The automatic restoration of image colours (inpainting) is an interesting challenge in computer vision. The aim is to restore/recover missing colour information in a region based on the surrounding region information in a way that looks acceptable to the human eye. We investigate two functional formulas based on the difference between the directional derivative of the gradient (and the Laplacian) of two channels. The Euler-Langrage process applied to the two functional produces a nonlinear second order (and a nonlinear fourth order) PDE, the numerical solutions of which restore the colour to the region of interest. The first method extends an already established, but only for one specific colour space. We shall establish the effectiveness of the corresponding image inpainting schemes, in both the spatial and wavelet domains for 8 different colour spaces. We demonstrate the success of both schemes for a large number of natural images with better performance in comparison with the popular Poisson formula.
Image inpainting is the process of filling in the missing region to preserve continuity of its overall content and semantic. In this paper, we present a novel approach to improve an existing scheme, called exemplar-based inpainting algorithm, using Topological Data Analysis (TDA). TDA is a mathematical approach concern studying shapes or objects to gain information about connectivity and closeness property of those objects. The challenge in using exemplar-based inpainting is that missing regions neighborhood area needs to have a relatively simple texture and structure. We studied the topological properties (e.g. number of connected components) of missing regions surrounding the missing area by building a sequence of simplicial complexes (known as persistent homology) based on a selected group of uniform Local binary Pattern LBP. Connected components of image regions generated by certain landmark pixels, at different thresholds, automatically quantify the texture nature of the missing regions surrounding areas. Such quantification help determine the appropriate size of patch propagation. We have modified the patch propagation priority function using geometrical properties of curvature of isophote and improved the matching criteria of patches by calculating the correlation coefficients from spatial, gradient and Laplacian domain. We use several image quality measures to illustrate the performance of our approach in comparison to similar inpainting algorithms. In particular, we shall illustrate that our proposed scheme outperforms the state-of-the-art exemplar-based inpainting algorithms.