A morphological approach to piecewise constant active contour model incorporated with the geodesic edge term

Abstract

Traditional level set-based image segmentation method has to solve the level set evolution equation which is the Euler–Lagrange equation of the energy functional defined on the image domain. Solving level set evolution equation is very time-consuming, and reinitialization is usually needed. The level set evolution equation can also be solved by mathematical morphology. The morphological implementation is very simple, fast and stable. The piecewise constant active contour model incorporated with the geodesic edge term is a hybrid active contour model which combines two active contour models which are active contour model without edges and geodesic active contour model. In this paper, the mathematical morphology-based level set evolution method is applied to the piecewise constant active contour model incorporated with the geodesic edge term. The curvature morphological operator is also improved. Experimental results show that, compared with the original piecewise constant active contour model incorporated the geodesic edge term, the new mathematical morphology-based model can segment images more accurately and there are significant gains in simplicity, speed and stability. The new mathematical morphology-based model is also compared to morphological piecewise constant active contour model, morphological geodesic active contour model, traditional piecewise constant active contour model and two other active contour models. Results show that the proposed method gets the segmentation result with faster speed and higher accuracy.