An efficient algorithm is presented for the computation of grayscale morphological operations with arbitrary 2D flat structuring elements (S.E.). The required computing time is independent of the image content and of the number of gray levels used. It always outperforms the only existing comparable method, which was proposed in the work by Van Droogenbroeck and Talbot, by a factor between 3.5 and 35.1, depending on the image type and shape of S.E. So far, filtering using multiple S.E.s is always done by performing the operator for each size and shape of the S.E. separately. With our method, filtering with multiple S.E.s can be performed by a single operator for a slightly reduced computational cost per size or shape, which makes this method more suitable for use in granulometries, dilation-erosion scale spaces, and template matching using the hit-or-miss transform. The discussion focuses on erosions and dilations, from which other transformations can be derived.

/pdf/efficient-2-d-grayscale-morphological-transformations-with-15vnn1rbid.pdf

Efficient 2-D Grayscale Morphological Transformations With Arbitrary Flat Structuring Elements

This paper is concerned with automatic segmentation of high resolution digitized metaphases. This includes automatic detection and rejection of interphase nuclei, stain debris, and other "noise"; automatic detection and segmentation of touching and overlapping chromosome clusters; and automatic rejection of cells which are evaluated as being incomplete, or incorrectly segmented, or where the cell is otherwise unsuitable for further analysis. In this paper, a rule-based approach is described which treats the cell as a whole rather than as a series of individual chromosomes or clusters. The rules adapt classification and segmentation parameters for each cell. Initially, different sets of parameters are chosen according to the staining method of the cells, and the goal of the segmentation. A chromosome number predictor is used to guide the adaptation of the parameters and to estimate the performance. The adaptation is iterative, and the self-adjustment will stop when either a satisfactory result is achieved or if the cell is rejected. The method was implemented on both a Sun workstation and a Cytoscan, a commercial machine for chromosome analysis. Seven hundred and thirteen cells from real data have been tested. A success rate of 90-95% has been achieved. The procedure has been implemented in an automatic aberration scoring system for routine use.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/cyto.990170303

Fully automatic chromosome segmentation

Fluorescent staining is a common tool for both quantitative and qualitative assessment of pro- and eukaryotic cells sub-population fractions by using microscopy and flow cytometry. However, direct cell counting by flow cytometry is often limited, for example when working with cells rigidly adhered either to each other or to external surfaces like bacterial biofilms or adherent cell lines and tissue samples. An alternative approach is provided by using fluorescent microscopy and confocal laser scanning microscopy (CLSM), which enables the evaluation of fractions of cells subpopulations in a given sample. For the quantitative assessment of cell fractions in microphotographs, we suggest a simple two-step algorithm that combines single cells selection and the statistical analysis. To facilitate the first step, we suggest a simple procedure that supports finding the balance between the detection threshold and the typical size of single cells based on objective cell size distribution analysis. Based on a series of experimental measurements performed on bacterial and eukaryotic cells under various conditions, we show explicitly that the suggested approach effectively accounts for the fractions of different cell sub-populations (like the live/dead staining in our samples) in all studied cases that are in good agreement with manual cell counting on microphotographs and flow cytometry data. This algorithm is implemented as a simple software tool that includes an intuitive and user-friendly graphical interface for the initial adjustment of algorithm parameters to the microphotographs analysis as well as for the sequential analysis of homogeneous series of similar microscopic images without further user intervention. The software tool entitled BioFilmAnalyzer is freely available online at https://bitbucket.org/rogex/biofilmanalyzer/downloads/.

/pdf/fast-and-simple-tool-for-the-quantification-of-biofilm-452yiymep6.pdf

Fast and simple tool for the quantification of biofilm-embedded cells sub-populations from fluorescent microscopic images.

Efficient morphological reconstruction: a downhill filter

The authors complement the standard algebraic view of mathematical morphology with a geometric, differential view. Three observations underlie this approach. (1) Certain structuring elements (convex) are scalable in that a sequence of repeated operations is equivalent to a single operation, but with a larger structuring element of the same shape. (2) To determine the outcome of the operation, it is sufficient to consider how the boundary is modified. (3) The modifications of the boundary are such that each point can be moved along the normal by a certain amount, which is dependent on the structuring element. Taken together, these observations, when the size of the structuring element shrinks to zero, assert that mathematical morphology operations with a convex structuring element are captured by a differential deformation of the boundary along the normal, governed by a Hamilton-Jacobi partial differential equation (PDE). A second theme is to show that mathematical morphology operations can be numerically implemented in a highly accurate fashion as the solution of these PDEs. >

Jing-Yan Tang

Papers

Erosion and dilation of binary images by arbitrary structuring elements using interval coding