Hexagonal grid layouts are advantageous in microarray technology; however, hexagonal grids appear in many fields, especially given the rise of new nanostructures and metamaterials, leading to the need for image analysis on such structures. This work proposes a shock-filter-based approach driven by mathematical morphology for the segmentation of image objects disposed in a hexagonal grid. The original image is decomposed into a pair of rectangular grids, such that their superposition generates the initial image. Within each rectangular grid, the shock-filters are once again used to confine the foreground information for each image object into an area of interest. The proposed methodology was successfully applied for microarray spot segmentation, whereas its character of generality is underlined by the segmentation results obtained for two other types of hexagonal grid layouts. Considering the segmentation accuracy through specific quality measures for microarray images, such as the mean absolute error and the coefficient of variation, high correlations of our computed spot intensity features with the annotated reference values were found, indicating the reliability of the proposed approach. Moreover, taking into account that the shock-filter PDE formalism is targeting the one-dimensional luminance profile function, the computational complexity to determine the grid is minimized. The order of growth for the computational complexity of our approach is at least one order of magnitude lower when compared with state-of-the-art microarray segmentation approaches, ranging from classical to machine learning ones.
Keywords: computational complexity; gene expression; hexagonal grids; image segmentation; machine learning; microarray; shock-filter.