Eirikur Agustsson

NTIRE 2017 Challenge on Single Image Super-Resolution: Methods and Results

This paper reviews the first challenge on single image super-resolution (restoration of rich details in an low resolution image) with focus on proposed solutions and results. A new DIVerse 2K resolution image dataset (DIV2K) was employed. The challenge had 6 competitions divided into 2 tracks with 3 magnification factors each. Track 1 employed the standard bicubic downscaling setup, while Track 2 had unknown downscaling operators (blur kernel and decimation) but learnable through low and high res train images. Each competition had ∽100 registered participants and 20 teams competed in the final testing phase. They gauge the state-of-the-art in single image super-resolution.

NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study

This paper introduces a novel large dataset for example-based single image super-resolution and studies the state-of-the-art as emerged from the NTIRE 2017 challenge. The challenge is the first challenge of its kind, with 6 competitions, hundreds of participants and tens of proposed solutions. Our newly collected DIVerse 2K resolution image dataset (DIV2K) was employed by the challenge. In our study we compare the solutions from the challenge to a set of representative methods from the literature and evaluate them using diverse measures on our proposed DIV2K dataset. Moreover, we conduct a number of experiments and draw conclusions on several topics of interest. We conclude that the NTIRE 2017 challenge pushes the state-of-the-art in single-image super-resolution, reaching the best results to date on the popular Set5, Set14, B100, Urban100 datasets and on our newly proposed DIV2K.

Neighborhood selection for thresholding-based subspace clustering

Subspace clustering refers to the problem of clustering high-dimensional data points into a union of low-dimensional linear subspaces, where the number of subspaces, their dimensions and orientations are all unknown. In this paper, we propose a variation of the recently introduced thresholding-based subspace clustering (TSC) algorithm, which applies spectral clustering to an adjacency matrix constructed from the nearest neighbors of each data point with respect to the spherical distance measure. The new element resides in an individual and data-driven choice of the number of nearest neighbors. Previous performance results for TSC, as well as for other subspace clustering algorithms based on spectral clustering, come in terms of an intermediate performance measure, which does not address the clustering error directly. Our main analytical contribution is a performance analysis of the modified TSC algorithm (as well as the original TSC algorithm) in terms of the clustering error directly.

Regressor Basis Learning for anchored super-resolution

A+ aka Adjusted Anchored Neighborhood Regression - is a state-of-the-art method for exemplar-based single image super-resolution with low time complexity at both train and test time. By robustly training a clustered regression model over a low-resolution dictionary, its performance keeps improving with the dictionary size - even when using tens of thousands of regressors. However, this can pose a memory issue where the model size can grow to more than a gigabyte, limiting applicability in memory constrained scenarios. To address this, we propose Regressor Basis Learning (RB), a novel variant of A+ where we restrict the regressor set to a learned low-dimensional subspace, such that each regressor is coded as a linear combination of few basis regressors. We learn the regressor basis by alternating between closed form solutions of the optimal coding of the regressor set (given the basis) and the optimal regressor basis (given the coding). We validate RB on several standard benchmarks and achieve comparable performance to A+ but by using orders of magnitude fewer basis regressors, ie. 32 basis regressors instead of 1024 regressors. This makes our RB method ideal for memory constrained applications.

Apparent and Real Age Estimation in Still Images with Deep Residual Regressors on Appa-Real Database

After decades of research, the real (biological) age estimation from a single face image reached maturity thanks to the availability of large public face databases and impressive accuracies achieved by recently proposed methods. The estimation of “apparent age” is a related task concerning the age perceived by human observers. Significant advances have been also made in this new research direction with the recent Looking At People challenges. In this paper we make several contributions to age estimation research. (i) We introduce APPA-REAL, a large face image database with both real and apparent age annotations. (ii)We study the relationship between real and apparent age. (iii) We develop a residual age regression method to further improve the performance. (iv) We show that real age estimation can be successfully tackled as an apparent age estimation followed by an apparent to real age residual regression. (v) We graphically reveal the facial regions on which the CNN focuses in order to perform apparent and real age estimation tasks.

Almost Lossless Analog Signal Separation and Probabilistic Uncertainty Relations

We propose an information-theoretic framework for analog signal separation. Specifically, we consider the problem of recovering two analog signals, modeled as general random vectors, from the noiseless sum of linear measurements of the signals. Our framework is inspired by the groundbreaking work of Wu and Verdú (2010) on analog compression and encompasses, inter alia, inpainting, declipping, super-resolution, the recovery of signals corrupted by impulse noise, and the separation of (e.g., audio or video) signals into two distinct components. The main results we report are general achievability bounds for the compression rate, i.e., the number of measurements relative to the dimension of the ambient space the signals live in, under either measurability or Hölder continuity imposed on the separator. Furthermore, we find a matching converse for sources of mixed discrete-continuous distribution. For measurable separators our proofs are based on a new probabilistic uncertainty relation, which shows that the intersection of generic subspaces with general sets of sufficiently small Minkowski dimension is empty. Hölder continuous separators are dealt with by introducing the concept of regularized probabilistic uncertainty relations. The probabilistic uncertainty relations we develop are inspired by embedding results in dynamical systems theory due to Sauer et al. (1991) and—conceptually—parallel classical Donoho-Stark and Elad-Bruckstein uncertainty principles at the heart of compressed sensing theory. Operationally, the new uncertainty relations take the theory of sparse signal separation beyond traditional sparsity—as measured in terms of the number of non-zero entries—to the more general notion of low description complexity as quantified by Minkowski dimension. Finally, our approach also allows to significantly strengthen key results in Wu and Verdú (2010).

From face images and attributes to attributes

The face is an important part of the identity of a person. Numerous applications benefit from the recent advances in prediction of face attributes, including biometrics (like age, gender, ethnicity) and accessories (eyeglasses, hat). We study the attributes’ relations to other attributes and to face images and propose prediction models for them. We show that handcrafted features can be as good as deep features, that the attributes themselves are powerful enough to predict other attributes and that clustering the samples according to their attributes can mitigate the training complexity for deep learning. We set new state-of-the-art results on two of the largest datasets to date, CelebA and Facebook BIG5, by predicting attributes either from face images, from other attributes, or from both face and other attributes. Particularly, on Facebook dataset, we show that we can accurately predict personality traits (BIG5) from tens of ‘likes’ or from only a profile picture and a couple of ‘likes’ comparing positively to human reference.

k2-means for fast and accurate large scale clustering

We propose \(k^2\)-means, a new clustering method which efficiently copes with large numbers of clusters and achieves low energy solutions. \(k^2\)-means builds upon the standard k-means (Lloyd’s algorithm) and combines a new strategy to accelerate the convergence with a new low time complexity divisive initialization. The accelerated convergence is achieved through only looking at \(k_n\) nearest clusters and using triangle inequality bounds in the assignment step while the divisive initialization employs an optimal 2-clustering along a direction. The worst-case time complexity per iteration of our \(k^2\)-means is \(O(nk_nd\,+\,k^2d)\), where d is the dimension of the n data points and k is the number of clusters and usually \(n\gg k \gg k_n\). Compared to k-means’ O(nkd) complexity, our \(k^2\)-means complexity is significantly lower, at the expense of slightly increasing the memory complexity by \(O(nk_n+k^2)\). In our extensive experiments \(k^2\)-means is order(s) of magnitude faster than standard methods in computing accurate clusterings on several standard datasets and settings with hundreds of clusters and high dimensional data. Moreover, the proposed divisive initialization generally leads to clustering energies comparable to those achieved with the standard k-means++ initialization, while being significantly faster.