Distributed Low-rank Subspace Segmentation

Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and corrupted input data. Low-Rank Representation (LRR), a convex formulation of the subspace segmentation problem, is provably and empirically accurate on small problems but does not scale to the massive sizes of modern vision datasets. Moreover, past work aimed at scaling up low-rank matrix factorization is not applicable to LRR given its non-decomposable constraints. In this work, we propose a novel divide-and-conquer algorithm for large-scale subspace segmentation that can cope with LRR's non-decomposable constraints and maintains LRR's strong recovery guarantees. This has immediate implications for the scalability of subspace segmentation, which we demonstrate on a benchmark face recognition dataset and in simulations. We then introduce novel applications of LRR-based subspace segmentation to large-scale semi-supervised learning for multimedia event detection, concept detection, and image tagging. In each case, we obtain state-of-the-art results and order-of-magnitude speed ups

Pooling-Invariant Image Feature Learning

Unsupervised dictionary learning has been a key component in state-of-the-art computer vision recognition architectures. While highly effective methods exist for patch-based dictionary learning, these methods may learn redundant features after the pooling stage in a given early vision architecture. In this paper, we offer a novel dictionary learning scheme to efficiently take into account the invariance of learned features after the spatial pooling stage. The algorithm is built on simple clustering, and thus enjoys efficiency and scalability. We discuss the underlying mechanism that justifies the use of clustering algorithms, and empirically show that the algorithm finds better dictionaries than patch-based methods with the same dictionary size

Confidence Propagation through CNNs for Guided Sparse Depth Regression

Generally, convolutional neural networks (CNNs) process data on a regular grid, e.g. data generated by ordinary cameras. Designing CNNs for sparse and irregularly spaced input data is still an open research problem with numerous applications in autonomous driving, robotics, and surveillance. In this paper, we propose an algebraically-constrained normalized convolution layer for CNNs with highly sparse input that has a smaller number of network parameters compared to related work. We propose novel strategies for determining the confidence from the convolution operation and propagating it to consecutive layers. We also propose an objective function that simultaneously minimizes the data error while maximizing the output confidence. To integrate structural information, we also investigate fusion strategies to combine depth and RGB information in our normalized convolution network framework. In addition, we introduce the use of output confidence as an auxiliary information to improve the results. The capabilities of our normalized convolution network framework are demonstrated for the problem of scene depth completion. Comprehensive experiments are performed on the KITTI-Depth and the NYU-Depth-v2 datasets. The results clearly demonstrate that the proposed approach achieves superior performance while requiring only about 1-5% of the number of parameters compared to the state-of-the-art methods.Comment: 14 pages, 14 Figure