One of the main theoretical challenges of vision science is to explain how the visual system interpolates missing structure. Two forms of visual completion have been distinguished on the basis of the phenomenological states that they induce. Modal completion refers to the formation of visible surfaces and/or contours in image regions where these properties are not specified locally. Amodal comp...

For a Heyting algebra A, we show that the following conditions are equivalent: (i) A is profinite; (ii) A is finitely approximable, complete, and completely joinprime generated; (iii) A is isomorphic to the Heyting algebra Up(X) of upsets of an image-finite poset X. We also show that A is isomorphic to its profinite completion iff A is finitely approximable, complete, and the kernel of every fi...

Object recognition, robot vision, image and film restoration may require the ability to perform disocclusion. We call disocclusion the recovery of occluded areas in a digital image by interpolation from their vicinity. It is shown in this paper how disocclusion can be performed by means of the level-lines structure, which offers a reliable, complete and contrast-invariant representation of imag...

Images posted to a social media site can employ image completion techniques to efficiently and seamlessly remove sensitive content and safeguard privacy. Image completion algorithms typically employ a time consuming patch matching stage derived nearest neighbour search algorithms. Typical patch matching processes perform poorly in the social media context which performs once-off edits on a rang...

This paper studies the problem of the restoration of images corrupted by mixed Gaussian-impulse noise. In recent years, low-rank matrix reconstruction has become a research hotspot in many scientific and engineering domains such as machine learning, image processing, computer vision and bioinformatics, which mainly involves the problem of matrix completion and robust principal component analysi...

The applications of super-resolution (SR) technology in the field image completion are successful. Nevertheless, industry demand not only but also topology and time-series completion. In this article, SR on a graph is studied scenario recovering measurements power distribution systems for cost saving security & stability improvement. flow voltage magnitude feeders reported at different frequenc...

Recently, there is a revival of interest in low-rank matrix completion-based unsupervised learning through the lens dual-graph regularization, which has significantly improved performance multidisciplinary machine tasks such as recommendation systems, genotype imputation and image inpainting. While regularization contributes major part success, computational costly hyper-parameter tunning usual...

We provide the explicit solutions of linear, left-invariant, (convection)-diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = RoT. These diffusion equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by groupconvolution with the corresponding Green...

The work investigates the powerlocales (lower, upper, Vietoris) of localic completions of generalized metric spaces. The main result is that all three are localic completions of generalized metric powerspaces, on the Kuratowski finite powerset. Applications: (1) A localic completion is always open, and is compact iff its generalized metric space is totally bounded. (2) The Heine-Borel Theorem i...

In recent years, tensor completion problem has received a significant amount of attention in computer vision, data mining and neuroscience. It is the higher order generalization of matrix completion. And these can be solved by the convex relaxation which minimizes the tensor nuclear norm instead of the n-rank of the tensor. In this paper, we introduce the weighted nuclear norm for tensor and de...