The current tissue evaluation method for breast cancer would greatly benefit from higher throughput and less inter-observer variation. Since quantitative phase imaging (QPI) measures physical parameters of tissue, it can be used to find quantitative markers, eliminating observer subjectivity. Furthermore, since the pixel values in QPI remain the same regardless of the instrument used, classifiers can be built to segment various tissue components without need for color calibration. In this work we use a texton-based approach to segment QPI images of breast tissue into various tissue components (epithelium, stroma or lumen). A tissue microarray comprising of 900 unstained cores from 400 different patients was imaged using Spatial Light Interference Microscopy. The training data were generated by manually segmenting the images for 36 cores and labelling each pixel (epithelium, stroma or lumen.). For each pixel in the data, a response vector was generated by the Leung-Malik (LM) filter bank and these responses were clustered using the k-means algorithm to find the centers (called textons). A random forest classifier was then trained to find the relationship between a pixel's label and the histogram of these textons in that pixel's neighborhood. The segmentation was carried out on the validation set by calculating the texton histogram in a pixel's neighborhood and generating a label based on the model learnt during training. Segmentation of the tissue into various components is an important step toward efficiently computing parameters that are markers of disease. Automated segmentation, followed by diagnosis, can improve the accuracy and speed of analysis leading to better health outcomes.