Aiming at the problems of low segmentation accuracy of noise image, poor noise immunity of the existing models and poor adaptability to complex noise environment, a noise image segmentation algorithm using anisotropic diffusion and nonconvex functional was proposed. First, focusing on the “staircase effect”, a nonconvex functional was introduced into the energy functional model for smooth denoising. Second, the validity and accuracy of the model were established by proving that there was no global minimum in the solution space of the nonconvex energy functional model; the improved model was then used to obtain a smooth and clear image edge while maintaining the edge integrity. Third, the smooth image obtained from the nonconvex energy functional model was combined with the level set model to obtain the anisotropic diffusion gray level set model. The optimal outline of the target was obtained by calculating the minimum value of the energy functional. Finally, an anisotropic diffusion equation with nonconvex energy functional model was built in this algorithm to segment noise image accurately and quickly. A series of comparative experiments on the proposed algorithm and similar algorithms were conducted. The results showed that the proposed algorithm had strong noise resistance and provided precise segmentation for noise image.

中文翻译：

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各向异性扩散结合非凸泛函用于噪声图像分割

针对噪声图像分割精度低、现有模型抗噪能力差、对复杂噪声环境适应性差等问题，提出了一种基于各向异性扩散和非凸泛函的噪声图像分割算法。首先，针对“阶梯效应”，在能量泛函模型中引入非凸泛函以实现平滑去噪。其次，通过证明非凸能量泛函模型的解空间中不存在全局最小值，建立了模型的有效性和准确性；然后使用改进的模型来获得平滑清晰的图像边缘，同时保持边缘完整性。第三，将非凸能量泛函模型得到的平滑图像与水平集模型相结合，得到各向异性扩散灰度集模型。通过计算能量泛函的最小值获得目标的最佳轮廓。最后，在该算法中建立了具有非凸能量泛函模型的各向异性扩散方程，以准确、快速地分割噪声图像。对提出的算法和类似算法进行了一系列对比实验。结果表明，该算法具有较强的抗噪声能力，为噪声图像提供了精确的分割。