This paper presents a new method for automatic recognition of cancerous tissues from an image of a microscopic section. Based on the shape and the size analysis of the observed cells, this method provides the physician with nonsubjective numerical values for four criteria of malignancy. This automatic approach is based on mathematical morphology, and more specifically on the use of Geodesy. This technique is used first to remove the background noise from the image and then to operate a segmentation of the nuclei of the cells and an analysis of their shape, their size, and their texture. From the values of the extracted criteria, an automatic classification of the image (cancerous or not) is finally operated.