Medical image segmentation based on level set and isoperimetric constraint

•A compact constraint is proposed for lesions segmentation on medical images.•The constraint is motivated by isoperimetric inequality to ensure a compact shape.•The constraint also keeps the contour smooth and copes with partial missing edges.•Efficiency of the approach is proved by segmenting various lesions on medical images. Level set based methods are being increasingly used in image segmentation. In these methods, various shape constraints can be incorporated into the energy functionals to obtain the desired shapes of the contours represented by their zero level sets of functions. Motivated by the isoperimetric inequality in differential geometry, we propose a segmentation method in which the isoperimetric constrain is integrated into a level set framework to penalize the ratio of its squared perimeter to its enclosed area of an active contour. The new model can ensure the compactness of segmenting objects and complete missing or/and blurred parts of their boundaries simultaneously. The isoperimetric shape constraint is free of explicit expressions of shapes and scale-invariant. As a result, the proposed method can handle various objects with different scales and does not need to estimate parameters of shapes. Our method can segment lesions with blurred or/and partially missing boundaries in ultrasound, Computed Tomography (CT) and Magnetic Resonance (MR) images efficiently. Quantitative evaluation also confirms that the proposed method can provide more accurate segmentation than two well-known level set methods. Therefore, our proposed method shows potential of accurate segmentation of lesions for applying in diagnoses and surgical planning.