Image Inpainting Based on Coherence Transport with Adapted Distance Functions

Abstract

Abstract.We discuss an extension of our method image inpainting based on coherence transport. For the latter method the pixels of the inpainting domain have to be serialized into an ordered list. Until now, to induce the serialization we have used the distance to boundary map. But there are inpainting problems where the distance to boundary serialization causes unsatisfactory inpainting results. In the present work we demonstrate cases where we can resolve the difficulties by employing other distance functions which better suit the problem at hand. Key words. image processing, image inpainting, distance functions AMS subject classifications. 65D18, 51K99DOI. 10.1137/1008072961. Introduction. Nontexture image inpainting, also termed image interpolation, is the task of determining the values of a digital image for a destroyed, or consciously masked, subregion of the image domain.The simple idea of the generic single pass method-which forms the basis for our method image inpainting based on coherence transport published in [5]-is to fill the inpainting domain by traversing its pixels in an onion peeling fashion from the boundary inward and thereby setting new image values as weighted means of given or already calculated ones.Telea has been the first to use such an algorithm in [13]: the pixels are serialized according to their Euclidean distance to the boundary of the inpainting domain, and the weight is such that image values are propagated mainly along the gradient of the distance map. By his choices of the weight and the pixel serialization, the method of Telea is not adapted to the image.In [5], we addressed the adaption of the weight: our method uses an image dependent weight such that image values are propagated along the estimated tangents of color lines which have been interrupted by the inpainting domain. In that way we could improve the quality of the inpainting results compared to Telea (see Figure 1). Beyond that, we illustrated in [5] Figure 2 illustrates. The image in the middle shows the

Using digital inpainting to estimate incident light intensity for the calculation of red blood cell oxygen saturation from microscopy images

“…If the direction field is parallel to the domain boundary (ie, ), the fast‐marching scheme will convect the image information perpendicular to the boundary instead of along the convection field. For this reason, we exclude parts of the boundary that are parallel to the convection field in the determination of the distance ordering, as in the study by März . Specifically, we require that: …”

“…In order to solve this nonlinear convection problem rapidly, we discretize and solve the PDE using a fast-marching scheme as described in various studies. [23][24][25] A fastmarching scheme is solved by calculating each point in the domain sequentially following a specified order. The value at each point, x !…”

A Universal Variational Framework for Sparsity-Based Image Inpainting

“…In these examples, we compare the effects of different regularization operator in our framework and we also compare our method with some of the existing pixelbased and patch-based inpainting methods. These methods include cubic interpolation based on Delaunay triangulation (implemented by MATLAB routine "griddata"), sparsity based methods ECM [19] and MCA [18] (the source codes MCAlab can be downloaded from web page 1 ), exemplar based method (EBM for short) in [24], coherence transport method [13] (CTM for short, see the source codes on webpage 2 ) and smooth ordering patches based method SOP [21]. All the key parameters are tuned carefully in each method and the optimal result is chosen to compare.…”

“…Tai et al [11] proposed an efficient algorithm for Euler elastica inpainting model. Marz et al [12], [13] proposed fast inpainting method based on coherence transportation. Ng et al [14] proposed to use the augmented Lagrangian method to solve the coupled problem of blurred image decomposition and inpainting.…”

Explicit Coherence Enhancing Filter With Spatial Adaptive Elliptical Kernel

“…The idea of anisotropic diffusion is generalized to Harr wavelet framework and applied in image inpainting problems in [6], [7]. Image inpainting methods based on coherence transport are studied in [3], [4] where the inpainting pixels need to be serialized and fast marching technique is involved in the numerical implementation.…”