PDE-based　image　segmentation　based　on　the　active　contour　model　attracts　many　researchers　due　to　its　high　precision　of　edge　detection　and　the　continuity　of　boundaries.　Its　basic　idea　is　to　define　an　energy　functional　on　a　dynamic　curve　which　achieves　its　minimum　when　the　curve　conforms　to　the　boundary　of　the　objects.　Thus,　the　image　segmentation　problem　is　in　essence　an　optimization　problem.　The　most　widely　used　optimization　method　is　the　gradient　descent　method　in　PDE-based　image　segmentation.　However,　the　convergence　of　the　gradient　descent　method　is　very　poor.　In　this　paper,　a　quasi-Newton　method　is　extended　to　the　generalized　quasi-Newton　method,　and　then　the　generalized　Newton　method　and　the　generalized　quasi-Newton　method　are　used　to　solve　a　simple　region-based　model　and　compared　with　the　gradient　decent　method.　Experimental　results　show　that　the　generalized　quasi-Newton　method　has　accurate　segmentation　results　in　the　least　possible　number　of　iteration.　Moreover　it　is　able　to　segment　noisy　images　correctly.