Quantitative measures of breast morphology can help a breast cancer survivor to understand outcomes of reconstructive surgeries. One bottleneck of quantifying breast morphology is that there are only a few reliable automation algorithms for detecting the breast contour. This study proposes a novel approach for detecting the breast contour, which is based on a parametric active contour model. In addition to employing the traditional parametric active contour model, the proposed approach enforces a mathematical shape constraint based on the catenary curve, which has been previously shown to capture the overall shape of the breast contour reliably. The mathematical shape constraint regulates the evolution of the active contour and helps the contour evolve towards the breast, while minimizing the undesired effects of other structures such as, the nipple/areola and scars. The efficacy of the proposed approach was evaluated on anterior posterior photographs of women who underwent or were scheduled for breast reconstruction surgery including autologous tissue reconstruction. The proposed algorithm shows promising results for detecting the breast contour.