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.
On D.Y. Gao and X. Lu paper “On the extrema of a nonconvex functional with double-well potential in 1D”