In this paper, we propose a new approach using a local version of the region-based active contour for object segmentation in images presenting heterogeneity in both the object of interest and the background. The local version was recently developed to deal with heterogeneous appearances by relying on extracting the local instead of global image statistics where the local extracted area is defined by using a disk, sketched at each point along the active contour, with a constant radius size inside and outside the contour. However, the use of a constant radius may prevent the active contour getting more information from its neighborhood and thus being trapped by undesired boundaries. To avoid this error segmentation, the local extracted area using our proposed approach is determined based on using two different radii to extract separately the interior and the exterior local information of the active contour. Using synthetic and real images, our approach shows an improvement in term of computation time and outperforms the conventional methods in noisy images presenting heterogeneity in both the object of interest and the background and using inadequate contour initialization.