Summary: In this paper we propose a new model for segmentation of an image under some geometrical constraints in order to detect special regions of interest. Our work is based on the recent work by C. Gout et al. [Numer. Algorithms 39, No. 1–3, 155–173 (2005; Zbl 1069.65016); C. Le Guyader and C. Gout, ibid. 48, No. 1–3, 105–133 (2008; Zbl 1146.65024)] using geodesic active contours models, by combining it with the idea of a piecewise constant Mumford-Shah model as with the non-selective Chan-Vese segmentation. Numerical tests show that our method is more robust than the previous works.