一种提花织物图像的有限元分割算法

A Finite Element Segmentation Algorithm for Jacquard Image

提花织物图像分割是提花图案设计的关键,曲线演化模型是一种流行的图像分割方法,但是该方法无法检测含噪环境下的图像特征.由于Mumford-Shah(MS)模型能够在噪声环境下对不连续边集进行检测,因此它比曲线演化模型更适于对含噪提花织物图像的分割.提出一种结合有限元法和拟牛顿法的MS模型数值求解算法,并有效用于含噪提花织物图像的分割.首先定义了自适应三角剖分空间上的离散MS模型,并在每次迭代前对有限元网格进行自适应调整,以提高迭代的性能.接着采用拟牛顿最小化方法,通过收敛意义上的离散有限元逼近得到离散MS模型的最小值.该算法被用到含噪提花织物图像的分割中,取得了良好的效果.

Jacquard image segmentation is the linchpin of jacquard pattern design. Curve evolution model is a popular method for image segmentation. However, it cannot detect image features in the presence of noise. The Mumford-Shah model is more robust than curve evolution model to detect discontinuities under noisy environment, so it is more suitable for segmentation of noisy jacquard images. In this paper, an algorithm is presented to implement the numerical solving of the Mumford-Shah model, which combines the merits of finite element method and quasi-Newton method. First, a discrete version of the model is defined on finite element spaces over adaptive triangulation. Then an adjustment scheme for the triangulation is enforced to improve the iteration efficiency before current iteration begins. Finally, a minimization method based on quasi-Newton algorithm is applied to find the absolute minimum of the discrete model in the sense of Gamma-convergence. The proposed algorithm works well when it is applied to segment noisy jacquard images.