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Shape and motion from image streams under orthography: a factorization method
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1992
"... Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an illconditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orth ..."
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Cited by 1094 (38 self)
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orthography without computing depth as an intermediate step. An image stream can be represented by the 2FxP measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Based on this observation, the factorization method
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 427 (36 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity
From subspace clustering to fullrank matrix completion
"... Subspace clustering is the problem of finding a multisubspace representation that best fits a collection of points taken from a highdimensional space. This type of structure occurs naturally in many applications ranging from bioinformatics, image/text clustering to semisupervised learning. The c ..."
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Cited by 1 (1 self)
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. This problem may also be viewed as a generalization of standard lowrank matrix completion to cases where the matrix is of high or potentially fullrank. Synthetic and real data experiments confirm the effectiveness of these methods. 1 Problem formulation and model Consider a realvalued n ×N dimensional
USING FULLRANK SPATIAL COVARIANCE MODELS FOR NOISEROBUST ASR
"... We present a joint spatial and spectral denoising frontend for Track 1 of the 2nd CHiME Speech Separation and Recognition Challenge based on the Flexible Audio Source Separation Toolbox (FASST). We represent the sources by nonnegative matrix factorization (NMF) and fullrank spatial covariances, wh ..."
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Cited by 4 (3 self)
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We present a joint spatial and spectral denoising frontend for Track 1 of the 2nd CHiME Speech Separation and Recognition Challenge based on the Flexible Audio Source Separation Toolbox (FASST). We represent the sources by nonnegative matrix factorization (NMF) and fullrank spatial covariances
A New Block Algorithm for FullRank Solution of the Sylvesterobserver Equation
"... A new block algorithm for computing a full rank solution of the Sylvesterobserver equation arising in state estimation is proposed. The major Computational Kernels of this algorithm are (i) solutions of ordinary Sylvester equations, in which case each one of the matrices is of much smaller order th ..."
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Cited by 2 (0 self)
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A new block algorithm for computing a full rank solution of the Sylvesterobserver equation arising in state estimation is proposed. The major Computational Kernels of this algorithm are (i) solutions of ordinary Sylvester equations, in which case each one of the matrices is of much smaller order
Designs and fullrank STBCs from DFT domain description of cyclic codes
 in IEEE ISIT
"... Abstract — Viewing an n length vector over Fqm as an m × n matrix over Fq, by expanding each entry of the vector with respect to a basis of Fqm over Fq, the rank weight of the n length vector over Fqm is the rank of the corresponding m×n matrix over Fq. It is known that under some conditions, nleng ..."
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Cited by 2 (1 self)
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length cyclic codes over Fqm,(nqm−1 and m ≤ n) have full rank. In this paper, using this result we obtain a design using which we construct fullrank SpaceTime Block Codes (STBCs) for m transmit antennas over signal sets matched to Fq where q =2or q is a prime of the form 4k +1. We also propose a construction
Sum Capacity of a Gaussian Vector Broadcast Channel
 IEEE Trans. Inform. Theory
, 2002
"... This paper characterizes the sum capacity of a class of nondegraded Gaussian vectB broadcast channels where a singletransmitter with multiple transmit terminals sends independent information to multiple receivers. Coordinat+[ is allowed among the transmit teminals, but not among the different recei ..."
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Cited by 279 (21 self)
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class of Gaussian channels whose saddlepoint satisfies a full rank condition. Furt her,t he sum capacity is achieved using a precoding method for Gaussian channels with additive side information noncausally known at the transmitter. The optimal precoding structure is shown t correspond to a decision
Recovering nonrigid 3D shape from image streams
 Conf. on Computer Vision and Pattern Recognition
, 2000
"... This paper addresses the problem of recovering 3D nonrigid shape models from image sequences. For example, given a video recording of a talking person, we would like to estimate a 3D model of the lips and the full face and its internal modes of variation. Many solutions that recover 3D shape from 2D ..."
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Cited by 270 (7 self)
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D image sequences have been proposed; these socalled structurefrommotion techniques usually assume that the 3D object is rigid. For example Tomasi and Kanade’s factorization technique is based on a rigid shape matrix, which produces a tracking matrix of rank 3 under orthographic projection. We
Complete enumeration of stopping sets of fullrank paritycheck matrices of Hamming codes
 IEEE Transactions on Information Theory
, 2007
"... Abstract — Stopping sets, and in particular their numbers and sizes, play an important role in determining the performance of iterative decoders of linear codes over binary erasure channels. In the 2004 Shannon Lecture, McEliece presented an expression for the number of stopping sets of size three f ..."
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Cited by 8 (1 self)
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for a fullrank paritycheck matrix of the Hamming code. In this correspondence, we derive an expression for the number of stopping sets of any given size for the same paritycheck matrix. Index Terms – Hamming code, linear code, paritycheck matrix, stopping set enumerator, weight enumerator.
Highrate Fullrank SpaceTime Block Codes from Cayley Algebra
 Intl Conf on Signal Proc and Comm (SPCOM 2004
, 2004
"... For a quasistatic, multipleinput multipleoutput (MIMO) fading channel, fulldiversity, highrate spacetime block codes (STBCs) for any number of transmit antennas have been constructed in [1] by using the regular matrix representation of an associative division algebra. While the 2 × 2 as well a ..."
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Cited by 5 (1 self)
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characteristic zero field F, a method of embedding this algebra into the ring of matrices over F is described, and highrate fullrank STBCs for 8m (m, an arbitrary integer) antennas are obtained. We also give a closed form expression for the coding gain of these STBCs. This embedding when specialized to F = R
Results 1  10
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1,636