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For some images of a single stem cell, the boundary delineating the cell is discontinuous or blurry at some locations. If the statistical region merging (SRM) method is applied directly on such images, the image segmentation results may not be ideal. In this paper, for each such image, we add some gradient information into the image; then apply a discontinuous filter on the image so that the image is smoothed a bit and the edges of the image are kept well. Next, closing operations of morphology are applied on the filtered image; and the processed image is segmented using SRM. Finally, apply a threshold on the segmented image to obtain a binary image; apply a hole-filling function to the binary image; extract the biggest connected component in the hole-filled image; and apply a linear transform on the image of the biggest component to match the input image as well as possible in terms of the least squares fitting. This transformed image is the segmentation result. We have applied SRM using connectivity of 4 and 8 as well as a hexagonal lattice. The corresponding segmentation results are tabulated for convenient comparisons; and the results can show that the proposed method may be helpful for the segmentation of such images. 

The statistical region merging (SRM) method for image segmentation is based on some solid probabilistic and statistical principles. It produces good segmentation results, and is efficient in term of the computational time. The original SRM algorithm is for Cartesian images sampled by square lattices (sqL). Because hexagonal lattices (hexL) have the advantage that each lattice point in a hexL has six equidistant adjacent lattice points, in this paper, we perform image segmentation for hexagonally sampled images using SRM. We first convert the SRM algorithm from sqLs to hexLs. Then we use some test images to compare the corresponding segmentation effect for hexLs versus sqLs. The experimental results have shown that a hexL exhibits evidently better image segmentation effect than the corresponding sqL (with the same spatial sampling rate as the hexL) using the usual 4-connectivity. Finally, we point out that CT image segmentation may benefit from using hexLs since they provide better image reconstruction effect than sqLs. 

In this paper, morphological operations on regular hexagonal structures are considered, where a regular hexagonal structure is a subset of a hexagonal lattice and consists of the sampled points for the discretization of a regular hexagonal region. First, a sequence of reasonable structure elements (SE) for hexagonal lattices are provided, and the decompositions of the SEs are shown. Second, based on the decompositions of the SEs, some efficient algorithms for morphological operations on the regular hexagonal structures are developed. Finally, the algorithms are tested using a computerized tomography (CT) image, and promising applications of such algorithms on CT image reconstruction and segmentation are pointed out.