TY - JOUR

T1 - Antipodally invariant metrics for fast regression-based super-resolution

AU - Perez-Pellitero, Eduardo

AU - Salvador, Jordi

AU - Ruiz-Hidalgo, Javier

AU - Rosenhahn, Bodo

N1 - Funding information: This work was supported in part by the Spanish Ministerio de Economia y Competitividad through the European Regional Development Fund under Project TEC2013-43935-R, in part by the European Research Council within the Starting Grant Dynamic MinVIP, and in part the Cluster of Excellence Rebirth.

PY - 2016/6

Y1 - 2016/6

N2 - Dictionary-based super-resolution (SR) algorithms usually select dictionary atoms based on the distance or similarity metrics. Although the optimal selection of the nearest neighbors is of central importance for such methods, the impact of using proper metrics for SR has been overlooked in literature, mainly due to the vast usage of Euclidean distance. In this paper, we present a very fast regression-based algorithm, which builds on the densely populated anchored neighborhoods and sublinear search structures. We perform a study of the nature of the features commonly used for SR, observing that those features usually lie in the unitary hypersphere, where every point has a diametrically opposite one, i.e., its antipode, with same module and angle, but the opposite direction. Even though, we validate the benefits of using antipodally invariant metrics, most of the binary splits use Euclidean distance, which does not handle antipodes optimally. In order to benefit from both the worlds, we propose a simple yet effective antipodally invariant transform that can be easily included in the Euclidean distance calculation. We modify the original spherical hashing algorithm with this metric in our antipodally invariant spherical hashing scheme, obtaining the same performance as a pure antipodally invariant metric. We round up our contributions with a novel feature transform that obtains a better coarse approximation of the input image thanks to iterative backprojection. The performance of our method, which we named antipodally invariant SR, improves quality (Peak Signal to Noise Ratio) and it is faster than any other state-of-the-art method.

AB - Dictionary-based super-resolution (SR) algorithms usually select dictionary atoms based on the distance or similarity metrics. Although the optimal selection of the nearest neighbors is of central importance for such methods, the impact of using proper metrics for SR has been overlooked in literature, mainly due to the vast usage of Euclidean distance. In this paper, we present a very fast regression-based algorithm, which builds on the densely populated anchored neighborhoods and sublinear search structures. We perform a study of the nature of the features commonly used for SR, observing that those features usually lie in the unitary hypersphere, where every point has a diametrically opposite one, i.e., its antipode, with same module and angle, but the opposite direction. Even though, we validate the benefits of using antipodally invariant metrics, most of the binary splits use Euclidean distance, which does not handle antipodes optimally. In order to benefit from both the worlds, we propose a simple yet effective antipodally invariant transform that can be easily included in the Euclidean distance calculation. We modify the original spherical hashing algorithm with this metric in our antipodally invariant spherical hashing scheme, obtaining the same performance as a pure antipodally invariant metric. We round up our contributions with a novel feature transform that obtains a better coarse approximation of the input image thanks to iterative backprojection. The performance of our method, which we named antipodally invariant SR, improves quality (Peak Signal to Noise Ratio) and it is faster than any other state-of-the-art method.

KW - antipodes

KW - regression

KW - spherical hashing

KW - Super-resolution

UR - http://www.scopus.com/inward/record.url?scp=84964627183&partnerID=8YFLogxK

U2 - 10.1109/tip.2016.2549362

DO - 10.1109/tip.2016.2549362

M3 - Article

AN - SCOPUS:84964627183

VL - 25

SP - 2456

EP - 2468

JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

SN - 1057-7149

IS - 6

M1 - 7445242

ER -