On orthogonal projections for dimension reduction and applications in augmented target loss functions for learning problems

The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well as numerical experiments show that a projection does usually not satisfy both objectives at once. In a standard classification problem we determine projections on the input data that balance the objectives and compare subsequent results. Next, we extend our application of orthogonal projections to deep learning tasks and introduce a general framework of augmented target loss functions. These loss functions integrate additional information via transformations and projections of the target data. In two supervised learning problems, clinical image segmentation and music information classification, the application of our proposed augmented target loss functions increase the accuracy

Adaptive Nonparametric Image Parsing

In this paper, we present an adaptive nonparametric solution to the image parsing task, namely annotating each image pixel with its corresponding category label. For a given test image, first, a locality-aware retrieval set is extracted from the training data based on super-pixel matching similarities, which are augmented with feature extraction for better differentiation of local super-pixels. Then, the category of each super-pixel is initialized by the majority vote of the $k$-nearest-neighbor super-pixels in the retrieval set. Instead of fixing $k$ as in traditional non-parametric approaches, here we propose a novel adaptive nonparametric approach which determines the sample-specific k for each test image. In particular, $k$ is adaptively set to be the number of the fewest nearest super-pixels which the images in the retrieval set can use to get the best category prediction. Finally, the initial super-pixel labels are further refined by contextual smoothing. Extensive experiments on challenging datasets demonstrate the superiority of the new solution over other state-of-the-art nonparametric solutions.Comment: 11 page

Learning a Mixture of Deep Networks for Single Image Super-Resolution

Single image super-resolution (SR) is an ill-posed problem which aims to recover high-resolution (HR) images from their low-resolution (LR) observations. The crux of this problem lies in learning the complex mapping between low-resolution patches and the corresponding high-resolution patches. Prior arts have used either a mixture of simple regression models or a single non-linear neural network for this propose. This paper proposes the method of learning a mixture of SR inference modules in a unified framework to tackle this problem. Specifically, a number of SR inference modules specialized in different image local patterns are first independently applied on the LR image to obtain various HR estimates, and the resultant HR estimates are adaptively aggregated to form the final HR image. By selecting neural networks as the SR inference module, the whole procedure can be incorporated into a unified network and be optimized jointly. Extensive experiments are conducted to investigate the relation between restoration performance and different network architectures. Compared with other current image SR approaches, our proposed method achieves state-of-the-arts restoration results on a wide range of images consistently while allowing more flexible design choices. The source codes are available in http://www.ifp.illinois.edu/~dingliu2/accv2016

Sparse-to-Dense: Depth Prediction from Sparse Depth Samples and a Single Image

We consider the problem of dense depth prediction from a sparse set of depth measurements and a single RGB image. Since depth estimation from monocular images alone is inherently ambiguous and unreliable, to attain a higher level of robustness and accuracy, we introduce additional sparse depth samples, which are either acquired with a low-resolution depth sensor or computed via visual Simultaneous Localization and Mapping (SLAM) algorithms. We propose the use of a single deep regression network to learn directly from the RGB-D raw data, and explore the impact of number of depth samples on prediction accuracy. Our experiments show that, compared to using only RGB images, the addition of 100 spatially random depth samples reduces the prediction root-mean-square error by 50% on the NYU-Depth-v2 indoor dataset. It also boosts the percentage of reliable prediction from 59% to 92% on the KITTI dataset. We demonstrate two applications of the proposed algorithm: a plug-in module in SLAM to convert sparse maps to dense maps, and super-resolution for LiDARs. Software and video demonstration are publicly available.Comment: accepted to ICRA 2018. 8 pages, 8 figures, 3 tables. Video at https://www.youtube.com/watch?v=vNIIT_M7x7Y. Code at https://github.com/fangchangma/sparse-to-dens