Moving Object Detection by Detecting Contiguous Outliers in the Low-Rank Representation

Object detection is a fundamental step for automated video analysis in many vision applications. Object detection in a video is usually performed by object detectors or background subtraction techniques. Often, an object detector requires manually labeled examples to train a binary classifier, while background subtraction needs a training sequence that contains no objects to build a background model. To automate the analysis, object detection without a separate training phase becomes a critical task. People have tried to tackle this task by using motion information. But existing motion-based methods are usually limited when coping with complex scenarios such as nonrigid motion and dynamic background. In this paper, we show that above challenges can be addressed in a unified framework named DEtecting Contiguous Outliers in the LOw-rank Representation (DECOLOR). This formulation integrates object detection and background learning into a single process of optimization, which can be solved by an alternating algorithm efficiently. We explain the relations between DECOLOR and other sparsity-based methods. Experiments on both simulated data and real sequences demonstrate that DECOLOR outperforms the state-of-the-art approaches and it can work effectively on a wide range of complex scenarios.Comment: 30 page

Convex and Network Flow Optimization for Structured Sparsity

We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l_infinity-norms can be computed exactly in polynomial time by solving a quadratic min-cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such as CUR matrix factorization, multi-task learning of tree-structured dictionaries, background subtraction in video sequences, image denoising with wavelets, and topographic dictionary learning of natural image patches.Comment: to appear in the Journal of Machine Learning Research (JMLR

Structured random measurements in signal processing

Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a minimal number of samples. While this was first shown for (unstructured) Gaussian random measurement matrices, applications require certain structure of the measurements leading to structured random measurement matrices. Near optimal recovery guarantees for such structured measurements have been developed over the past years in a variety of contexts. This article surveys the theory in three scenarios: compressed sensing (sparse recovery), low rank matrix recovery, and phaseless estimation. The random measurement matrices to be considered include random partial Fourier matrices, partial random circulant matrices (subsampled convolutions), matrix completion, and phase estimation from magnitudes of Fourier type measurements. The article concludes with a brief discussion of the mathematical techniques for the analysis of such structured random measurements.Comment: 22 pages, 2 figure

Object detection in videos using principal component pursuit and convolutional neural networks

Object recognition in videos is one of the main challenges in computer vision. Several methods have been proposed to achieve this task, such as background subtraction, temporal differencing, optical flow, particle filtering among others. Since the introduction of Convolutonal Neural Networks (CNN) for object detection in the Imagenet Large Scale Visual Recognition Competition (ILSVRC), its use for image detection and classification has increased, becoming the state-of-the-art for such task, being Faster R-CNN the preferred model in the latest ILSVRC challenges. Moreover, the Faster R-CNN model, with minimum modifications, has been succesfully used to detect and classify objects (either static or dynamic) in video sequences; in such setup, the frames of the video are input “as is” i.e. without any pre-processing. In this thesis work we propose to use Robust PCA (RPCA, a.k.a. Principal Component Pursuit, PCP), as a video background modeling pre-processing step, before using the Faster R-CNN model, in order to improve the overall performance of detection and classification of, specifically, the moving objects. We hypothesize that such pre-processing step, which segments the moving objects from the background, would reduce the amount of regions to be analyzed in a given frame and thus (i) improve the classification time and (ii) reduce the error in classification for the dynamic objects present in the video. In particular, we use a fully incremental RPCA / PCP algorithm that is suitable for real-time or on-line processing. Furthermore, we present extensive computational results that were carried out in three different platforms: A high-end server with a Tesla K40m GPU, a desktop with a Tesla K10m GPU and the embedded system Jetson TK1. Our classification results attain competitive or superior performance in terms of Fmeasure, achieving an improvement ranging from 3.7% to 97.2%, with a mean improvement of 22% when the sparse image was used to detect and classify the object with the neural network, while at the same time, reducing the classification time in all architectures by a factor raging between 2% and 25%.Tesi