Image Interpolation with Geometric Contour Stencils

Abstract

We consider the image interpolation problem where, given an image v with uniformly-sampled pixels v m,n and point spread function h, the goal is to find a function u(x, y) satisfying v m,n = (h * u)(m, n) for all m, n ∈ Z (1) so that u approximates the underlying function from which v was sampled. This article improves upon the IPOL article "Image Interpolation with Contour Stencils" [7]. In the previous work, contour stencils are used to estimate the image contours locally as short line segments. This article begins with a continuous formulation of total variation integrated over a collection of curves and defines contour stencils as a consistent discretization. This discretization is more reliable than the previous approach and can effectively distinguish contours that are locally shaped like lines, curves, corners, and circles. These improved contour stencils sense more of the geometry in the image. Interpolation is performed using an extension of the method described in the previous article. Using the improved contour stencils, there is an increase in image quality while maintaining similar computational efficiency. Source CodeANSI C source code to produce the same results as the demo is accessible on the article web page http://dx.doi.org/10.5201/ipol.2011.g_igcs. Future software releases and updates will be posted at http://dev.ipol.im/~getreuer/code.

Geometric Total Variation for Image Vectorization, Zooming and Pixel Art Depixelizing

“…To measure its performance, several other super-resolution methods have been tested on the set of images given in the first column of Figure 4, with parameters kept constant across all input images. First, we experimented the method based on geometric stencils proposed by Getreuer [6] with default parameters, which is implemented in the online demonstrator [7]. As shown in the second column of the figure, results appear noisy with oscillations near edges, which are well visible on pixel art images (e.g.…”

“…For instance linear/cubic interpolation just fits linear/cubic functions, but much more complicated spaces have been considered. For instance the method proposed by Getreuer introduces the concept of contour stencils [6,7] to accurately estimate the edge orientation. Roussos and Maragos proposed another strategy using a tensor driven diffusion [19] (see also [8]).…”

Image Processing in the Optical Microscopy: Decoding, Photometry Correction and Compression

“…The correlation method is used to put in correspondence pixels in a recovering zone. The idea is to define a similarity measurement between the pixels of two images [6].…”