Jacquard image segmentation is one of the primary steps in image analysis for jacquard pattern identification. The main aim is to recognize homogeneous regions within a jacquard image as distinct, which belongs to different patterns. Active contour models have become popular for finding the contours of a pattem with a complex shape. However, the performance of active contour models is often inadequate under noisy environment. In this paper, a robust algorithm based on the Mumford-Shah model is proposed for the segmentation of noisy jacquard images. First, the Mumford-Shah model is discretized on piecewise linear finite element spaces to yield greater stability. Then, an iterative relaxation algorithm for numerically solving the discrete version of the model is presented. In this algorithm, an adaptiye triangular mesh is refined to generate Delaunay type triangular mesh defined on structured triangulations, and then a quasi-Newton numerical method is applied to find the absolute minimum of the discrete model. Experimental results on noisy jacquard images demonstrated the efficacy of the proposed algorithm.