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Robust Subspace Estimation Using LowRank Optimization. Theory and Applications in Scene Reconstruction, Video Denoising, and Activity Recognition.
 Date Issued:
 2013
 Abstract/Description:
 In this dissertation, we discuss the problem of robust linear subspace estimation using lowrank optimization and propose three formulations of it. We demonstrate how these formulations can be used to solve fundamental computer vision problems, and provide superior performance in terms of accuracy and running time.Consider a set of observations extracted from images (such as pixel gray values, local features, trajectories...etc). If the assumption that these observations are drawn from a liner subspace (or can be linearly approximated) is valid, then the goal is to represent each observation as a linear combination of a compact basis, while maintaining a minimal reconstruction error. One of the earliest, yet most popular, approaches to achieve that is Principal Component Analysis (PCA). However, PCA can only handle Gaussian noise, and thus suffers when the observations are contaminated with gross and sparse outliers. To this end, in this dissertation, we focus on estimating the subspace robustly using lowrank optimization, where the sparse outliers are detected and separated through the `1 norm. The robust estimation has a twofold advantage: First, the obtained basis better represents the actual subspace because it does not include contributions from the outliers. Second, the detected outliers are often of a specific interest in many applications, as we will show throughout this thesis. We demonstrate four different formulations and applications for lowrank optimization. First, we consider the problem of reconstructing an underwater sequence by removing the turbulence caused by the water waves. The main drawback of most previous attempts to tackle this problem is that they heavily depend on modelling the waves, which in fact is illposed since the actual behavior of the waves along with the imaging process are complicated and include several noise components; therefore, their results are not satisfactory. In contrast, we propose a novel approach which outperforms the stateoftheart. The intuition behind our method is that in a sequence where the water is static, the frames would be linearly correlated. Therefore, in the presence of water waves, we may consider the frames as noisy observations drawn from a the subspace of linearly correlated frames. However, the noise introduced by the water waves is not sparse, and thus cannot directly be detected using lowrank optimization. Therefore, we propose a datadriven twostage approach, where the first stage (")sparsifies(") the noise, and the second stage detects it. The first stage leverages the temporal mean of the sequence to overcome the structured turbulence of the waves through an iterative registration algorithm. The result of the first stage is a high quality mean and a better structured sequence; however, the sequence still contains unstructured sparse noise. Thus, we employ a second stage at which we extract the sparse errors from the sequence through rank minimization. Our method converges faster, and drastically outperforms state of the art on all testing sequences. Secondly, we consider a closely related situation where an independently moving object is also present in the turbulent video. More precisely, we consider video sequences acquired in a desert battlefields, where atmospheric turbulence is typically present, in addition to independently moving targets. Typical approaches for turbulence mitigation follow averaging or dewarping techniques. Although these methods can reduce the turbulence, they distort the independently moving objects which can often be of great interest. Therefore, we address the problem of simultaneous turbulence mitigation and moving object detection. We propose a novel threeterm lowrank matrix decomposition approach in which we decompose the turbulence sequence into three components: the background, the turbulence, and the object. We simplify this extremely difficult problem into a minimization of nuclear norm, Frobenius norm, and L1 norm. Our method is based on two observations: First, the turbulence causes dense and Gaussian noise, and therefore can be captured by Frobenius norm, while the moving objects are sparse and thus can be captured by L1 norm. Second, since the object's motion is linear and intrinsically different than the Gaussianlike turbulence, a Gaussianbased turbulence model can be employed to enforce an additional constraint on the search space of the minimization. We demonstrate the robustness of our approach on challenging sequences which are significantly distorted with atmospheric turbulence and include extremely tiny moving objects. In addition to robustly detecting the subspace of the frames of a sequence, we consider using trajectories as observations in the lowrank optimization framework. In particular, in videos acquired by moving cameras, we track all the pixels in the video and use that to estimate the camera motion subspace. This is particularly useful in activity recognition, which typically requires standard preprocessing steps such as motion compensation, moving object detection, and object tracking. The errors from the motion compensation step propagate to the object detection stage, resulting in missdetections, which further complicates the tracking stage, resulting in cluttered and incorrect tracks. In contrast, we propose a novel approach which does not follow the standard steps, and accordingly avoids the aforementioned difficulties. Our approach is based on Lagrangian particle trajectories which are a set of dense trajectories obtained by advecting optical flow over time, thus capturing the ensemble motions of a scene. This is done in frames of unaligned video, and no object detection is required. In order to handle the moving camera, we decompose the trajectories into their camerainduced and objectinduced components. Having obtained the relevant object motion trajectories, we compute a compact set of chaotic invariant features, which captures the characteristics of the trajectories. Consequently, a SVM is employed to learn and recognize the human actions using the computed motion features. We performed intensive experiments on multiple benchmark datasets, and obtained promising results.Finally, we consider a more challenging problem referred to as complex event recognition, where the activities of interest are complex and unconstrained. This problem typically pose significant challenges because it involves videos of highly variable content, noise, length, frame size ... etc. In this extremely challenging task, highlevel features have recently shown a promising direction as in [53, 129], where core lowlevel events referred to as concepts are annotated and modeled using a portion of the training data, then each event is described using its content of these concepts. However, because of the complex nature of the videos, both the concept models and the corresponding highlevel features are significantly noisy. In order to address this problem, we propose a novel lowrank formulation, which combines the precisely annotated videos used to train the concepts, with the rich highlevel features. Our approach finds a new representation for each event, which is not only lowrank, but also constrained to adhere to the concept annotation, thus suppressing the noise, and maintaining a consistent occurrence of the concepts in each event. Extensive experiments on large scale real world dataset TRECVID Multimedia Event Detection 2011 and 2012 demonstrate that our approach consistently improves the discriminativity of the highlevel features by a significant margin.
Title:  Robust Subspace Estimation Using LowRank Optimization. Theory and Applications in Scene Reconstruction, Video Denoising, and Activity Recognition. 
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Name(s): 
Oreifej, Omar, Author Shah, Mubarak, Committee Chair Da Vitoria Lobo, Niels, Committee CoChair Stanley, Kenneth, Committee Member Lin, Mingjie, Committee Member Li, Xin, Committee Member University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2013  
Publisher:  University of Central Florida  
Language(s):  English  
Abstract/Description:  In this dissertation, we discuss the problem of robust linear subspace estimation using lowrank optimization and propose three formulations of it. We demonstrate how these formulations can be used to solve fundamental computer vision problems, and provide superior performance in terms of accuracy and running time.Consider a set of observations extracted from images (such as pixel gray values, local features, trajectories...etc). If the assumption that these observations are drawn from a liner subspace (or can be linearly approximated) is valid, then the goal is to represent each observation as a linear combination of a compact basis, while maintaining a minimal reconstruction error. One of the earliest, yet most popular, approaches to achieve that is Principal Component Analysis (PCA). However, PCA can only handle Gaussian noise, and thus suffers when the observations are contaminated with gross and sparse outliers. To this end, in this dissertation, we focus on estimating the subspace robustly using lowrank optimization, where the sparse outliers are detected and separated through the `1 norm. The robust estimation has a twofold advantage: First, the obtained basis better represents the actual subspace because it does not include contributions from the outliers. Second, the detected outliers are often of a specific interest in many applications, as we will show throughout this thesis. We demonstrate four different formulations and applications for lowrank optimization. First, we consider the problem of reconstructing an underwater sequence by removing the turbulence caused by the water waves. The main drawback of most previous attempts to tackle this problem is that they heavily depend on modelling the waves, which in fact is illposed since the actual behavior of the waves along with the imaging process are complicated and include several noise components; therefore, their results are not satisfactory. In contrast, we propose a novel approach which outperforms the stateoftheart. The intuition behind our method is that in a sequence where the water is static, the frames would be linearly correlated. Therefore, in the presence of water waves, we may consider the frames as noisy observations drawn from a the subspace of linearly correlated frames. However, the noise introduced by the water waves is not sparse, and thus cannot directly be detected using lowrank optimization. Therefore, we propose a datadriven twostage approach, where the first stage (")sparsifies(") the noise, and the second stage detects it. The first stage leverages the temporal mean of the sequence to overcome the structured turbulence of the waves through an iterative registration algorithm. The result of the first stage is a high quality mean and a better structured sequence; however, the sequence still contains unstructured sparse noise. Thus, we employ a second stage at which we extract the sparse errors from the sequence through rank minimization. Our method converges faster, and drastically outperforms state of the art on all testing sequences. Secondly, we consider a closely related situation where an independently moving object is also present in the turbulent video. More precisely, we consider video sequences acquired in a desert battlefields, where atmospheric turbulence is typically present, in addition to independently moving targets. Typical approaches for turbulence mitigation follow averaging or dewarping techniques. Although these methods can reduce the turbulence, they distort the independently moving objects which can often be of great interest. Therefore, we address the problem of simultaneous turbulence mitigation and moving object detection. We propose a novel threeterm lowrank matrix decomposition approach in which we decompose the turbulence sequence into three components: the background, the turbulence, and the object. We simplify this extremely difficult problem into a minimization of nuclear norm, Frobenius norm, and L1 norm. Our method is based on two observations: First, the turbulence causes dense and Gaussian noise, and therefore can be captured by Frobenius norm, while the moving objects are sparse and thus can be captured by L1 norm. Second, since the object's motion is linear and intrinsically different than the Gaussianlike turbulence, a Gaussianbased turbulence model can be employed to enforce an additional constraint on the search space of the minimization. We demonstrate the robustness of our approach on challenging sequences which are significantly distorted with atmospheric turbulence and include extremely tiny moving objects. In addition to robustly detecting the subspace of the frames of a sequence, we consider using trajectories as observations in the lowrank optimization framework. In particular, in videos acquired by moving cameras, we track all the pixels in the video and use that to estimate the camera motion subspace. This is particularly useful in activity recognition, which typically requires standard preprocessing steps such as motion compensation, moving object detection, and object tracking. The errors from the motion compensation step propagate to the object detection stage, resulting in missdetections, which further complicates the tracking stage, resulting in cluttered and incorrect tracks. In contrast, we propose a novel approach which does not follow the standard steps, and accordingly avoids the aforementioned difficulties. Our approach is based on Lagrangian particle trajectories which are a set of dense trajectories obtained by advecting optical flow over time, thus capturing the ensemble motions of a scene. This is done in frames of unaligned video, and no object detection is required. In order to handle the moving camera, we decompose the trajectories into their camerainduced and objectinduced components. Having obtained the relevant object motion trajectories, we compute a compact set of chaotic invariant features, which captures the characteristics of the trajectories. Consequently, a SVM is employed to learn and recognize the human actions using the computed motion features. We performed intensive experiments on multiple benchmark datasets, and obtained promising results.Finally, we consider a more challenging problem referred to as complex event recognition, where the activities of interest are complex and unconstrained. This problem typically pose significant challenges because it involves videos of highly variable content, noise, length, frame size ... etc. In this extremely challenging task, highlevel features have recently shown a promising direction as in [53, 129], where core lowlevel events referred to as concepts are annotated and modeled using a portion of the training data, then each event is described using its content of these concepts. However, because of the complex nature of the videos, both the concept models and the corresponding highlevel features are significantly noisy. In order to address this problem, we propose a novel lowrank formulation, which combines the precisely annotated videos used to train the concepts, with the rich highlevel features. Our approach finds a new representation for each event, which is not only lowrank, but also constrained to adhere to the concept annotation, thus suppressing the noise, and maintaining a consistent occurrence of the concepts in each event. Extensive experiments on large scale real world dataset TRECVID Multimedia Event Detection 2011 and 2012 demonstrate that our approach consistently improves the discriminativity of the highlevel features by a significant margin.  
Identifier:  CFE0004732 (IID), ucf:49835 (fedora)  
Note(s): 
20130501 Ph.D. Engineering and Computer Science, Electrical Engineering and Computing Doctoral This record was generated from author submitted information. 

Subject(s):  LowRank Representation  LowRank  Sparse Representation  Sparse  Activity Recognition  Turbulence Mitigation  Video Denoising  Complex Event Recognition  Nuclear Norm  Augmented Lagrange Multiplier  Camera Motion Estimation  TRECVID  HOHA  Water Waves  Rank  Trajectories  Particle Advection  Registration  Decomposition  Moving Object Detection  Background Subtraction  Atmospheric Turbulence  
Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0004732  
Restrictions on Access:  public 20130515  
Host Institution:  UCF 