Antipodally Invariant Metrics for Fast Regression-Based Super-Resolution

Eduardo Perez-Pellitero, Jordi Salvador, Javier Ruiz-Hidalgo, Bodo Rosenhahn

This is the project website of the papers "Half Hypersphere Confinement for Piecewise Linear Regression" (WACV 2016) and "Antipodally Invariant Metrics for Fast Regression-Based Super-Resolution" (TIP 2016).
[WACV] [TIP] [poster] [SR code]


Abstract

Recent research in piecewise linear regression for Super-Resolution has shown the positive impact of training regressors with densely populated clusters whose datapoints are tight in the Euclidean space. In this paper we further research how to improve the locality condition during the training of regressors and how to better select them during testing time. We study the characteristics of the metrics best suited for the piecewise regression algorithms, in which comparisons are usually made between normalized vectors that lie on the unitary hypersphere. Even though Euclidean distance has been widely used for this purpose, it is suboptimal since it does not handle antipodal points (i.e. diametrically opposite points) properly, as vectors with same module and angle but opposite directions are, for linear regression purposes, identical. Therefore, we propose the usage of antipodally invariant metrics and introduce the Half Hypersphere Confinement (HHC), a fast alternative to Multidimensional Scaling (MDS) that allows to map antipodally invariant distances in the Euclidean space with very little approximation error. By doing so, we enable the usage of fast search structures based on Euclidean distances without undermining their speed gains with complex distance transformations. The performance of our method, which we named HHC Regression (HHCR), applied to Super-Resolution (SR) improves both in quality (PSNR) and it is faster than any other state-of-the-art method. Additionally, under an application-agnostic interpretation of our regression framework, we also test our algorithm for denoising and depth upscaling with promising results.

The implementation to reproduce results can be downloaded here. It is a MATLAB + MEX implementation and we provide binaries both for windows and linux. You can find more information about its usage in the README.txt. We will publish the regressors for the upscaling factor x4 in the upcoming days.

Furthermore, in this website we show a selection of the results published in the paper so that they can be compared in a computer screen. It is programmed to load all the images first so that there is no delay when clicking the buttons. The whole image set weights ~40 MB so it might take some time until it is fully loaded.
When zooming in through the web browser, there is little control on the related upscaling process (which should be nearest neighbor interpolation in order to be as neutral as possible). We recommend to download the results in this zipped file, and inspect them in your system with a proper image viewer.

Please note that the images are initialized with the Ground truth.


1. Luminance Super-Resolution

In this website we compare our super-resolution (SR) method with a subset of methods from the paper benchmark:

[A+] R. Timofte, V. D. Smet, and L. V. Gool. A+: Adjusted anchored neighborhood regression for fast super-resolution. In ACCV 2014.
[SRCNN] C. Dong, C. Loy, K. He, and X. Tang. Learning a deep convolutional network for image super-resolution. In ECCV 2014.
[ASRF] S. Schulter, C. Leistner, and H. Bischof. Fast and accurate image upscaling with super-resolution forests. In CVPR 2015


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