In the image processing, the segmentation of overlapping objects is considered to be the chal-lenging task that tries to address the segmentation of multiple objects with partial views. The presence of multiple occluded objects is the main difficulty for segmenting of overlapping ob-jects. Several methods have been proposed to solve the complexity observed in the segmentation of overlapping objects. In the following these methods are briefly reviewed.
In [9], automated morphology analysis coupled with a statistical model for contour inference is applied in order to separate the partially overlapping nano particles, here after referred to as Nano Particles Segmentation (NPS). NPS is based on, a two stage processing model: 1) im-age segmentation and 2) contour inference along the shape classification. In the first stim-age, a modified Ultimate Erosion model specific to convex-shape objects, namely Ultimate Erosion for Convex-Shape (UECS), followed by an edge-to-marker association method is used for separat-ing individual particles from an agglomerate of overlappseparat-ing nano-objects. In the second stage, the proposed model solves the problem of contour inference and shape classification simultane-ously by the Gaussian mixture model on B-splines, where the unknown parameters of model are estimated using the Expectation Conditional Maximization (ECM) algorithm.
In [8] an approach for segmentation of overlapping cell nuclei in digital histopathology images is presented. This method is the composition of foreground extraction, seed point extraction and seed point watershed segmentation. The method particularly follows a four-component process-ing pipeline. First, a global-local thresholdprocess-ing is applied to extract the foreground regions from the background, and then proceeds to seed point detection. Seed point detection is performed by combining morphological filtering and intensity based region growing. The obtained seed points are then introduced to the seed point watershed algorithm by which the cluster nuclei are segmented. Finally, the method outputs the final result through a post-processing in which the off-spec cell nuclei are eliminated.
[48] introduces a semi automatic approach for detection and segmentation of cell nuclei. The
approach follows a two stage procedure, in which an automatic segmentation model is first used, the cell nuclei are determined, and then improved via the expert’s interaction. The automatic segmentation of nuclei consist of three specific steps: 1) image binarization, and 2) seed de-tection, and 3) segmentation. Through the process of binarization, performed by the graph-cut binarization algorithm, the foreground is separated from the image background. The seed points in an image are detected using a compound model of multi-scale Laplacian-of-Gaussian filtering along with distance-map-based scale adaptive selection. Upon the detection of seed points, and in order to achieve a better delineation of true edge between the cell nuclei, the segmentation results are obtained by a second graph-cuts-based algorithm incorporating the method of alpha expansions and graph coloring to reduce computational complexity.
A method for the estimation of the bubble size distribution is introduced in [7], here after referred to as Concave-point Based Contour Segmentation (CBCS). The method solves the problem of overlapping bubbles in the three steps: 1) image pre-processing and contour extraction , 2) con-tour segmentation and, 3) concon-tour segment grouping. In the pre-processing step, the Otsu’s method [10] is used to convert the image into the binary image, and then the boundaries are ex-tracted and smoothed. After extracting the boundaries, the polygonal approximation is used for detecting the dominant points. The obtained dominant points support the contour segmentation based on the assumption that concave points in the sequence of dominant points are considered the points connecting the contour segments. In the third step, for the purpose of grouping the contour segments, ellipse fitting combined with the average distance deviation criteria is used.
Additionally, two constraints are applied to prevent missgrouping. Although the proposed frame-work is an efficient segmentation method for overlapping objects, it does not frame-work with an object shape that largely deviates from a perfect ellipse.
The authors in [49] presents a generative supervised learning approach for segmenting of over-lapping objects. In this method, it is assumed that the input image, which may contain multiple instances of a certain object class, can be detected by a region based detection method. For the detection purpose, a set of candidate regions are detected using the Maximally Stable Extremal Regions (MSER) algorithm. A set of classifiers is used to evaluate the similarity of those regions to each of the classes indicating the number of object instances in the regions. By this means, a value is assigned to each region, which implies the number of objects in those region. The learning process is done by a structured output SVM framework [50] and dynamic programming detects the subset of those regions that have the highest similarity to the class of the cell.
3 Framework for Overlapping Convex Object Segmentation
There is no universal methodology that can be used for segmentation of overlapping convex ob-jects. However, the majority of works employed in this domain fall under a three-step framework, in which three particular sub-tasks either in order or in parallel are addressed. In this framework, through the detection of any individual object and eventually the relevant visual contour parts, the overlapping objects are segmented by the deduced complete contours. This Chapter presents the details of this scheme and the steps involved.
3.1 General Framework
A typical framework for segmenting the overlapping convex objects consists of three specific steps (see Figure 8): 1) seed region/point extraction, 2) contour evidence extraction, and 3) contour estimation [9, 7, 8].
Figure 8.The general framework.
The first step is to extract the seed points or regions corresponding to each overlapping object.
The seed points, usually refer to the geometric central points or a point in the interior of the object, which conceptually provide a basic cue to separate overlapping objects. The goal is to recognize the presence and the number of the individual objects in an image as identified by seed points. The detected seed points within the process of segmentation of the object with occlusion is considered priori information by which the performance of the ultimate segmentation results can be improved.
The second step is determining the contour evidence. The contour evidence is the visible parts of the objects boundaries that can be used to inference the occluded parts of overlapped objects.
The contour evidence extraction aims to group of edge points that belonged to each object using seed points or seed regions.
The last step in segmentation of overlapping objects is dedicated to contour estimation, where, by means of the visual information produced from the previous two steps, the missing parts of the object contours are estimated.
Several approaches have been proposed to address the each step of the framework. In Sections 3.2, 3.3, and 3.4 common methods used for seed point extraction, contour evidence extraction, and contour estimation are reviewed.