Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition

This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript submitted to CVI

Outlier Edge Detection Using Random Graph Generation Models and Applications

Outliers are samples that are generated by different mechanisms from other normal data samples. Graphs, in particular social network graphs, may contain nodes and edges that are made by scammers, malicious programs or mistakenly by normal users. Detecting outlier nodes and edges is important for data mining and graph analytics. However, previous research in the field has merely focused on detecting outlier nodes. In this article, we study the properties of edges and propose outlier edge detection algorithms using two random graph generation models. We found that the edge-ego-network, which can be defined as the induced graph that contains two end nodes of an edge, their neighboring nodes and the edges that link these nodes, contains critical information to detect outlier edges. We evaluated the proposed algorithms by injecting outlier edges into some real-world graph data. Experiment results show that the proposed algorithms can effectively detect outlier edges. In particular, the algorithm based on the Preferential Attachment Random Graph Generation model consistently gives good performance regardless of the test graph data. Further more, the proposed algorithms are not limited in the area of outlier edge detection. We demonstrate three different applications that benefit from the proposed algorithms: 1) a preprocessing tool that improves the performance of graph clustering algorithms; 2) an outlier node detection algorithm; and 3) a novel noisy data clustering algorithm. These applications show the great potential of the proposed outlier edge detection techniques.Comment: 14 pages, 5 figures, journal pape

Consistent ICP for the registration of sparse and inhomogeneous point clouds

In this paper, we derive a novel iterative closest point (ICP) technique that performs point cloud alignment in a robust and consistent way. Traditional ICP techniques minimize the point-to-point distances, which are successful when point clouds contain no noise or clutter and moreover are dense and more or less uniformly sampled. In the other case, it is better to employ point-to-plane or other metrics to locally approximate the surface of the objects. However, the point-to-plane metric does not yield a symmetric solution, i.e. the estimated transformation of point cloud p to point cloud q is not necessarily equal to the inverse transformation of point cloud q to point cloud p. In order to improve ICP, we will enforce such symmetry constraints as prior knowledge and make it also robust to noise and clutter. Experimental results show that our method is indeed much more consistent and accurate in presence of noise and clutter compared to existing ICP algorithms

A Fast Algorithm for Robust Regression with Penalised Trimmed Squares

The presence of groups containing high leverage outliers makes linear regression a difficult problem due to the masking effect. The available high breakdown estimators based on Least Trimmed Squares often do not succeed in detecting masked high leverage outliers in finite samples. An alternative to the LTS estimator, called Penalised Trimmed Squares (PTS) estimator, was introduced by the authors in \cite{ZiouAv:05,ZiAvPi:07} and it appears to be less sensitive to the masking problem. This estimator is defined by a Quadratic Mixed Integer Programming (QMIP) problem, where in the objective function a penalty cost for each observation is included which serves as an upper bound on the residual error for any feasible regression line. Since the PTS does not require presetting the number of outliers to delete from the data set, it has better efficiency with respect to other estimators. However, due to the high computational complexity of the resulting QMIP problem, exact solutions for moderately large regression problems is infeasible. In this paper we further establish the theoretical properties of the PTS estimator, such as high breakdown and efficiency, and propose an approximate algorithm called Fast-PTS to compute the PTS estimator for large data sets efficiently. Extensive computational experiments on sets of benchmark instances with varying degrees of outlier contamination, indicate that the proposed algorithm performs well in identifying groups of high leverage outliers in reasonable computational time.Comment: 27 page

Towards Real-Time Detection and Tracking of Spatio-Temporal Features: Blob-Filaments in Fusion Plasma

A novel algorithm and implementation of real-time identification and tracking of blob-filaments in fusion reactor data is presented. Similar spatio-temporal features are important in many other applications, for example, ignition kernels in combustion and tumor cells in a medical image. This work presents an approach for extracting these features by dividing the overall task into three steps: local identification of feature cells, grouping feature cells into extended feature, and tracking movement of feature through overlapping in space. Through our extensive work in parallelization, we demonstrate that this approach can effectively make use of a large number of compute nodes to detect and track blob-filaments in real time in fusion plasma. On a set of 30GB fusion simulation data, we observed linear speedup on 1024 processes and completed blob detection in less than three milliseconds using Edison, a Cray XC30 system at NERSC.Comment: 14 pages, 40 figure