Breast cancer is the most common cancer among women worldwide with about half a million cases reported each year. Mammary thermography can offer early diagnosis at low cost if adequate thermographic images of the breasts are taken. The identification of breast cancer in an automated way can accelerate many tasks and applications of pathology. This can help complement diagnosis. The aim of this work is to develop a system that automatically captures thermographic images of breast and classifies them as normal and abnormal (without cancer and with cancer). This paper focuses on a segmentation method based on a combination of the curvature function k and the gradient vector flow, and for classification, we proposed a convolutional neural network (CNN) using the segmented breast. The aim of this paper is to compare CNN results with other classification techniques. Thus, every breast is characterized by its shape, colour, and texture, as well as left or right breast. These data were used for training as well as to compare the performance of CNN with three classification techniques: tree random forest (TRF), multilayer perceptron (MLP), and Bayes network (BN). CNN presents better results than TRF, MLP, and BN.