Robust Recovery of Subspace Structures by Low-Rank Representation

In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible errors as well. To this end, we propose a novel method termed Low-Rank Representation (LRR), which seeks the lowest-rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that LRR well solves the subspace recovery problem: when the data is clean, we prove that LRR exactly captures the true subspace structures; for the data contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for the data corrupted by arbitrary errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace segmentation and error correction, in an efficient way.Comment: IEEE Trans. Pattern Analysis and Machine Intelligenc

Outlier detection and robust normal-curvature estimation in mobile laser scanning 3D point cloud data

This paper proposes two robust statistical techniques for outlier detection and robust saliency features, such as surface normal and curvature, estimation in laser scanning 3D point cloud data. One is based on a robust z-score and the other uses a Mahalanobis type robust distance. The methods couple the ideas of point to plane orthogonal distance and local surface point consistency to get Maximum Consistency with Minimum Distance (MCMD). The methods estimate the best-fit-plane based on most probable outlier free, and most consistent, points set in a local neighbourhood. Then the normal and curvature from the best-fit-plane will be highly robust to noise and outliers. Experiments are performed to show the performance of the algorithms compared to several existing well-known methods (from computer vision, data mining, machine learning and statistics) using synthetic and real laser scanning datasets of complex (planar and non-planar) objects. Results for plane fitting, denoising, sharp feature preserving and segmentation are significantly improved. The algorithms are demonstrated to be significantly faster, more accurate and robust. Quantitatively, for a sample size of 50 with 20% outliers the proposed MCMD_Z is approximately 5, 15 and 98 times faster than the existing methods: uLSIF, RANSAC and RPCA, respectively. The proposed MCMD_MD method can tolerate 75% clustered outliers, whereas, RPCA and RANSAC can only tolerate 47% and 64% outliers, respectively. In terms of outlier detection, for the same dataset, MCMD_Z has an accuracy of 99.72%, 0.4% false positive rate and 0% false negative rate; for RPCA, RANSAC and uLSIF, the accuracies are 97.05%, 47.06% and 94.54%, respectively, and they have misclassification rates higher than the proposed methods. The new methods have potential for local surface reconstruction, fitting, and other point cloud processing tasks

Towards Developing Computer Vision Algorithms and Architectures for Real-world Applications

abstract: Computer vision technology automatically extracts high level, meaningful information from visual data such as images or videos, and the object recognition and detection algorithms are essential in most computer vision applications. In this dissertation, we focus on developing algorithms used for real life computer vision applications, presenting innovative algorithms for object segmentation and feature extraction for objects and actions recognition in video data, and sparse feature selection algorithms for medical image analysis, as well as automated feature extraction using convolutional neural network for blood cancer grading. To detect and classify objects in video, the objects have to be separated from the background, and then the discriminant features are extracted from the region of interest before feeding to a classifier. Effective object segmentation and feature extraction are often application specific, and posing major challenges for object detection and classification tasks. In this dissertation, we address effective object flow based ROI generation algorithm for segmenting moving objects in video data, which can be applied in surveillance and self driving vehicle areas. Optical flow can also be used as features in human action recognition algorithm, and we present using optical flow feature in pre-trained convolutional neural network to improve performance of human action recognition algorithms. Both algorithms outperform the state-of-the-arts at their time. Medical images and videos pose unique challenges for image understanding mainly due to the fact that the tissues and cells are often irregularly shaped, colored, and textured, and hand selecting most discriminant features is often difficult, thus an automated feature selection method is desired. Sparse learning is a technique to extract the most discriminant and representative features from raw visual data. However, sparse learning with \textit{L1} regularization only takes the sparsity in feature dimension into consideration; we improve the algorithm so it selects the type of features as well; less important or noisy feature types are entirely removed from the feature set. We demonstrate this algorithm to analyze the endoscopy images to detect unhealthy abnormalities in esophagus and stomach, such as ulcer and cancer. Besides sparsity constraint, other application specific constraints and prior knowledge may also need to be incorporated in the loss function in sparse learning to obtain the desired results. We demonstrate how to incorporate similar-inhibition constraint, gaze and attention prior in sparse dictionary selection for gastroscopic video summarization that enable intelligent key frame extraction from gastroscopic video data. With recent advancement in multi-layer neural networks, the automatic end-to-end feature learning becomes feasible. Convolutional neural network mimics the mammal visual cortex and can extract most discriminant features automatically from training samples. We present using convolutinal neural network with hierarchical classifier to grade the severity of Follicular Lymphoma, a type of blood cancer, and it reaches 91\% accuracy, on par with analysis by expert pathologists. Developing real world computer vision applications is more than just developing core vision algorithms to extract and understand information from visual data; it is also subject to many practical requirements and constraints, such as hardware and computing infrastructure, cost, robustness to lighting changes and deformation, ease of use and deployment, etc.The general processing pipeline and system architecture for the computer vision based applications share many similar design principles and architecture. We developed common processing components and a generic framework for computer vision application, and a versatile scale adaptive template matching algorithm for object detection. We demonstrate the design principle and best practices by developing and deploying a complete computer vision application in real life, building a multi-channel water level monitoring system, where the techniques and design methodology can be generalized to other real life applications. The general software engineering principles, such as modularity, abstraction, robust to requirement change, generality, etc., are all demonstrated in this research.Dissertation/ThesisDoctoral Dissertation Computer Science 201