Fast Approximate KK-Means via Cluster Closures

$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are computed and each data point is re-assigned to its nearest center. The cluster re-assignment step becomes prohibitively expensive when the number of data points and cluster centers are large. In this paper, we propose a novel approximate $k$-means algorithm to greatly reduce the computational complexity in the assignment step. Our approach is motivated by the observation that most active points changing their cluster assignments at each iteration are located on or near cluster boundaries. The idea is to efficiently identify those active points by pre-assembling the data into groups of neighboring points using multiple random spatial partition trees, and to use the neighborhood information to construct a closure for each cluster, in such a way only a small number of cluster candidates need to be considered when assigning a data point to its nearest cluster. Using complexity analysis, image data clustering, and applications to image retrieval, we show that our approach out-performs state-of-the-art approximate $k$-means algorithms in terms of clustering quality and efficiency

Quasiconvex optimization for robust geometric reconstruction

Geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show that, for various geometric reconstruction problems, their reprojection error functions share a common and quasiconvex formulation. Based on the quasiconvexity, we present a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of small-scale convex programs that are ready to solve. Our final reconstruction algorithm is simple and has intuitive geometric interpretation. In contrast to existing random sampling or local minimization approaches, our algorithm is deterministic and guarantees a predefined accuracy of the minimization result. We demonstrate the effectiveness of our algorithm by experiments on both synthetic and real data.

The clinical application of mesenchymal stromal cells in hematopoietic stem cell transplantation

Abstract Mesenchymal stromal cells (MSCs) are multipotent stem cells well known for repairing tissue, supporting hematopoiesis, and modulating immune and inflammation response. These outstanding properties make MSCs as an attractive candidate for cellular therapy in immune-based disorders, especially hematopoietic stem cell transplantation (HSCT). In this review, we outline the progress of MSCs in preventing and treating engraftment failure (EF), graft-versus-host disease (GVHD) following HSCT and critically discuss unsolved issues in clinical applications

Robust L1 norm factorization in the presence of outliers and missing data by alternative convex programming

Matrix factorization has many applications in computer vision. Singular Value Decomposition (SVD) is the standard algorithm for factorization. When there are outliers and missing data, which often happen in real measurements, SVD is no longer applicable. For robustness Iteratively Re-weighted Least Squares (IRLS) is often used for factorization by assigning a weight to each element in the measurements. Because it uses L2 norm, good initialization in IRLS is critical for success, but is non-trivial. In this paper, we formulate matrix factorization as a L1 norm minimization problem that is solved efficiently by alternative convex programming. Our formulation 1) is robust without requiring initial weighting, 2) handles missing data straightforwardly, and 3) provides a framework in which constraints and prior knowledge (if available) can be conveniently incorporated. In the experiments we apply our approach to factorization-based structure from motion. It is shown that our approach achieves better results than other approaches (including IRLS) on both synthetic and real data

A Subspace Approach to Layer Extraction, Patch-Based SFM, and Video Compression

Representing videos with layers has important applications such as video compression, motion analysis, 3D modeling and rendering. This thesis proposes a subspace approach to extracting layers from video by taking advantages of the fact that homographies induced by planar patches in the scene form a low dimensional linear subspace. In the subspace, layers in the input images are mapped onto well-defined clusters, and can be reliably identified by a standard clustering algorithm (e.g., mean-shift). Global optimality is achieved since both spatial and temporal redundancy are simultaneously taken into account, and noise can be effectively reduced by enforcing the subspace constraint. The existence of subspace also enables outlier detection, making the subspace computation robust. Based on the subspace constraint, we propose a patch-based scheme for affine structure from motion (SFM), which recovers the plane equation of each planar patch in the scene, as well as the camera epipolar geometry. We propose two approaches to patch-based SFM: (1) factorization approach; and (2) layer based approach. Patch-based SFM provides a compact video representation that can be used to construct a high quality texture map for each layer. We plan to apply our approach to generating Video Object Planes (VOPs) defined by MPEG-4 standard. VOP generation is a critical but unspecified step in MPEG-4 standard. Our motion model for each VOP consists of a global planar motion and localized deformations, which has a closed-form solution. Our goals are: (1) combining different low level cues to model VOPs; and (2) extracting VOPs that undergo more complicated motion (non-planar or non-rigid). 1

Robust Subspace Clustering by Combined Use of kNND Metric and SVD Algorithm

vision, such as image/video segmentation and pattern classification. The major issue in subspace clustering is to obtain the most appropriate subspace from the given noisy data. Typical methods (e.g., SVD, PCA, and Eigendecomposition) use least squares techniques, and are sensitive to outliers. In this paper, we present the k-th Nearest Neighbor Distance (kNND) metric, which, without actually clustering the data, can exploit the intrinsic data cluster structure to detect and remove influential outliers as well as small data clusters. The remaining data provide a good initial inlier data set that resides in a linear subspace whose rank (dimension) is upper-bounded. Such linear subspace constraint can then be exploited by simple algorithms, such as iterative SVD algorithm, to (1) detect the remaining outliers that violate the correlation structure enforced by the low rank subspace, and (2) reliably compute the subspace. As an example, we apply our method to extracting layers from image sequences containing dynamically moving objects

Robust subspace computation using l1 norm

Linear subspace has many important applications in computer vision, such as structure from motion, motion estimation, layer extraction, object recognition, and object tracking. Singular Value Decomposition (SVD) algorithm is a standard technique to compute the subspace from the input data. The SVD algorithm, however, is sensitive to outliers as it uses L2 norm metric, and it can not handle missing data either. In this paper, we propose using L1 norm metric to compute the subspace. We show that it is robust to outliers and can handle missing data. We present two algorithms to optimize the L1 norm metric: the weighted median algorithm and the quadratic programming algorithm. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Carnegie Mellon University or the U.S. Government