@article {14868,
	title = {Illumination Recovery From Image With Cast Shadows Via Sparse Representation},
	journal = {Image Processing, IEEE Transactions on},
	volume = {20},
	year = {2011},
	month = {2011/08//},
	pages = {2366 - 2377},
	abstract = {In this paper, we propose using sparse representation for recovering the illumination of a scene from a single image with cast shadows, given the geometry of the scene. The images with cast shadows can be quite complex and, therefore, cannot be well approximated by low-dimensional linear subspaces. However, it can be shown that the set of images produced by a Lambertian scene with cast shadows can be efficiently represented by a sparse set of images generated by directional light sources. We first model an image with cast shadows composed of a diffusive part (without cast shadows) and a residual part that captures cast shadows. Then, we express the problem in an <i> $\#$x2113;</i><sub>1</sub>-regularized least-squares formulation, with nonnegativity constraints (as light has to be non-negative at any point in space). This sparse representation enjoys an effective and fast solution thanks to recent advances in compressive sensing. In experiments on synthetic and real data, our approach performs favorably in comparison with several previously proposed methods.},
	keywords = {$\#$x2113;<sub>1</sub>-regularized, approximations;, coding;image, compression;image, constraints;sparse, formulation;Lambertian, illumination, image, least-square, light, linear, reconstruction;image, recovery;low-dimensional, representation;data, representation;least, scene;cast, sensing;directional, shadows;compressive, sources;image, squares, subspaces;nonnegativity},
	isbn = {1057-7149},
	doi = {10.1109/TIP.2011.2118222},
	author = {Mei,Xue and Ling,Haibin and Jacobs, David W.}
}
@conference {13096,
	title = {Action recognition based on human movement characteristics},
	booktitle = {Motion and Video Computing, 2009. WMVC {\textquoteright}09. Workshop on},
	year = {2009},
	month = {2009/12//},
	pages = {1 - 8},
	abstract = {We present a motion descriptor for human action recognition where appearance and shape information are unreliable. Unlike other motion-based approaches, we leverage image characteristics specific to human movement to achieve better robustness and lower computational cost. Drawing on recent work on motion recognition with ballistic dynamics, an action is modeled as a series of short correlated linear movements and represented with a probability density function over motion vector data. We are targeting common human actions composed of ballistic movements, and our descriptor can handle both short actions (e.g. reaching with the hand) and long actions with events at relatively stable time offsets (e.g. walking). The proposed descriptor is used for both classification and detection of action instances, in a nearest-neighbor framework. We evaluate the descriptor on the KTH action database and obtain a recognition rate of 90\% in a relevant test setting, comparable to the state-of-the-art approaches that use other cues in addition to motion. We also acquired a database of actions with slight occlusion and a human actor manipulating objects of various shapes and appearances. This database makes the use of appearance and shape information problematic, but we obtain a recognition rate of 95\%. Our work demonstrates that human movement has distinctive patterns, and that these patterns can be used effectively for action recognition.},
	keywords = {action, ballistic, characteristics;motion, correlated, cost;human, data;probability, databases;, density, descriptor;motion, dynamics;computational, function;robustness;shape, information;short, linear, Movement, movements;computer, recognition;human, recognition;stability;visual, vector, vision;pattern},
	doi = {10.1109/WMVC.2009.5399233},
	author = {Dondera,R. and David Doermann and Davis, Larry S.}
}
@conference {12516,
	title = {Locally time-invariant models of human activities using trajectories on the grassmannian},
	booktitle = {Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on},
	year = {2009},
	month = {2009/06//},
	pages = {2435 - 2441},
	abstract = {Human activity analysis is an important problem in computer vision with applications in surveillance and summarization and indexing of consumer content. Complex human activities are characterized by non-linear dynamics that make learning, inference and recognition hard. In this paper, we consider the problem of modeling and recognizing complex activities which exhibit time-varying dynamics. To this end, we describe activities as outputs of linear dynamic systems (LDS) whose parameters vary with time, or a time-varying linear dynamic system (TV-LDS). We discuss parameter estimation methods for this class of models by assuming that the parameters are locally time-invariant. Then, we represent the space of LDS models as a Grassmann manifold. Then, the TV-LDS model is defined as a trajectory on the Grassmann manifold. We show how trajectories on the Grassmannian can be characterized using appropriate distance metrics and statistical methods that reflect the underlying geometry of the manifold. This results in more expressive and powerful models for complex human activities. We demonstrate the strength of the framework for activity-based summarization of long videos and recognition of complex human actions on two datasets.},
	keywords = {action, activity, analysis;local, analysis;video, content, dynamic, Estimation, estimation;statistical, Grassmann, indexing;distance, linear, manifold;activity-based, method;statistical, method;surveillance;time-varying, metrics;human, model;parameter, recognition;human, recognition;indexing;parameter, summarization;computer, surveillance;, system;computer, time-invariant, vision;consumer, vision;image},
	doi = {10.1109/CVPR.2009.5206710},
	author = {Turaga,P. and Chellapa, Rama}
}
@conference {16847,
	title = {Indexing Point Triples Via Triangle Geometry},
	booktitle = {Data Engineering, 2007. ICDE 2007. IEEE 23rd International Conference on},
	year = {2007},
	month = {2007/04//},
	pages = {936 - 945},
	abstract = {Database search for images containing icons with specific mutual spatial relationships can be facilitated by an appropriately structured index. For the case of images containing subsets each of which consist of three icons, the one-to-one correspondence between (distinct) point triples and triangles allows the use of such triangle attributes as position, size, orientation, and "shape" in constructing a point-based index, in which each triangle maps to a single point in a resulting hyperdimensional index space. Size (based on the triangle perimeter) can be represented by a single linear dimension. The abstract "shape" of a triangle induces a space that is inherently two-dimensional, and a number of alternative definitions of a basis for this space are examined. Within a plane, orientation reduces to rotation, and (after assignment of a reference direction for the triangle) can be represented by a single, spatially closed dimension. However, assignment of a reference direction for triangles possessing a k-fold rotational symmetry presents a significant challenge. Methods are described for characterizing shape and orientation of triangles, and for mapping these attributes onto a set of linear axes to form a combined index. The shape attribute is independent of size, orientation, and position, and the characterization of shape and orientation is stable with respect to small variations in the indexed triangles.},
	keywords = {database, databases;, dimension;spatial, geometry;database, hyperdimensional, index, index;single, index;triangle, indexing;query, linear, point;k-fold, processing;visual, relationships;structured, rotational, search;indexing, space;image, symmetry;point-based},
	doi = {10.1109/ICDE.2007.367939},
	author = {Cranston,C.B. and Samet, Hanan}
}
@conference {12250,
	title = {Robust Routing with Unknown Traffic Matrices},
	booktitle = {INFOCOM 2007. 26th IEEE International Conference on Computer Communications. IEEE},
	year = {2007},
	month = {2007/05//},
	pages = {2436 - 2440},
	abstract = {In this paper, we present an algorithm for intra-domain traffic engineering. We assume that the traffic matrix, which specifies traffic load between every source-destination pair in the network, is unknown and varies with time, but that always lies inside an explicitly defined region. Our goal is to compute a fixed robust routing with best worst case performance for all traffic matrices inside the bounding region. We formulate this problem as a semi-infinite programming problem. Then, we focus on a special case with practical merits, where (1) the traffic matrix region is assumed to be a polytope specified by a finite set of linear inequalities, and (2) our objective is to find the routing that minimizes the maximum link utilization. Under these assumptions, the problem can be formulated as a polynomial size linear programming (LP) problem with finite number of constraints. We further consider two specific set of constraints for the traffic matrix region. The first set is based on the hose model and limits the total traffic rate of network point of presence (PoP) nodes. The second set is based on the pipe model and limits the traffic between source-destination pairs. We study the effectiveness of each set of constraints using extensive simulations.},
	keywords = {engineering;linear, inequalities;maximum, intradomain, linear, link, matrices;linear, matrix, network, nodes;polynomial, of, point, presence, problem;traffic, Programming, programming;semiinfinite, programming;telecommunication, region;unknown, routing;telecommunication, size, traffic, traffic;, utilization;network},
	doi = {10.1109/INFCOM.2007.296},
	author = {Tabatabaee,V. and Kashyap,A. and Bhattacharjee, Bobby and La,R.J. and Shayman,M.A.}
}
@conference {12650,
	title = {An algebraic approach to surface reconstruction from gradient fields},
	booktitle = {Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on},
	volume = {1},
	year = {2005},
	month = {2005/10//},
	pages = {174 - 181 Vol. 1 - 174 - 181 Vol. 1},
	abstract = {Several important problems in computer vision such as shape from shading (SFS) and photometric stereo (PS) require reconstructing a surface from an estimated gradient field, which is usually non-integrable, i.e. have non-zero curl. We propose a purely algebraic approach to enforce integrability in discrete domain. We first show that enforcing integrability can be formulated as solving a single linear system Ax =b over the image. In general, this system is under-determined. We show conditions under which the system can be solved and a method to get to those conditions based on graph theory. The proposed approach is non-iterative, has the important property of local error confinement and can be applied to several problems. Results on SFS and PS demonstrate the applicability of our method.},
	keywords = {algebra;, algebraic, approach;, Computer, confinement;, discrete, domain, error, field;, from, gradient, graph, image, integrability;, linear, local, methods;, photometric, reconstruction;, shading;, SHAPE, stereo;, surface, system;, theory;, vision;},
	doi = {10.1109/ICCV.2005.31},
	author = {Agrawal,A. and Chellapa, Rama and Raskar, R.}
}
@conference {14026,
	title = {The manifolds of spatial hearing},
	booktitle = {Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP {\textquoteright}05). IEEE International Conference on},
	volume = {3},
	year = {2005},
	month = {2005/03//},
	pages = {iii/285 - iii/288 Vol. 3 - iii/285 - iii/288 Vol. 3},
	abstract = {We present exploratory studies on learning the non-linear manifold structure, in head related impulse responses (HRIRs). We use the recently popular locally linear embedding technique. The lower dimensional manifold encodes the perceptual information in the HRIRs, namely the direction of the sound source. Based on this, we propose a new method for HRIR interpolation. We also propose that the distance between two HRIRs of an individual be taken as the geodesic distance on the learned manifold.},
	keywords = {acoustics;, dimensional, direction, distance;, EMBEDDING, encoding;, geodesic, Head, hearing, hearing;, HRIR, impulse, information, interpolation;, learned, linear, localization;, locally, low, manifold, manifold;, manifolds;, nonlinear, perceptual, related, response;, responses;, sound, source, spatial, structure;, technique;, transient},
	doi = {10.1109/ICASSP.2005.1415702},
	author = {Duraiswami, Ramani and Raykar,V.C.}
}
@conference {12693,
	title = {Classification probability analysis of principal component space analysis},
	booktitle = {Pattern Recognition, 2004. ICPR 2004. Proceedings of the 17th International Conference on},
	volume = {1},
	year = {2004},
	month = {2004/08//},
	pages = {240 - 243 Vol.1 - 240 - 243 Vol.1},
	abstract = {In a previous paper, we have presented a new linear classification algorithm, principal component space analysis (PCNSA) which is designed for problems like object recognition where different classes have unequal and non-white noise covariance matrices. PCNSA first obtains a principal components space (PCA space) for the entire data and in this PCA space, it finds for each class "i", an M<sub>i</sub> dimensional subspace along which the class{\textquoteright}s intra-class variance is the smallest. We call this subspace an approximate space (ANS) since the lowest variance is usually "much smaller" than the highest. A query is classified into class "i" if its distance from the class{\textquoteright}s mean in the class{\textquoteright}s ANS is a minimum. In this paper, we discuss the PCNSA algorithm more precisely and derive tight upper bounds on its classification error probability. We use these expressions to compare classification performance of PCNSA with that of subspace linear discriminant analysis (SLDA).},
	keywords = {algorithm;, analysis;, approximate, classification, classification;, component, covariance, discriminant, error, intraclass, linear, matrices;, matrix;, noise;, nonwhite, object, pattern, PCA;, principal, probability;, recognition;, space, space;, statistics;, subspace, variance;},
	doi = {10.1109/ICPR.2004.1334068},
	author = {Vaswani, N. and Chellapa, Rama}
}
@conference {12696,
	title = {Role of shape and kinematics in human movement analysis},
	booktitle = {Computer Vision and Pattern Recognition, 2004. CVPR 2004. Proceedings of the 2004 IEEE Computer Society Conference on},
	volume = {1},
	year = {2004},
	month = {2004/07/02/june},
	pages = {I-730 - I-737 Vol.1 - I-730 - I-737 Vol.1},
	abstract = {Human gait and activity analysis from video is presently attracting a lot of attention in the computer vision community. In this paper we analyze the role of two of the most important cues in human motion-shape and kinematics. We present an experimental framework whereby it is possible to evaluate the relative importance of these two cues in computer vision based recognition algorithms. In the process, we propose a new gait recognition algorithm by computing the distance between two sequences of shapes that lie on a spherical manifold. In our experiments, shape is represented using Kendall{\textquoteright}s definition of shape. Kinematics is represented using a Linear Dynamical system We place particular emphasis on human gait. Our conclusions show that shape plays a role which is more significant than kinematics in current automated gait based human identification algorithms. As a natural extension we study the role of shape and kinematics in activity recognition. Our experiments indicate that we require models that contain both shape and kinematics in order to perform accurate activity classification. These conclusions also allow us to explain the relative performance of many existing methods in computer-based human activity modeling.},
	keywords = {activity, algorithm;, algorithms;, analysis;, autoregressive, average, based, classification;, community;, Computer, definition;, dynamical, extraction;, feature, Gait, hidden, human, identification, image, Kendall, linear, manifold;, Markov, modeling;, models;, MOTION, Movement, moving, processes;, recognition, sequences;, SHAPE, spherical, system;, VISION, vision;},
	doi = {10.1109/CVPR.2004.1315104},
	author = {Veeraraghavan,A. and Chowdhury, A.R. and Chellapa, Rama}
}
@conference {15029,
	title = {Strategies for exploring large scale data},
	booktitle = {Parallel Architectures, Algorithms and Networks, 2004. Proceedings. 7th International Symposium on},
	year = {2004},
	month = {2004/05//},
	pages = {2 - 2},
	abstract = {We consider the problem of querying large scale multidimensional time series data to discover events of interest, test and validate hypotheses, or to associate temporal patterns with specific events. This type of data currently dominates most other types of available data, and will very likely become even more prevalent in the future given the current trends in collecting time series of business, scientific, demographic, and simulation data. The ability to explore such collections interactively, even at a coarse level, will be critical in discovering the information and knowledge embedded in such collections. We develop indexing techniques and search algorithms to efficiently handle temporal range value querying of multidimensional time series data. Our indexing uses linear space data structures that enable the handling of queries in I/O time that is essentially the same as that of handling a single time slice, assuming the availability of a logarithmic number of processors as a function of the temporal window. A data structure with provably almost optimal asymptotic bounds is also presented for the case when the number of multidimensional objects is relatively small. These techniques improve significantly over standard techniques for either serial or parallel processing, and are evaluated by extensive experimental results that confirm their superior performance.},
	keywords = {algorithms;, association;, asymptotic, bounds;, business, data, data;, database, databases;, demographic, discovery;, Indexing, indexing;, information, knowledge, large, linear, mining;, multidimensional, objects;, optimal, Parallel, pattern, processing;, query, querying;, range, scale, scientific, search, serial, series, series;, simulation, space, structure;, structures;, techniques;, temporal, TIME, value, very, window;},
	doi = {10.1109/ISPAN.2004.1300447},
	author = {JaJa, Joseph F.}
}
@conference {12694,
	title = {A system identification approach for video-based face recognition},
	booktitle = {Pattern Recognition, 2004. ICPR 2004. Proceedings of the 17th International Conference on},
	volume = {4},
	year = {2004},
	month = {2004/08//},
	pages = {175 - 178 Vol.4 - 175 - 178 Vol.4},
	abstract = {The paper poses video-to-video face recognition as a dynamical system identification and classification problem. We model a moving face as a linear dynamical system whose appearance changes with pose. An autoregressive and moving average (ARMA) model is used to represent such a system. The choice of ARMA model is based on its ability to take care of the change in appearance while modeling the dynamics of pose, expression etc. Recognition is performed using the concept of sub space angles to compute distances between probe and gallery video sequences. The results obtained are very promising given the extent of pose, expression and illumination variation in the video data used for experiments.},
	keywords = {and, autoregressive, average, dynamical, Face, gallery, identification;, image, linear, model;, moving, processes;, processing;, recognition;, sequences;, signal, system, system;, video, video-based},
	doi = {10.1109/ICPR.2004.1333732},
	author = {Aggarwal,G. and Chowdhury, A.K.R. and Chellapa, Rama}
}
@article {14886,
	title = {Lambertian reflectance and linear subspaces},
	journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
	volume = {25},
	year = {2003},
	month = {2003/02//},
	pages = {218 - 233},
	abstract = {We prove that the set of all Lambertian reflectance functions (the mapping from surface normals to intensities) obtained with arbitrary distant light sources lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution. These results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions. We also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4D linear space. We apply these algorithms to perform face recognition by finding the 3D model that best matches a 2D query image.},
	keywords = {2D, 4D, 9D, analog;, analytic, characterization;, convex, convolution, distant, functions;, harmonics;, image, image;, intensities;, Lambertian, light, lighting, linear, methods;, nonnegative, normals;, object, optimization;, programming;, query, recognition;, reflectance;, reflectivity;, set;, sources;, space;, spherical, subspace;, subspaces;, surface},
	isbn = {0162-8828},
	doi = {10.1109/TPAMI.2003.1177153},
	author = {Basri,R. and Jacobs, David W.}
}
@conference {12763,
	title = {An experimental evaluation of linear and kernel-based methods for face recognition},
	booktitle = {Applications of Computer Vision, 2002. (WACV 2002). Proceedings. Sixth IEEE Workshop on},
	year = {2002},
	month = {2002///},
	pages = {13 - 18},
	abstract = {In this paper we present the results of a comparative study of linear and kernel-based methods for face recognition. The methods used for dimensionality reduction are Principal Component Analysis (PCA), Kernel Principal Component Analysis (KPCA), Linear Discriminant Analysis (LDA) and Kernel Discriminant Analysis (KDA). The methods used for classification are Nearest Neighbor (NN) and Support Vector Machine (SVM). In addition, these classification methods are applied on raw images to gauge the performance of these dimensionality reduction techniques. All experiments have been performed on images from UMIST Face Database.},
	keywords = {analysis;, classification;, component, discriminant, Face, image, Kernel, linear, Machine;, nearest, neighbor;, principal, recognition;, Support, vector},
	doi = {10.1109/ACV.2002.1182137},
	author = {Gupta, H. and Agrawala, Ashok K. and Pruthi, T. and Shekhar, C. and Chellapa, Rama}
}
@article {15399,
	title = {Perturbation technique for LLG dynamics in uniformly magnetized bodies subject to RF fields},
	journal = {Magnetics, IEEE Transactions on},
	volume = {38},
	year = {2002},
	month = {2002/09//},
	pages = {2403 - 2405},
	abstract = {The problem of magnetization dynamics of a uniformly magnetized uniaxial particle or film, under elliptically polarized applied field, is considered. In the special case of circularly polarized applied field and particles (films) with a symmetry axis, pure time-harmonic magnetization modes exist that can be computed analytically. Deviations from these highly symmetric conditions are treated as perturbation of the symmetric case. The perturbation technique leads to the exactly solvable system of linear differential equations for the perturbations which enables one to compute higher order magnetization harmonic. The analytical solutions are obtained and then compared with numerical results.},
	keywords = {analytical, anisotropy, anisotropy;, applied, bodies;, circularly, component;, constant-in-time, constant;, damping, demagnetisation;, demagnetizing, differential, dynamics;, effective, elliptically, equation;, equations;, exactly, factors;, field;, film;, films;, Frequency, gyromagnetic, harmonic;, higher, Landau-Lifshitz-Gilbert, large, linear, magnetic, magnetisation;, magnetization, magnetization;, magnetized, modes;, MOTION, order, partial, particle;, particles;, perturbation, polarized, radio, ratio;, RF, saturation, solution;, solvable, system;, technique;, techniques;, thin, time-harmonic, uniaxial, uniformly},
	isbn = {0018-9464},
	doi = {10.1109/TMAG.2002.803596},
	author = {Bertotti,G. and Mayergoyz, Issak D and Serpico,C.}
}
@article {17735,
	title = {The decompositional approach to matrix computation},
	journal = {Computing in Science Engineering},
	volume = {2},
	year = {2000},
	month = {2000/02//jan},
	pages = {50 - 59},
	abstract = {The introduction of matrix decomposition into numerical linear algebra revolutionized matrix computations. The article outlines the decompositional approach, comments on its history, and surveys the six most widely used decompositions: Cholesky decomposition; pivoted LU decomposition; QR decomposition; spectral decomposition; Schur decomposition; and singular value decomposition},
	keywords = {Algebra, approach;history;matrix, Cholesky, computation;matrix, computations;pivoted, computing;matrix, decomposition;, decomposition;bibliographies;history;mathematics, decomposition;decompositional, decomposition;numerical, decomposition;QR, decomposition;Schur, decomposition;singular, decomposition;spectral, linear, LU, matrix, revolutionized, value},
	isbn = {1521-9615},
	doi = {10.1109/5992.814658},
	author = {Stewart, G.W.}
}
@conference {14839,
	title = {Error propagation in full 3D-from-2D object recognition},
	booktitle = {Computer Vision and Pattern Recognition, 1994. Proceedings CVPR {\textquoteright}94., 1994 IEEE Computer Society Conference on},
	year = {1994},
	month = {1994/06//},
	pages = {892 - 898},
	abstract = {Robust recognition systems require a careful understanding of the effects of error in sensed features. Error in these image features results in uncertainty in the possible image location of each additional model feature. We present an accurate, analytic approximation for this uncertainty when model poses are based on matching three image and model points. This result applies to objects that are fully three-dimensional, where past results considered only two-dimensional objects. Further, we introduce a linear programming algorithm to compute this uncertainty when poses are based on any number of initial matches},
	keywords = {3D-from-2D, algorithm;, error, extraction;, feature, features;, handling;, image, initial, linear, matches;, object, Programming, programming;, propagation;, recognition, recognition;, robust, sequences;, systems;, Uncertainty, uncertainty;},
	doi = {10.1109/CVPR.1994.323920},
	author = {Alter,T. D. and Jacobs, David W.}
}
@conference {14896,
	title = {Finding structurally consistent motion correspondences},
	booktitle = {Pattern Recognition, 1994. Vol. 1 - Conference A: Computer Vision Image Processing., Proceedings of the 12th IAPR International Conference on},
	volume = {1},
	year = {1994},
	month = {1994/10//},
	pages = {650 -653 vol.1 - 650 -653 vol.1},
	abstract = {Much work on deriving scene structure and motion from features assumes as input a set of tracked image features that share a common 3D motion. Producing this input requires segmenting independent motions, and detecting image features that do not correspond to 3D features, originating instead, for example in occlusion boundaries or specularities. We derive a linear program that tells when a set of tracked points might have come from 3D points that share a single motion, assuming affine motion and bounded error. We can also use linear programming to place conservative bounds on the structure of the scene that corresponds to tracked points. We implement and test this algorithm on real images},
	keywords = {3D, boundaries;, common, consistent, correspondences;, estimation;, features;, image, independent, linear, MOTION, motion;, occlusion, programming;, scene, segmentation;, specularities;, structurally, structure;, tracked},
	doi = {10.1109/ICPR.1994.576388},
	author = {Jacobs, David W. and Chennubhotla,C.}
}
@conference {14881,
	title = {Segmenting independently moving, noisy points},
	booktitle = {Motion of Non-Rigid and Articulated Objects, 1994., Proceedings of the 1994 IEEE Workshop on},
	year = {1994},
	month = {1994/11//},
	pages = {96 - 103},
	abstract = {There has been much work on using point features tracked through a video sequence to determine structure and motion. In many situations, to use this work, we must first isolate subsets of points that share a common motion. This is hard because we must distinguish between independent motions and apparent deviations from a single motion due to noise. We propose several methods of searching for point-sets with consistent 3D motions. We analyze the potential sensitivity of each method for detecting independent motions, and experiment with each method on a real image sequence},
	keywords = {3D, common, consistent, estimation;, features;, image, independently, linear, MOTION, motion;, moving, noisy, point, points;, programming;, real, segmentation;, sequence;, sequences;, video},
	doi = {10.1109/MNRAO.1994.346249},
	author = {Jacobs, David W. and Chennubhotla,C.}
}
@conference {14838,
	title = {2D images of 3-D oriented points},
	booktitle = {Computer Vision and Pattern Recognition, 1993. Proceedings CVPR {\textquoteright}93., 1993 IEEE Computer Society Conference on},
	year = {1993},
	month = {1993/06//},
	pages = {226 - 232},
	abstract = {A number of vision problems have been shown to become simpler when one models projection from 3-D to 2-D as a nonrigid linear transformation. These results have been largely restricted to models and scenes that consist only of 3-D points. It is shown that, with this projection model, several vision tasks become fundamentally more complex in the somewhat more complicated domain of oriented points. More space is required for indexing models in a database, more images are required to derive structure from motion, and new views of an object cannot be synthesized linearly from old views},
	keywords = {2D, 3-D, database, derivation;, image, images;, indexing;, linear, model, nonrigid, oriented, points;, processing;, recovery;, structure-form-motion, structure-from-motion, transformation;},
	doi = {10.1109/CVPR.1993.340985},
	author = {Jacobs, David W.}
}
@conference {15207,
	title = {Efficient minimum cost matching using quadrangle inequality},
	booktitle = {Foundations of Computer Science, 1992. Proceedings., 33rd Annual Symposium on},
	year = {1992},
	month = {1992/10//},
	pages = {583 - 592},
	abstract = {The authors present efficient algorithms for finding a minimum cost perfect matching, and for solving the transportation problem in bipartite graphs, G = (Red cup; Blue, Red times; Blue), where |Red| = n, |Blue| = m, n les; m, and the cost function obeys the quadrangle inequality. The first results assume that all the red points and all the blue points lie on a curve that is homeomorphic to either a line or a circle and the cost function is given by the Euclidean distance along the curve. They present a linear time algorithm for the matching problem. They generalize the method to solve the corresponding transportation problem in O((m+n)log(m+n)) time. The next result is an O(n log m) algorithm for minimum cost matching when the cost array is a bitonic Monge array. An example of this is when the red points lie on one straight line and the blue points lie on another straight line (that is not necessarily parallel to the first one). Finally, they provide a weakly polynomial algorithm for the transportation problem in which the associated cost array is a bitonic Monge array},
	keywords = {algorithm;, array;, bipartite, bitonic, blue, complexity;, computational, cost, distance;, Euclidean, function;, geometry;, graph, graphs;, inequality;, linear, MATCHING, matching;, minimisation;, minimum, Monge, perfect, points;, polynomial, problem;, quadrangle, red, theory;, TIME, transportation, transportation;, weakly},
	doi = {10.1109/SFCS.1992.267793},
	author = {Aggarwal,A. and Bar-Noy,A. and Khuller, Samir and Kravets,D. and Schieber,B.}
}
@article {15047,
	title = {VLSI architectures for multidimensional transforms},
	journal = {Computers, IEEE Transactions on},
	volume = {40},
	year = {1991},
	month = {1991/09//},
	pages = {1053 - 1057},
	abstract = {The authors propose a family of VLSI architectures with area-time tradeoffs for computing (<e1>N</e1> times;<e1>N</e1> times; . . . times;<e1>N</e1>) <e1>d</e1>-dimensional linear separable transforms. For fixed-precision arithmetic with <e1>b</e1> bits, the architectures have an area <e1>A</e1>=<e1>O</e1>(<e1>N</e1><sup>d+2a</sup>) and computation time <e1>T</e1>=<e1>O</e1>(<e1>dN</e1><sup>d/2-a</sup><e1>b </e1>), and achieve the <e1>AT</e1><sup>2</sup> bound of <e1>AT</e1><sup>2</sup>=<e1>O</e1>(<e1>n</e1><sup>2</sup><e1>b</e1> <sup>2</sup>) for constant <e1>d</e1>, where <e1>n</e1>=<e1>N</e1><sup>d </sup> and <e1>O</e1> lt;<e1>a</e1> les;<e1>d</e1>/2},
	keywords = {architecture;, architectures;, arithmetic;, complexity;, computational, Computer, digital, fixed-precision, linear, multidimensional, separable, transforms;, VLSI},
	isbn = {0018-9340},
	doi = {10.1109/12.83648},
	author = {Chakrabarti,C. and JaJa, Joseph F.}
}
