基于梯度曲面面积与稀疏约束的图像平滑方法

针对纹理图像在平滑过程中低对比度边缘易丢失和纹理细节抑制不彻底等问题，提出基于梯度曲面面积与稀疏约束的图像平滑方法。首先，将图像视作三维空间中的二维嵌入曲面，再在此基础上分析图像的几何特征并提出梯度曲面面积约束正则化项，以提高纹理抑制性能；其次，根据图像的统计特性，建立L₀梯度稀疏与自适应梯度曲面面积约束的混合正则化约束图像平滑模型；最后，采用交替方向乘子法对非凸非光滑的优化模型进行高效求解。通过纹理抑制、边缘检测、纹理增强和图像融合等方面的实验结果可知，所提出的图像平滑算法克服了L₀梯度最小化平滑方法易造成的阶梯效应和欠滤波等缺陷，能够在去除大量纹理信息的同时保持并锐化图像显著的边缘轮廓。

Image smoothing method based on gradient surface area and sparsity constraints

Concerning the problems of easy loss of low-contrast edges and incomplete suppression of texture details during texture image smoothing, an image smoothing method based on gradient surface area and sparsity constraints was proposed. Firstly, the image was regarded as a two-dimensional embedded surface in three-dimensional space. On this basis, geometric characteristics of the image were analyzed and the regularization term of the gradient surface area constraint was proposed, which improves the texture suppression performance. Secondly, based on the statistical characteristics of the image, a hybrid regularization constrained image smoothing model with L₀ gradient sparseness and adaptive gradient surface area constraints was established. At last, the alternating direction multiplier method was used to solve the non-convex non-smooth optimization model efficiently. The experimental results in texture suppression, edge detection, texture enhancement and image fusion show that the proposed algorithm overcomes the defects of L₀ gradient minimization smoothing method, such as staircase effect and insufficient filtering, and is able to maintain and sharpen the significant edge contours of the image while removing a large amount of texture information.