16 research outputs found
Matrix recovery using Split Bregman
In this paper we address the problem of recovering a matrix, with inherent
low rank structure, from its lower dimensional projections. This problem is
frequently encountered in wide range of areas including pattern recognition,
wireless sensor networks, control systems, recommender systems, image/video
reconstruction etc. Both in theory and practice, the most optimal way to solve
the low rank matrix recovery problem is via nuclear norm minimization. In this
paper, we propose a Split Bregman algorithm for nuclear norm minimization. The
use of Bregman technique improves the convergence speed of our algorithm and
gives a higher success rate. Also, the accuracy of reconstruction is much
better even for cases where small number of linear measurements are available.
Our claim is supported by empirical results obtained using our algorithm and
its comparison to other existing methods for matrix recovery. The algorithms
are compared on the basis of NMSE, execution time and success rate for varying
ranks and sampling ratios
Scalable Dense Monocular Surface Reconstruction
This paper reports on a novel template-free monocular non-rigid surface
reconstruction approach. Existing techniques using motion and deformation cues
rely on multiple prior assumptions, are often computationally expensive and do
not perform equally well across the variety of data sets. In contrast, the
proposed Scalable Monocular Surface Reconstruction (SMSR) combines strengths of
several algorithms, i.e., it is scalable with the number of points, can handle
sparse and dense settings as well as different types of motions and
deformations. We estimate camera pose by singular value thresholding and
proximal gradient. Our formulation adopts alternating direction method of
multipliers which converges in linear time for large point track matrices. In
the proposed SMSR, trajectory space constraints are integrated by smoothing of
the measurement matrix. In the extensive experiments, SMSR is demonstrated to
consistently achieve state-of-the-art accuracy on a wide variety of data sets.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October
201
3D Face reconstruction from moving camera with stationary lighting conditions
This paper describes the development of a 3D face reconstruction algorithm which is able to reconstruct the depth map of a face from a handheld moving camera, where the face remains stationary in space and the lighting conditions remain constant. Camera calibration is used to undistorted the movie frames and local template matching is applied by matching keypoints between consecutive frames. The described algorithm sets the first steps in the development of a tool which can output a 3D printed facial mask for clinical use
Schatten- Quasi-Norm Regularized Matrix Optimization via Iterative Reweighted Singular Value Minimization
In this paper we study general Schatten- quasi-norm (SPQN) regularized
matrix minimization problems. In particular, we first introduce a class of
first-order stationary points for them, and show that the first-order
stationary points introduced in [11] for an SPQN regularized
minimization problem are equivalent to those of an SPQN regularized
minimization reformulation. We also show that any local minimizer of the SPQN
regularized matrix minimization problems must be a first-order stationary
point. Moreover, we derive lower bounds for nonzero singular values of the
first-order stationary points and hence also of the local minimizers of the
SPQN regularized matrix minimization problems. The iterative reweighted
singular value minimization (IRSVM) methods are then proposed to solve these
problems, whose subproblems are shown to have a closed-form solution. In
contrast to the analogous methods for the SPQN regularized
minimization problems, the convergence analysis of these methods is
significantly more challenging. We develop a novel approach to establishing the
convergence of these methods, which makes use of the expression of a specific
solution of their subproblems and avoids the intricate issue of finding the
explicit expression for the Clarke subdifferential of the objective of their
subproblems. In particular, we show that any accumulation point of the sequence
generated by the IRSVM methods is a first-order stationary point of the
problems. Our computational results demonstrate that the IRSVM methods
generally outperform some recently developed state-of-the-art methods in terms
of solution quality and/or speed.Comment: This paper has been withdrawn by the author due to major revision and
correction
Forward-backward truncated Newton methods for convex composite optimization
This paper proposes two proximal Newton-CG methods for convex nonsmooth
optimization problems in composite form. The algorithms are based on a a
reformulation of the original nonsmooth problem as the unconstrained
minimization of a continuously differentiable function, namely the
forward-backward envelope (FBE). The first algorithm is based on a standard
line search strategy, whereas the second one combines the global efficiency
estimates of the corresponding first-order methods, while achieving fast
asymptotic convergence rates. Furthermore, they are computationally attractive
since each Newton iteration requires the approximate solution of a linear
system of usually small dimension
A Sequential Factorization Method for Recovering Shape and Motion from Image Streams
We present a sequential factorization method for recovering the three-dimensional shape of an object and the motion of the camera from a sequence of images, using tracked features. The factorization method originally proposed by Tomasi and Kanade produces robust and accurate results incorporating the singular value decomposition. However, it is still difficult to apply the method to real-time applications since it is based on a batch-type operation and the cost of the singular value decomposition is large. We develop the factorization method into a sequential method by regarding the feature positions as a vector time series. The new method produces estimates of shape and motion at each frame. The singular value decomposition is replaced with an updating computation of only three dominant eigenvectors, which can be performed in time, while the complete singular value decomposition requires operations for an matrix. Also, the method is able to handle infinite sequences since it does not ..
A Sequential Factorization Method for Recovering Shape and Motion From Image Streams
We present a sequential factorization method for recovering the three-dimensional shape of an object and the motion of the camera from a sequence of images, using tracked features. The factorization method originally proposed by Tomasi and Kanade produces robust and accurate results incorporating the singular value decomposition. However, it is still difficult to apply the method to real-time applications, since it is based on a batch-type operation and the cost of the singular value decomposition is large. We develop the factorization method into a sequential method by regarding the feature positions as a vector time series. The new method produces estimates of shape and motion at each frame. The singular value decomposition is replaced with an updating computation of only three dominant eigenvectors, which can be performed in OP() 2 time, while the complete singular value decomposition requires OFP () 2 operations for an FP matrix. Also, the method is able to handle infinite sequences, since it does not store any increasingly large matrices. Experiments using synthetic and real images illustrate that the method has nearly the same accuracy and robustness as the original method. Index Terms---Shape from motion, singular value decomposition, feature tracking, 3D object reconstruction, image understanding, real-time vision. ------------------------------ F ------------------------------ 1I NTRODUCTION ECOVERING both the 3D shape of an object and the motion of the camera simultaneously from a stream of images is an important task and has wide applicability in many tasks, such as navigation and robot manipulation. Tomasi and Kanade [1] first developed a factorization method to recover shape and motion under an orthographic projection model, and obtained robust and ..