Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning or robust PCA (RPCA). For long data sequences, if one tries to use a single lower dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition (S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an entire data vector is either an outlier or an inlier. The S+LR formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201

rSVDdpd: A Robust Scalable Video Surveillance Background Modelling Algorithm

A basic algorithmic task in automated video surveillance is to separate background and foreground objects. Camera tampering, noisy videos, low frame rate, etc., pose difficulties in solving the problem. A general approach that classifies the tampered frames, and performs subsequent analysis on the remaining frames after discarding the tampered ones, results in loss of information. Several robust methods based on robust principal component analysis (PCA) have been introduced to solve this problem. To date, considerable effort has been expended to develop robust PCA via Principal Component Pursuit (PCP) methods with reduced computational cost and visually appealing foreground detection. However, the convex optimizations used in these algorithms do not scale well to real-world large datasets due to large matrix inversion steps. Also, an integral component of these foreground detection algorithms is singular value decomposition which is nonrobust. In this paper, we present a new video surveillance background modelling algorithm based on a new robust singular value decomposition technique rSVDdpd which takes care of both these issues. We also demonstrate the superiority of our proposed algorithm on a benchmark dataset and a new real-life video surveillance dataset in the presence of camera tampering. Software codes and additional illustrations are made available at the accompanying website rSVDdpd Homepage (https://subroy13.github.io/rsvddpd-home/

Provable Dynamic Robust PCA or Robust Subspace Tracking

Dynamic robust PCA refers to the dynamic (time-varying) extension of robust PCA (RPCA). It assumes that the true (uncorrupted) data lies in a low-dimensional subspace that can change with time, albeit slowly. The goal is to track this changing subspace over time in the presence of sparse outliers. We develop and study a novel algorithm, that we call simple-ReProCS, based on the recently introduced Recursive Projected Compressive Sensing (ReProCS) framework. Our work provides the first guarantee for dynamic RPCA that holds under weakened versions of standard RPCA assumptions, slow subspace change and a lower bound assumption on most outlier magnitudes. Our result is significant because (i) it removes the strong assumptions needed by the two previous complete guarantees for ReProCS-based algorithms; (ii) it shows that it is possible to achieve significantly improved outlier tolerance, compared with all existing RPCA or dynamic RPCA solutions by exploiting the above two simple extra assumptions; and (iii) it proves that simple-ReProCS is online (after initialization), fast, and, has near-optimal memory complexity.Comment: Minor writing edits. The paper has been accepted to IEEE Transactions on Information Theor

Deep Learning-Based Low Complexity and High Efficiency Moving Object Detection Methods

Moving object detection (MOD) is the process of extracting dynamic foreground content from the video frames, such as moving vehicles or pedestrians, while discarding the nonmoving background. It plays an essential role in computer vision field. The traditional methods meet difficulties when applied in complex scenarios, such as videos with illumination changes, shadows, night scenes,and dynamic backgrounds. Deep learning methods have been actively applied to moving object detection in recent years and demonstrated impressive results. However, many existing models render superior detection accuracy at the cost of high computational complexity and slow inference speed. This fact has hindered the development of such models in mobile and embedded vision tasks, which need to be carried out in a timely fashion on a computationally limited platform. The current research aims to use the technique of separable convolution in both 2D and 3D CNN together with our proposed multi-input multi-output strategy and two-branch structure to devise new deep network models that significantly improve inference speed, yet require smaller model size and achieve reduction in floating-point operations as compared to existing deep learning models with competitive detection accuracy. This research devised three deep neural network models, addressing the following main problems in the area of moving object detection: 1. Improving Detection Accuracy by extracting both spatial and temporal information: To improve detection accuracy, the proposed models adopt 3D convolution which is more suitable to extract both spatial and temporal information in video data than 2D convolution. We also put this 3D convolution into two-branch network that extracts both high-level global features and low-level detailed features can further increase the accuracy. 2. Reduce model size and computational complexity by changing network structure: The standard 2D and 3D convolution are further decomposed into depthwise and pointwise convolutions. While existing 3D separable CNN all addressed other problems such as gesture recognition, force prediction, 3D object classification or reconstruction, our work applied it to the moving object detection task for the first time in the literature. 3. Increasing inference speed by changing the input-output relationship: We proposed a multi-input multi-output (MIMO) strategy to increase inference speed, which can take multiple frames as the network input and output multiple frames of detection results. This MIMO embedded in 3Dseparable CNN can further increase model inference speed significantly and maintain high detection accuracy. Compared to state-of-the-art approaches, our proposed methods significantly increases the inference speed, reduces the model size, meanwhile achieving the highest detection accuracy in the scene dependent evaluation (SDE) setup and maintaining a competitive detection accuracy in the scene independent evaluation (SIE) setup. The SDE setup is widely used to tune and test the model on a specific video as the training and test sets are from the same video. The SIE setup is designed to assess the generalization capability of the model on completely unseen videos

Computational models of object motion detectors accelerated using FPGA technology

The detection of moving objects is a trivial task when performed by vertebrate retinas, yet a complex computer vision task. This PhD research programme has made three key contributions, namely: 1) a multi-hierarchical spiking neural network (MHSNN) architecture for detecting horizontal and vertical movements, 2) a Hybrid Sensitive Motion Detector (HSMD) algorithm for detecting object motion and 3) the Neuromorphic Hybrid Sensitive Motion Detector (NeuroHSMD) , a real-time neuromorphic implementation of the HSMD algorithm. The MHSNN is a customised 4 layers Spiking Neural Network (SNN) architecture designed to reflect the basic connectivity, similar to canonical behaviours found in the majority of vertebrate retinas (including human retinas). The architecture, was trained using images from a custom dataset generated in laboratory settings. Simulation results revealed that each cell model is sensitive to vertical and horizontal movements, with a detection error of 6.75% contrasted against the teaching signals (expected output signals) used to train the MHSNN. The experimental evaluation of the methodology shows that the MH SNN was not scalable because of the overall number of neurons and synapses which lead to the development of the HSMD. The HSMD algorithm enhanced an existing Dynamic Background subtraction (DBS) algorithm using a customised 3-layer SNN. The customised 3-layer SNN was used to stabilise the foreground information of moving objects in the scene, which improves the object motion detection. The algorithm was compared against existing background subtraction approaches, available on the Open Computer Vision (OpenCV) library, specifically on the 2012 Change Detection (CDnet2012) and the 2014 Change Detection (CDnet2014) benchmark datasets. The accuracy results show that the HSMD was ranked overall first and performed better than all the other benchmarked algorithms on four of the categories, across all eight test metrics. Furthermore, the HSMD is the first to use an SNN to enhance the existing dynamic background subtraction algorithm without a substantial degradation of the frame rate, being capable of processing images 720 × 480 at 13.82 Frames Per Second (fps) (CDnet2014) and 720 × 480 at 13.92 fps (CDnet2012) on a High Performance computer (96 cores and 756 GB of RAM). Although the HSMD analysis shows good Percentage of Correct Classifications (PCC) on the CDnet2012 and CDnet2014, it was identified that the 3-layer customised SNN was the bottleneck, in terms of speed, and could be improved using dedicated hardware. The NeuroHSMD is thus an adaptation of the HSMD algorithm whereby the SNN component has been fully implemented on dedicated hardware [Terasic DE10-pro Field-Programmable Gate Array (FPGA) board]. Open Computer Language (OpenCL) was used to simplify the FPGA design flow and allow the code portability to other devices such as FPGA and Graphical Processing Unit (GPU). The NeuroHSMD was also tested against the CDnet2012 and CDnet2014 datasets with an acceleration of 82% over the HSMD algorithm, being capable of processing 720 × 480 images at 28.06 fps (CDnet2012) and 28.71 fps (CDnet2014)