Mixed geometry information regularization for image multiplicative denoising

This paper focuses on solving the multiplicative gamma denoising problem via a variation model. Variation-based regularization models have been extensively employed in a variety of inverse problem tasks in image processing. However, sufficient geometric priors and efficient algorithms are still very difficult problems in the model design process. To overcome these issues, in this paper we propose a mixed geometry information model, incorporating area term and curvature term as prior knowledge. In addition to its ability to effectively remove multiplicative noise, our model is able to preserve edges and prevent staircasing effects. Meanwhile, to address the challenges stemming from the nonlinearity and non-convexity inherent in higher-order regularization, we propose the efficient additive operator splitting algorithm (AOS) and scalar auxiliary variable algorithm (SAV). The unconditional stability possessed by these algorithms enables us to use large time step. And the SAV method shows higher computational accuracy in our model. We employ the second order SAV algorithm to further speed up the calculation while maintaining accuracy. We demonstrate the effectiveness and efficiency of the model and algorithms by a lot of numerical experiments, where the model we proposed has better features texturepreserving properties without generating any false information.

Re-initialization-free Level Set Method via Molecular Beam Epitaxy Equation Regularization for Image Segmentation

Variational level set method has become a powerful tool in image segmentation due to its ability to handle complex topological changes and maintain continuity and smoothness in the process of evolution. However its evolution process can be unstable, which results in over flatted or over sharpened contours and segmentation failure. To improve the accuracy and stability of evolution, we propose a high-order level set variational segmentation method integrated with molecular beam epitaxy (MBE) equation regularization. This method uses the crystal growth in the MBE process to limit the evolution of the level set function, and thus can avoid the re-initialization in the evolution process and regulate the smoothness of the segmented curve. It also works for noisy images with intensity inhomogeneity, which is a challenge in image segmentation. To solve the variational model, we derive the gradient flow and design scalar auxiliary variable (SAV) scheme coupled with fast Fourier transform (FFT), which can significantly improve the computational efficiency compared with the traditional semi-implicit and semi-explicit scheme. Numerical experiments show that the proposed method can generate smooth segmentation curves, retain fine segmentation targets and obtain robust segmentation results of small objects. Compared to existing level set methods, this model is state-of-the-art in both accuracy and efficiency.