Statistical analysis of genetic changes within cell nuclei that are far from the primary tumor would help determine whether such changes have occurred prior to tumor invasion. To determine whether the gene amplification in cells is morphologically and/or genetically related to the primary tumor requires quantitative evaluation of a large number of cell nuclei from continuous meaningful structures such as milk-ducts, tumors, etc., located relatively far from the primary tumor. To address this issue, we have designed an integrated image analysis software system for high-throughput segmentation of nuclei. Filters such as Beltrami flow-based reaction-diffusion, directional diffusion, etc., were used to pre-process the images resulting in a better segmentation. The accurate shape of the segmented nucleus was recovered using an iterative "shrink-wrap" operation. The study of two cases of ductal carcinoma in situ in breast tissue supports the biological observation regarding the existence of a preferential intraductal invasion, and therefore a common origin, between the primary tumor and the gene amplification in the cell-nuclei lining the ductal structures in the breast.