Breast tumor segmentation and analysis is an important step for doctors in deciding the stage of cancer and to proceed for further treatment. Segmentation of image is a crucial step in image processing which further helps in classification of image based on the features extracted. The segmentation technique in most of the approaches uses similar kind of algorithm for segmentation of region of interest. This paper presents a new approach for preprocessing and segmenting out the infiltration and tumor regions from digital mammograms using two techniques involving iterative and non iterative algorithms of Delaunay triangulation. The preprocessing involves hybrid filter for noise removal and image enhancement. The iterative algorithm for segmentation works to get an idea of shape of infiltration/tumor in the breast. The proposed algorithm uses Voronoi properties to partition an image into regions of similarity followed by Delaunay triangulation. The advantage of this technique is it works on the histogram of the image instead of the entire image hence it is effective for large sized mammograms reducing the load on algorithm. This is fully automated and unsupervised process. No parameter is needed for segmentation which is an advantage over other popular segmentation methods like k-means and watershed. The Voronoi and Delaunay segmentation are region growing method which looks for similarity in the images and segment outs the high intensity region (in this case the probable infiltration/tumor) from the entire image. We also propose divide and conquer algorithm for Delaunay triangulation to get faster output (average execution time is 0.4 sec). To evaluate our proposed method a comparison with k-means and watershed segmentation and the results of feature extraction is carried out.