PDE-based Image Inpainting Research Articles

A linear fourth-order PDE-based gray-scale image inpainting model

In this paper, we will present a variational PDE-based image inpainting model in which we have used the square of the $$L^2$$ norm of Hessian of the image u as regularization term. The Euler–Lagrange equation will lead us to a fourth-order linear PDE. For time discretization, we have used convexity splitting and the resulting semi-discrete scheme is solved in Fourier domain. Stability analysis for the semi-discrete scheme is carried out. We will demonstrate some numerical results and compare with $$\text {TV}-L^2$$ and $$\text {TV}-H^{-1}$$ model.

PDE-based unsupervised repair of hair-occluded information in dermoscopy images of melanoma

The repair of hair-occluded information is one of the key problems for the precise segmentation and analysis of the skin malignant melanoma image with hairs. Aimed at dermoscopy images of pigmented skin lesions, an unsupervised repair algorithm for the hair-occluded information is proposed in this paper. This algorithm includes three steps: first, the melanoma image with hairs are enhanced by morphologic closing-based top-hat operator and then segmented through statistic threshold; second, the hairs are extracted based on the elongate of connected region; third, the hair-occluded information is repaired by the PDE-based image inpainting. As a matter of fact, with the morphologic closing-based top-hat operator both strong and weak hairs can be enhanced simultaneously, and the elongate state of band-like connected region can be correctly described by the elongate function proposed in this paper so as to measure the hair effectively. Therefore, the unsupervised repair problem of the hair-occluded information can be resolved very well through combining the hair extracting with the image inpainting technology. The experiment results show that the repaired images can satisfy the requirement of medical diagnosis by the proposed algorithm and the segmentation veracity is effectively improved after repairing the hair-occluded information.

Strong-continuation, contrast-invariant inpainting with a third-order optimal PDE

PDE-based image inpainting has become a very active area of research after the pioneering works of Masnou and Morel, Bertalmío et al., and Ballester et al. In this paper, we take a different approach, inspired by the excellent work of Caselles et al. We view the inpainting problem as a particular case of image interpolation in which we intend to propagate level lines. Expressing this in terms of local neighborhoods and using a Taylor expansion we derive a third-order PDE that performs inpainting. This PDE is optimal in the sense that it is the most accurate third-order PDE which can ensure continuation of level lines. The continuation is strong, allowing the restoration of thin structures occluded by a wide gap. The result is also contrast invariant. This is a novel PDE, which, in both its accuracy and contrast invariance, outperforms the approaches cited above.