An adaptive level set evolution equation for contour extraction

Level set evolution without re-initialization is a novel variational level set method for edge contour extraction, which has many advantages over the traditional level set formulations. The resulting evolution equation is derived from the minimization of an energy functional which is a linear combination of a weighted length, weighted area and deviation penalization energy. However, the zero level set always keeps evolving in only one direction during evolution, depending on the sign of the scale parameter associated with the weighted area. This inconvenient makes the evolution highly sensitive to the contour initializations. In this paper, we propose an adaptive level set evolution equation following this method, wherein the scale parameter associated with the weighted area is modified as an adaptive variable sign function and one of two terms associated with the weighted length is removed to reduce computational cost. The proposed equation avoids completely the intrinsic limitation mentioned above and offers many advantages over the original equation, as illustrated by several examples of contour extraction, such as robustness to noise and detection of objects with discontinuous boundaries.