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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.