Similarity-Aware Spectral Sparsification by Edge Filtering

In recent years, spectral graph sparsification techniques that can compute ultra-sparse graph proxies have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time spectral sparsification methods first extract low-stretch spanning tree from the original graph to form the backbone of the sparsifier, and then recover small portions of spectrally-critical off-tree edges to the spanning tree to significantly improve the approximation quality. However, it is not clear how many off-tree edges should be recovered for achieving a desired spectral similarity level within the sparsifier. Motivated by recent graph signal processing techniques, this paper proposes a similarity-aware spectral graph sparsification framework that leverages efficient spectral off-tree edge embedding and filtering schemes to construct spectral sparsifiers with guaranteed spectral similarity (relative condition number) level. An iterative graph densification scheme is introduced to facilitate efficient and effective filtering of off-tree edges for highly ill-conditioned problems. The proposed method has been validated using various kinds of graphs obtained from public domain sparse matrix collections relevant to VLSI CAD, finite element analysis, as well as social and data networks frequently studied in many machine learning and data mining applications

Video Registration in Egocentric Vision under Day and Night Illumination Changes

With the spread of wearable devices and head mounted cameras, a wide range of application requiring precise user localization is now possible. In this paper we propose to treat the problem of obtaining the user position with respect to a known environment as a video registration problem. Video registration, i.e. the task of aligning an input video sequence to a pre-built 3D model, relies on a matching process of local keypoints extracted on the query sequence to a 3D point cloud. The overall registration performance is strictly tied to the actual quality of this 2D-3D matching, and can degrade if environmental conditions such as steep changes in lighting like the ones between day and night occur. To effectively register an egocentric video sequence under these conditions, we propose to tackle the source of the problem: the matching process. To overcome the shortcomings of standard matching techniques, we introduce a novel embedding space that allows us to obtain robust matches by jointly taking into account local descriptors, their spatial arrangement and their temporal robustness. The proposal is evaluated using unconstrained egocentric video sequences both in terms of matching quality and resulting registration performance using different 3D models of historical landmarks. The results show that the proposed method can outperform state of the art registration algorithms, in particular when dealing with the challenges of night and day sequences

Segmentation-Aware Convolutional Networks Using Local Attention Masks

We introduce an approach to integrate segmentation information within a convolutional neural network (CNN). This counter-acts the tendency of CNNs to smooth information across regions and increases their spatial precision. To obtain segmentation information, we set up a CNN to provide an embedding space where region co-membership can be estimated based on Euclidean distance. We use these embeddings to compute a local attention mask relative to every neuron position. We incorporate such masks in CNNs and replace the convolution operation with a "segmentation-aware" variant that allows a neuron to selectively attend to inputs coming from its own region. We call the resulting network a segmentation-aware CNN because it adapts its filters at each image point according to local segmentation cues. We demonstrate the merit of our method on two widely different dense prediction tasks, that involve classification (semantic segmentation) and regression (optical flow). Our results show that in semantic segmentation we can match the performance of DenseCRFs while being faster and simpler, and in optical flow we obtain clearly sharper responses than networks that do not use local attention masks. In both cases, segmentation-aware convolution yields systematic improvements over strong baselines. Source code for this work is available online at http://cs.cmu.edu/~aharley/segaware