Antipodally Invariant Metrics for Fast Regression-Based Super-Resolution

Abstract

Abstract-Dictionary-based Super-Resolution algorithms usually select dictionary atoms based on distance or similarity metrics. Although the optimal selection of nearest neighbors is of central importance for such methods, the impact of using proper metrics for Super-Resolution (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 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 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 worlds, we propose a simple yet effective Antipodally Invariant Transform (AIT) 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 Back Projection. The performance of our method, which we named Antipodally Invariant SuperResolution (AIS), improves quality (PSNR) and it is faster than any other state-of-the-art method.

Piecewise linear regression-based single image super-resolution via Hadamard transform

“…In this section we present our method for fast regression-based SR. Our proposed method is based on the idea of piecewise linear regression presented in [47,48]. It employs an ensemble of piecewise linear mapping models (piecewise linear regressors)…”

“…These LR-HR patch pairs are cropped from a database composed of LR-HR image pairs. Many learning algorithms have been proposed to learn the mapping models, including dictionary learning [17, 18, 22, 40, 41, 46, 56, 58-60, 65, 66, 70, 76], regression [11,47,48,58,59,64], decision tree [24,62], random forest [23,25,53] and convolutional neural network (CNN) [13,14,33,34,36,37,52,57]. Linear regression models [31] have higher prediction speed than non-linear regressions models.…”

“…Linear regression models [31] have higher prediction speed than non-linear regressions models. These methods [11,13,14,33,34,36,37,47,48,52,58,59,64] learn the relationship between the LR space and the HR space, and use it to solve SR problem.…”

“…Timofte et al [58,59] assumed that the mapping relationship between the LR space and the HR space is locally linear and therefore lots of linear regressors are learned and anchored to the feature space as a piecewise linearization. The methods [47,48] divide the feature space into many subspaces based on antipodally invariant metrics and learn a linear regressor for each subspace. In the papers [13,14,33,34,36,37,52], the mapping from the LR space to the HR space is described as a deep CNN that takes an LR image as the input and outputs an HR image, which is an end to end mapping (i.e.…”

Single Image Super-Resolution Quality Assessment: A Real-World Dataset, Subjective Studies, and an Objective Metric

“…The existing SISR algorithms can be classified into two branches: non-deep models and deep models. In this study, we evaluate 10 representative SISR algorithms, including BCI, ASDS [42], SPM [43], Aplus [44], AIS [45], SRCNN [46], CSCN [47], VDSR [48], SRGAN [49], and USRnet [50]. The set of SISR methods considered in our study equally samples from the two branches, i.e., the former five methods are nondeep methods while the latter five methods are deep learningbased SISR methods, and covers recent major publications in the field (either to be widely used or the latest ones).…”