Osteosarcoma is one of the most common types of bone cancer in children. To gauge the extent of cancer treatment response in the patient after surgical resection, the H&E stained image slides are manually evaluated by pathologists to estimate the percentage of necrosis, a time consuming process prone to observer bias and inaccuracy. Digital image analysis is a potential method to automate this process, thus saving time and providing a more accurate evaluation. The slides are scanned in Aperio Scanscope, converted to digital Whole Slide Images (WSIs) and stored in SVS format. These are high resolution images, of the order of 109 pixels, allowing up to 40X magnification factor. This paper proposes an image segmentation and analysis technique for segmenting tumor and non-tumor regions in histopathological WSIs of osteosarcoma datasets. Our approach is a combination of pixel-based and object-based methods which utilize tumor properties such as nuclei cluster, density, and circularity to classify tumor regions as viable and non-viable. A K-Means clustering technique is used for tumor isolation using color normalization, followed by multi-threshold Otsu segmentation technique to further classify tumor region as viable and non-viable. Then a Flood-fill algorithm is applied to cluster similar pixels into cellular objects and compute cluster data for further analysis of regions under study. To the best of our knowledge this is the first comprehensive solution that is able to produce such a classification for Osteosarcoma cancer. The results are very conclusive in identifying viable and non-viable tumor regions. In our experiments, the accuracy of the discussed approach is 100% in viable tumor and coagulative necrosis identification while it is around 90% for fibrosis and acellular/hypocellular tumor osteoid, for all the sampled datasets used. We expect the developed software to lead to a significant increase in accuracy and decrease in inter-observer variability in assessment of necrosis by the pathologists and a reduction in the time spent by the pathologists in such assessments.

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Given a set R of n red points and a set B of m blue points, we study the problem of finding a rectangle that contains all the red points, the minimum number of blue points and has the largest area. We call such rectangle a maximum separating rectangle. We address the planar, axis-aligned (2D) version, and present an O(m log m + n) time, O(m + n) space algorithm. The running time reduces to O(m + n) if the points are pre-sorted by one of the coordinates. We further prove that our algorithm is optimal in the decision model of computation.

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