Localized region-based active contour proposed by S. Lankton and A. Tannenbaum [10] is a segmentation method described in terms of small local regions. Referring to Lankton and Tannenbaum [10] localized region-based active contour denotes x and y as independent spatial variables each representing a single point in Ω. We adopt B(x,y) as a ball (or a circular) mask to define the local region as defined in (4).