This thesis deals with the detection of microcalcifications on mammography. Among the various findings can be found on a mammogram microcalcifications are important because they allow for early detection, as almost half of the tumors detected clinically are hidden thanks to the presence of microcalcifications. Microcalcifications are significant only isolated from a radiological point of view, but when they are forming groups. Detection is used for digital image processing, specifically the combination of mathematical morphology and Markov random fields. One chapter is devoted to each of these areas. The next chapter is devoted to algorithm specific model Markov random field to the case of interaction between pairs of pixels in a neighborhood of order 2. Also included in the model the contribution due to individual pixels. To take advantage of microcalcifications is likely to be clustered around the neighborhood extends to a region of radius 0.5 cm for those pixels labeled microcalcificación. In relation to the proposed use of mathematical morphology operators highlight microcalcifications unstarred other regions such as contrasting regions corresponding to the fibers. To minimize the excessive sensitivity to very small regions contrasted morphological changes are proposed with associated operations such as opening superficial. For the chapter of results have been used mammograms from the database provided by courtesy of the National Expert and Training Center for Breast Cancer Screening and the Department of Radiology at teh University of Nijmegen, the Netherlands