TY - GEN

T1 - Half hypersphere confinement for piecewise linear regression

AU - Perez-Pellitero, Eduardo

AU - Salvador, Jordi

AU - Ruiz-Hidalgo, Javier

AU - Rosenhahn, Bodo

PY - 2016/5/23

Y1 - 2016/5/23

N2 - 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 SuperResolution (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.

AB - 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 SuperResolution (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.

UR - http://www.scopus.com/inward/record.url?scp=84977649970&partnerID=8YFLogxK

U2 - 10.1109/wacv.2016.7477651

DO - 10.1109/wacv.2016.7477651

M3 - Conference contribution

AN - SCOPUS:84977649970

BT - 2016 IEEE Winter Conference on Applications of Computer Vision, WACV 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - IEEE Winter Conference on Applications of Computer Vision, WACV 2016

Y2 - 7 March 2016 through 10 March 2016

ER -