The classic region-based filter for edge extraction for polarimetric synthetic aperture radar images is theoretically founded and efficient. However, in practical use, its performance is limited because the assumption of independence and identical distribution is often not met, particularly in heterogeneous areas. In this letter, we present a degenerate filter design integrated with the weighted maximum likelihood estimation to overcome this limitation. The performance of the proposed methodology is presented and analyzed on both simulated and real experimental data sets using visual presentation, as well as numerical evaluation and comparison with the classic method. They both demonstrate the availability and advantage of the proposed method.