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Summary With the rapid advance of three-dimensional (3D) confocal imaging technology, more and more 3D cellular images will be available. Segmentation of intact cells is a critical task in automated image analysis and quantification of cellular microscopic images. One of the major complications in the automatic segmentation of cellular images arises due to the fact that cells are often closely clustered. Several algorithms are proposed for segmenting cell clusters but most of them are 2D based. In other words, these algorithms are designed to segment 2D cell clusters from a single image. Given 2D segmentation methods developed, they can certainly be applied to each image slice with the 3D cellular volume to obtain the segmented cell clusters. Apparently, in such case, the 3D depth information with the volumetric images is not really used. Often, 3D reconstruction is conducted after the individualized segmentation to build the 3D cellular models from segmented 2D cellular contours. Such 2D native process is not appropriate as stacking of individually segmented 2D cells or nuclei do not necessarily form the correct and complete 3D cells or nuclei in 3D. This paper proposes a novel and efficient 3D cluster splitting algorithm based on concavity analysis and interslice spatial coherence. We have taken the advantage of using the 3D boundary points detected using higher order statistics as an input contour for performing the 3D cluster splitting algorithm. The idea is to separate the touching or overlapping cells or nuclei in a 3D native way. Experimental results show the efficiency of our algorithm for 3D microscopic cellular images.

Summary In recent years, cell biologists have benefited greatly from using confocal microscopy to study intracellular organelles. For high-level image analysis, 3D boundary extraction of cell structure is a preliminary requisite in confocal cellular imaging. To detect the object boundaries, most investigators have used gradient/Laplacian operator as a principal tool. In this paper we propose a higher order statistics (HOS) based boundary extraction algorithm for confocal cellular image data set using kurtosis. After the initial pre-processing, kurtosis boundary map is estimated locally for the entire volume using a cubic sliding window and subsequently the noisy kurtosis value is removed by thresholding. Voxels having positive kurtosis value with zero-crossing on its surface are then identified as boundary voxels. Typically used in signal processing, kurtosis for 3D cellular image processing is a novel application of HOS. Its reliable and robust nature of computing makes it very suitable for volumetric cellular boundary extraction.

With the rapid advance of three-dimensional (3D) confocal imaging technology, more and more 3D cellular images will be available. Segmentation of intact cells is a critical task in automated image analysis and quantification of cellular microscopic images. One of the major complications in the automatic segmentation of cellular images arises due to the fact that cells are often closely clustered. Several algorithms are proposed for segmenting cell clusters but most of them are 2D based. In other words, these algorithms are designed to segment 2D cell clusters from a single image. Given 2D segmentation methods developed, they can certainly be applied to each image slice with the 3D cellular volume to obtain the segmented cell clusters. Apparently, in such case, the 3D depth information with the volumetric images is not really used. Often, 3D reconstruction is conducted after the individualized segmentation to build the 3D cellular models from segmented 2D cellular contours. Such 2D native process is not appropriate as stacking of individually segmented 2D cells or nuclei do not necessarily form the correct and complete 3D cells or nuclei in 3D. This paper proposes a novel and efficient 3D cluster splitting algorithm based on concavity analysis and interslice spatial coherence. We have taken the advantage of using the 3D boundary points detected using higher order statistics as an input contour for performing the 3D cluster splitting algorithm. The idea is to separate the touching or overlapping cells or nuclei in a 3D native way. Experimental results show the efficiency of our algorithm for 3D microscopic cellular images.

Gradients play an important role in 2D image processing. Many edge detection algorithms are gradient-based. We are interested in 3D boundary detection which can be considered as an extension of 2D edge detection in 3D space. In this paper, an algorithm to automatically and quantitatively measure the suitability of gradient magnitudes in detection of 3D boundary points of confocal image stacks is presented. A Measurement Function is defined to evaluate the suitability of each gradient magnitude chosen to be the threshold for 3D boundary detection. The application of Gauss's Divergence Theorem provides a solution to calculate the Measurement Function numerically. The gradient magnitude at which the maximum of the Measurement Function is achieved can be utilized as the most appropriate threshold for gradient-based boundary detection and other operations like volume visualization.