In this thesis, we will discuss several topics in image analysis. The commonality among these topics is that the data to be analyzed can be approximated by a low-rank matrix. Based on such low-rank property of data, we propose several frameworks to address related issues in these topics. The proposed frameworks not only result in robust algorithms but also bring alternative insights into these issues.

More specifically, this thesis covers three topics. The first is moving object detection from a video. Existing methods are often limited when addressing a complex background or foreground. We try to solve this issue by a novel framework named DEtecting Contiguous Outliers in the LOw-rank Representation (DECOLOR). It can naturally model complex background and avoid motion computat...[ Read more ]

In this thesis, we will discuss several topics in image analysis. The commonality among these topics is that the data to be analyzed can be approximated by a low-rank matrix. Based on such low-rank property of data, we propose several frameworks to address related issues in these topics. The proposed frameworks not only result in robust algorithms but also bring alternative insights into these issues.

More specifically, this thesis covers three topics. The first is moving object detection from a video. Existing methods are often limited when addressing a complex background or foreground. We try to solve this issue by a novel framework named DEtecting Contiguous Outliers in the LOw-rank Representation (DECOLOR). It can naturally model complex background and avoid motion computation. We have successfully applied DECOLOR to mitral leaflet tracking, which is a challenging problem in medical image analysis. The second topic is object segmentation from a group of related images. We propose to model the shape similarity of objects in order to improve the robustness of active contours. To achieve this, we introduce a low-rank constraint and integrate it into the active contour model. Our method can be interpreted as an unsupervised approach to shape-prior modeling. The last topic is the analysis of array-based comparative genomic hybridization data. Each data set from multiple samples can be regarded as a 2-D image. Our goal is to detect the pattern of copy number variation in this image. To recover the pattern from noisy data, we make use of the smoothness and correlation properties of the signal by approximating the raw data set with a matrix whose total variation and spectral norm are minimized simultaneously.