Image super-pixels segmentation method based on the non-convex low-rank and sparse constraints

Image super-pixels segmentation is considered as the subspace clustering problem. A new constraint condition is presented to be equivalent to using the clean data as the dictionary. The non-convex proximal p-norm of the coefficients matrix is used for the sparse constraint, and, the non-convex proximal p-norm of the singular values of the coefficients matrix is used for the low-rank constraint. Then a non-convex minimization model is proposed. The augmented Lagrangian method and the AM (alternating minimization) method are applied for solving the unknown matrices. The results of numerical experiments show that the constraint condition presented in this paper is better than using the original data as the dictionary, and that the non-convex proximal p-norm has a better segmentation result than the convex nuclear norm and l1 norm.