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Unrestricted LR detection for biomedical applications using coarse-to-fine hierarchical approach

In this study, the authors present a simple, reliable, fast, unrestricted-shape geometry, and accurate algorithm which runs in O(log2  n) time to find the axis-parallel largest rectangle (LR) inside a given region of interest (ROI), where n is the image size in one dimension, which means that the proposed model can work in real time. The proposed approach is successful in detecting the LR of arbitrary orientation that is fully contained in the ROI as well. Also, the present algorithm can find the largest empty rectangle in a space containing a set of zero points, whether the axis-parallel rectangle or the oriented one. The strategy followed here is to accelerate LR detection process by searching the rectangle with the largest area inscribed in the ROI, by starting first with the lowest-resolution version of the original image for determining the LR four corners’ coordinates, then next searching the new LR corners’ scaled coordinates in the higher power resolutions in a multiple resolutions hierarchical model and therefore, a corresponding coarse-to-fine inference procedure recursively eliminates the search space of the LR four corners coordinates. For finding the largest oriented rectangle, the same hierarchical procedures are followed, but combined with rotation-angle resolution.