Accurate segmentation of the breast region in a breast thermogram is a very crucial step in the diagnosis of breast cancer, and at the same time, it is also a very challenging problem. To tackle issues related to the breast region segmentation, first, we have proposed a novel method to identify the upper boundary (UB) of the breast based on the arc approximation algorithm. Then, the lower boundary curve (LBC) of the breast is identified by the segregation of the inframammary fold region (IFR) of the breast followed by an IFR isolation method. The actual LBC of the breast is traced in the respective edge image using the segmented IFR of that breast. Then, the traced LBC is extrapolated on both the sides using our proposed triangular-space search technique. Finally, the two breasts are separated based on the point-of-intersection (PoI) of LBCs of breasts. The efficacy of the proposed method is validated on the images of Database for Mastology Research with Infrared Images (DMR-IR) database both qualitatively and quantitatively based on the ground-truths. The average segmentation accuracy of 95.75% confirms the superiority of our method in segmenting the breast region over the existing state-of-the-art breast region segmentation methods.