# Image Interpolation with Geometric Contour Stencils

P. Getreuer, “Image Interpolation with Geometric Contour Stencils.” *Image Processing On Line*, 2011. DOI: 10.5201/ipol.2011.g_igcs.

Article permalink: http://dx.doi.org/10.5201/ipol.2011.g_igcs

```
@article{getreuer2011geometric,
title = {Image Interpolation with Geometric Contour Stencils},
author = {Pascal Getreuer},
journal = {Image Processing On Line},
year = {2011},
doi = {10.5201/ipol.2011.g_igcs},
}
```

This work was published jointly with SIIMS article “Contour Stencils: Total Variation along Curves for Adaptive Image Interpolation.”

## 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 function \(u(x,y)\) satisfying so that \(u\) approximates the underlying function from which \(v\) was sampled. This article is a joint submission with [8] and improves upon the IPOL article Image Interpolation with Contour Stencils [7]. In [7], 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.

©2011, IPOL Image Processing On Line & the authors.