algorithms to determine the Freshet, Gromov – Freshet, Hausdorff and Gromov – Hausdorff distances for convex contours and regions are developed. The software tool is designed and developed, and computer experiments are made. The software system is developed on Delphi programming language and is oriented on Windows based workstations. The system is used for morphometric research of breast cancer histological images. Conclusion. The algorithms based on the metrics for estimating the quality of image segmentation are developed. It is possible to combine segmentation algorithms to ensure minimum error segmentation. Further we are going to research the development of parallel algorithms for calculating distances and improved metrics for the effective estimating of distances. The software is developed under the state budget theme «Intelligent system for diagnosing various forms of breast cancer based on analysis of histological and cytological images» (№ 0112U000736).
