@conference {14850,
	title = {Trainable 3D recognition using stereo matching},
	booktitle = {Computer Vision Workshops (ICCV Workshops), 2011 IEEE International Conference on},
	year = {2011},
	month = {2011///},
	pages = {625 - 631},
	abstract = {Stereo matching has been used for face recognition in the presence of pose variation. In this approach, stereo matching is used to compare two 2-D images based on correspondences that reflect the effects of viewpoint variation and allow for occlusion. We show how to use stereo matching to derive image descriptors that can be used to train a classifier. This improves face recognition performance, producing the best published results on the CMU PIE dataset. We also demonstrate that classification based on stereo matching can be used for general object classification in the presence of pose variation. In preliminary experiments we show promising results on the 3D object class dataset, a standard, challenging 3D classification data set.},
	keywords = {2D, 3D, class, classification, classification;image, data, dataset;CMU, dataset;face, descriptor;occlusion;pose, estimation;solid, image, image;3D, matching;pose, matching;trainable, modelling;stereo, object, PIE, processing;, recognition;face, recognition;image, set;3D, variation;stereo},
	doi = {10.1109/ICCVW.2011.6130301},
	author = {Castillo,C. D and Jacobs, David W.}
}
@conference {14831,
	title = {Wide-baseline stereo for face recognition with large pose variation},
	booktitle = {Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on},
	year = {2011},
	month = {2011/06//},
	pages = {537 - 544},
	abstract = {2-D face recognition in the presence of large pose variations presents a significant challenge. When comparing a frontal image of a face to a near profile image, one must cope with large occlusions, non-linear correspondences, and significant changes in appearance due to viewpoint. Stereo matching has been used to handle these problems, but performance of this approach degrades with large pose changes. We show that some of this difficulty is due to the effect that foreshortening of slanted surfaces has on window-based matching methods, which are needed to provide robustness to lighting change. We address this problem by designing a new, dynamic programming stereo algorithm that accounts for surface slant. We show that on the CMU PIE dataset this method results in significant improvements in recognition performance.},
	keywords = {2D, algorithm;frontal, dataset;dynamic, estimation;stereo, Face, image, image;near, image;pose, MATCHING, matching;pose, matching;surface, method;dynamic, performance;stereo, PIE, processing;, profile, Programming, programming;face, recognition;CMU, recognition;image, slant;wide-baseline, stereo, stereo;window-based, variation;recognition},
	doi = {10.1109/CVPR.2011.5995559},
	author = {Castillo,C. D and Jacobs, David W.}
}
@conference {14846,
	title = {Using Stereo Matching for 2-D Face Recognition Across Pose},
	booktitle = {Computer Vision and Pattern Recognition, 2007. CVPR {\textquoteright}07. IEEE Conference on},
	year = {2007},
	month = {2007/06//},
	pages = {1 - 8},
	abstract = {We propose using stereo matching for 2-D face recognition across pose. We match one 2-D query image to one 2-D gallery image without performing 3-D reconstruction. Then the cost of this matching is used to evaluate the similarity of the two images. We show that this cost is robust to pose variations. To illustrate this idea we built a face recognition system on top of a dynamic programming stereo matching algorithm. The method works well even when the epipolar lines we use do not exactly fit the viewpoints. We have tested our approach on the PIE dataset. In all the experiments, our method demonstrates effective performance compared with other algorithms.},
	keywords = {2D, estimation;stereo, Face, gallery, image, image;2D, image;dynamic, matching;dynamic, matching;pose, processing;, programming;face, programming;pose, query, recognition;2D, recognition;image, variation;stereo},
	doi = {10.1109/CVPR.2007.383111},
	author = {Castillo,C. D and Jacobs, David W.}
}
@conference {12608,
	title = {Shape-Regulated Particle Filtering for Tracking Non-Rigid Objects},
	booktitle = {Image Processing, 2006 IEEE International Conference on},
	year = {2006},
	month = {2006/10//},
	pages = {2813 - 2816},
	abstract = {This paper presents an active contour based algorithm for tracking non-rigid objects in heavily cluttered scenes. We decompose the non-rigid contour tracking problem into three subproblems: 2D motion estimation, deformation detection, and shape regulation. First, we employ a particle filter to estimate the affine transform parameters between successive frames. Second, by using a dynamic object model, we generate a probabilistic map of deformation to reshape its contour. Finally, we project the updated model onto a trained shape subspace to constrain deformations to be within possible object appearances. Our experiments show that the proposed algorithm significantly improves the performance of the tracker},
	keywords = {(numerical, 2D, algorithm;affine, based, contour, detection;dynamic, detection;motion, detection;parameter, estimation;active, estimation;object, estimation;particle, Filtering, filtering;probabilistic, filters;, map;shape-regulation;affine, methods);tracking, model;nonrigid, MOTION, object, scenes;deformation, tracking;parameter, transform;cluttered, transforms;clutter;edge},
	doi = {10.1109/ICIP.2006.312993},
	author = {Jie Shao and Chellapa, Rama and Porikli, F.}
}
@conference {14034,
	title = {Computation of Green{\textquoteright}s function for finite-size photonic crystals by boundary element method},
	booktitle = {Antennas and Propagation Society International Symposium, 2004. IEEE},
	volume = {4},
	year = {2004},
	month = {2004/06//},
	pages = {4320 - 4323 Vol.4 - 4320 - 4323 Vol.4},
	abstract = {We have derived a new integral equation method for computing the Green{\textquoteright}s function for 2D electromagnetic wave propagation in a finite size photonic crystal. The method is also used for deriving the multipole expansions for the case of circular cylinders. This derivation is different from the ones in the literature. Our numerical results show an excellent agreement of the two algorithms. In the future we would like to expand the method to the numerical solution of the three-dimensional electromagnetic problem.},
	keywords = {2D, boundary, boundary-elements, circular, crystals;, cylinders;, electromagnetic, element, equation, equations;, expansions;, finite-size, function, function;, Green, Green{\textquoteright}s, integral, method;, methods;, multipole, photonic, propagation;, wave},
	doi = {10.1109/APS.2004.1330307},
	author = {Seydou,F. and Ramahi,O. and Duraiswami, Ramani and Seppdnen,T.}
}
@article {12699,
	title = {Wide baseline image registration with application to 3-D face modeling},
	journal = {Multimedia, IEEE Transactions on},
	volume = {6},
	year = {2004},
	month = {2004/06//},
	pages = {423 - 434},
	abstract = {Establishing correspondence between features in two images of the same scene taken from different viewing angles is a challenging problem in image processing and computer vision. However, its solution is an important step in many applications like wide baseline stereo, three-dimensional (3-D) model alignment, creation of panoramic views, etc. In this paper, we propose a technique for registration of two images of a face obtained from different viewing angles. We show that prior information about the general characteristics of a face obtained from video sequences of different faces can be used to design a robust correspondence algorithm. The method works by matching two-dimensional (2-D) shapes of the different features of the face (e.g., eyes, nose etc.). A doubly stochastic matrix, representing the probability of match between the features, is derived using the Sinkhorn normalization procedure. The final correspondence is obtained by minimizing the probability of error of a match between the entire constellation of features in the two sets, thus taking into account the global spatial configuration of the features. The method is applied for creating holistic 3-D models of a face from partial representations. Although this paper focuses primarily on faces, the algorithm can also be used for other objects with small modifications.},
	keywords = {2D, 3D, algorithm;, baseline, biometrics;, Computer, configuration;, correspondence, doubly, error, extraction;, Face, feature, holistic, image, matching;, matrix;, minimization;, modeling;, models;, normalization, probability, probability;, procedure;, processes;, processing;, recognition;, registration;, representation;, sequences;, shapes;, Sinkhorn, spatial, statistics;, Stochastic, video, vision;, wide},
	isbn = {1520-9210},
	doi = {10.1109/TMM.2004.827511},
	author = {Roy-Chowdhury, A.K. and Chellapa, Rama and Keaton, T.}
}
@conference {14055,
	title = {A 2D profile reconstruction in a multilayered waveguide structure},
	booktitle = {Antennas and Propagation Society International Symposium, 2003. IEEE},
	volume = {1},
	year = {2003},
	month = {2003/06//},
	pages = {531 - 534 vol.1 - 531 - 534 vol.1},
	abstract = {We discuss the problem of finding a profile or its location for a 2D scattering of electromagnetic waves with fixed frequencies in a waveguide multilayered domain. We use the dual space method (DSM) of Colton and Monk. Our goal is to extend our previous work of TE and TM cases to the more complicated case of a waveguide. We emphasize on the frequency range in the reconstruction.},
	keywords = {(mathematics);, 2D, dual, duality, electromagnetic, equations;, inhomogeneous, Maxwell, media;, method;, multilayered, multilayers;, profile, reconstruction;, scattering;, space, structure;, theory;, wave, waveguide, waveguides;},
	doi = {10.1109/APS.2003.1217513},
	author = {Seydou,F. and Duraiswami, Ramani and Seppanen,T.}
}
@conference {12729,
	title = {Activity recognition using the dynamics of the configuration of interacting objects},
	booktitle = {Computer Vision and Pattern Recognition, 2003. Proceedings. 2003 IEEE Computer Society Conference on},
	volume = {2},
	year = {2003},
	month = {2003/06//},
	pages = {II - 633-40 vol.2 - II - 633-40 vol.2},
	abstract = {Monitoring activities using video data is an important surveillance problem. A special scenario is to learn the pattern of normal activities and detect abnormal events from a very low resolution video where the moving objects are small enough to be modeled as point objects in a 2D plane. Instead of tracking each point separately, we propose to model an activity by the polygonal {\textquoteright}shape{\textquoteright} of the configuration of these point masses at any time t, and its deformation over time. We learn the mean shape and the dynamics of the shape change using hand-picked location data (no observation noise) and define an abnormality detection statistic for the simple case of a test sequence with negligible observation noise. For the more practical case where observation (point locations) noise is large and cannot be ignored, we use a particle filter to estimate the probability distribution of the shape given the noisy observations up to the current time. Abnormality detection in this case is formulated as a change detection problem. We propose a detection strategy that can detect both {\textquoteright}drastic{\textquoteright} and {\textquoteright}slow{\textquoteright} abnormalities. Our framework can be directly applied for object location data obtained using any type of sensors - visible, radar, infrared or acoustic.},
	keywords = {2D, abnormal, abnormality, abnormality;, acoustic, activity, analysis;, change;, Computer, configuration, configuration;, data;, DETECTION, detection;, distribution;, drastic, dynamics;, event;, filter;, hand-picked, image, infrared, interacting, learning;, location, low, mean, model;, monitoring;, MOTION, moving, noise;, noisy, object, object;, observation, observation;, particle, pattern, plane;, point, polygonal, probability, probability;, problem;, processing;, radar, recognition;, resolution, sensor;, sensors;, sequence;, SHAPE, shape;, signal, slow, statistic;, strategy;, Surveillance, surveillance;, target, test, tracking;, video, video;, visible, vision;},
	doi = {10.1109/CVPR.2003.1211526},
	author = {Vaswani, N. and RoyChowdhury, A. 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.}
}
@article {12748,
	title = {Optimal edge-based shape detection},
	journal = {Image Processing, IEEE Transactions on},
	volume = {11},
	year = {2002},
	month = {2002/11//},
	pages = {1209 - 1227},
	abstract = {We propose an approach to accurately detecting two-dimensional (2-D) shapes. The cross section of the shape boundary is modeled as a step function. We first derive a one-dimensional (1-D) optimal step edge operator, which minimizes both the noise power and the mean squared error between the input and the filter output. This operator is found to be the derivative of the double exponential (DODE) function, originally derived by Ben-Arie and Rao (1994). We define an operator for shape detection by extending the DODE filter along the shape{\textquoteright}s boundary contour. The responses are accumulated at the centroid of the operator to estimate the likelihood of the presence of the given shape. This method of detecting a shape is in fact a natural extension of the task of edge detection at the pixel level to the problem of global contour detection. This simple filtering scheme also provides a tool for a systematic analysis of edge-based shape detection. We investigate how the error is propagated by the shape geometry. We have found that, under general assumptions, the operator is locally linear at the peak of the response. We compute the expected shape of the response and derive some of its statistical properties. This enables us to predict both its localization and detection performance and adjust its parameters according to imaging conditions and given performance specifications. Applications to the problem of vehicle detection in aerial images, human facial feature detection, and contour tracking in video are presented.},
	keywords = {1D, 2D, aerial, analysis;, boundary, conditions;, contour, cross, detection;, DODE, double, edge, edge-based, error, error;, exponential, extraction;, facial, feature, filter, filter;, Filtering, function;, geometry;, global, human, images;, imaging, localization, mean, methods;, NOISE, operator;, optimal, optimisation;, output;, performance;, pixel;, power;, propagation;, properties;, section;, SHAPE, square, squared, statistical, step, theory;, tracking;, two-dimensional, vehicle, video;},
	isbn = {1057-7149},
	doi = {10.1109/TIP.2002.800896},
	author = {Moon, H. and Chellapa, Rama and Rosenfeld, A.}
}
@conference {12761,
	title = {Quasi-invariants for human action representation and recognition},
	booktitle = {Pattern Recognition, 2002. Proceedings. 16th International Conference on},
	volume = {1},
	year = {2002},
	month = {2002///},
	pages = {307 - 310 vol.1 - 307 - 310 vol.1},
	abstract = {Although human action recognition has been the subject of much research in the past, the issue of viewpoint invariance has received scarce attention. In this paper, we present an approach to detect human action with a high tolerance to viewpoint change. Canonical body poses are modeled in a view invariant manner to enable detection from a general viewpoint. While there exist no invariants for 3D to 2D projection, there exists a wealth of techniques in 2D invariance that can be used to advantage in 3D to 2D projection. We employ 2D invariants to recognize canonical poses of the human body leading to an effective way to represent and recognize human action which we evaluate theoretically and experimentally on 2D projections of publicly available human motion capture data.},
	keywords = {2D, action, analysis;, body, canonical, change, human, image, invariance;, MOTION, poses;, quasi-invariants;, recognition;, representation;, tolerance;, viewpoint},
	doi = {10.1109/ICPR.2002.1044699},
	author = {Parameswaran, V. and Chellapa, Rama}
}
@conference {12747,
	title = {Wide baseline image registration using prior information},
	booktitle = {Multimedia Signal Processing, 2002 IEEE Workshop on},
	year = {2002},
	month = {2002/12//},
	pages = {37 - 40},
	abstract = {Establishing correspondence between features in two images of the same scene taken from different viewing angles in a challenging problem in image processing and computer vision. However, its solution is an important step in many applications like wide baseline stereo, 3D model alignment, creation of panoramic views etc. In this paper, we propose a technique for registration of two images of a face obtained from different viewing angles. We show that prior information about the general characteristics of a face obtained from video sequences of different faces can be used to design a robust correspondence algorithm. The method works by matching 2D shapes of the different features of the face. A doubly stochastic matrix, representing the probability of match between the features, is derived using the Sinkhorn normalization procedure. The final correspondence is obtained by minimizing the probability of error of a match between the entire constellations of features in the two sets, thus taking into account the global spatial configuration of the features. The method is applied for creating holistic 3D models of a face from partial representations. Although this paper focuses primarily on faces, the algorithm can also be used for other objects with small modifications.},
	keywords = {2D, 3D, algorithm;, alignment;, angles;, baseline, Computer, configuration;, constellation;, correspondence, creation;, doubly, error, extraction;, Face, feature, global, holistic, image, images;, matching;, matrix;, model, models;, normalization, panoramic, probability;, procedure;, processes;, processing;, registration;, robust, sequences;, SHAPE, signal, Sinkhorn, spatial, statistics;, stereo;, Stochastic, video, view, viewing, vision;, wide},
	doi = {10.1109/MMSP.2002.1203242},
	author = {Chowdhury, AM and Chellapa, Rama and Keaton, T.}
}
@article {15596,
	title = {Approximating large convolutions in digital images},
	journal = {Image Processing, IEEE Transactions on},
	volume = {10},
	year = {2001},
	month = {2001/12//},
	pages = {1826 - 1835},
	abstract = {Computing discrete two-dimensional (2-D) convolutions is an important problem in image processing. In mathematical morphology, an important variant is that of computing binary convolutions, where the kernel of the convolution is a 0-1 valued function. This operation can be quite costly, especially when large kernels are involved. We present an algorithm for computing convolutions of this form, where the kernel of the binary convolution is derived from a convex polygon. Because the kernel is a geometric object, we allow the algorithm some flexibility in how it elects to digitize the convex kernel at each placement, as long as the digitization satisfies certain reasonable requirements. We say that such a convolution is valid. Given this flexibility we show that it is possible to compute binary convolutions more efficiently than would normally be possible for large kernels. Our main result is an algorithm which, given an m times;n image and a k-sided convex polygonal kernel K, computes a valid convolution in O(kmn) time. Unlike standard algorithms for computing correlations and convolutions, the running time is independent of the area or perimeter of K, and our techniques do not rely on computing fast Fourier transforms. Our algorithm is based on a novel use of Bresenham{\textquoteright}s (1965) line-drawing algorithm and prefix-sums to update the convolution incrementally as the kernel is moved from one position to another across the image},
	keywords = {2D, algorithm;binary, approximation;mathematical, convolution, convolution;binary, convolutions;Bresenham{\textquoteright}s, convolutions;convex, convolutions;geometric, images;discrete, kernel;convex, kernel;digital, line-drawing, morphology;, morphology;approximation, object;image, polygonal, processing;large, processing;mathematical, theory;convolution;image, two-dimensional},
	isbn = {1057-7149},
	doi = {10.1109/83.974567},
	author = {Mount, Dave and Kanungo,T. and Netanyahu,N. S and Piatko,C. and Silverman,R. and Wu,A. Y}
}
@article {15369,
	title = {2-D MOSFET modeling including surface effects and impact ionization by self-consistent solution of the Boltzmann, Poisson, and hole-continuity equations},
	journal = {Electron Devices, IEEE Transactions on},
	volume = {44},
	year = {1997},
	month = {1997/02//},
	pages = {257 - 267},
	abstract = {We present a new two-dimensional (2-D) MOSFET simulation method achieved by directly solving the Boltzmann transport equation for electrons, the hole-current continuity equation, and the Poisson equation self-consistently. The spherical harmonic method is used for the solution of the Boltzmann equation. The solution directly gives the electron distribution function, electrostatic potential, and the hole concentration for the entire 2-D MOSFET. Average quantities such as electron concentration and electron temperature are obtained directly from the integration of the distribution function. The collision integral is formulated to arbitrarily high spherical harmonic order, and new collision terms are included that incorporate effects of surface scattering and electron-hole pair recombination/generation. I-V characteristics, which agree with experiment, are calculated directly from the distribution function for an LDD submicron MOSFET. Electron-hole pair generation due to impact ionization is also included by direct application of the collision integral. The calculations are efficient enough for day-to-day engineering design on workstation-type computers},
	keywords = {2D, characteristics;LDD, concentration;electron, concentration;hole-continuity, density;electron-hole, density;impact, device, distribution, effects;surface, equation;collision, equation;I-V, equation;MOSFET;electron, equations;impact, equations;semiconductor, function;electron, generation;electron-hole, harmonic, integral;electron, ionisation;integral, ionization;self-consistent, method;Boltzmann, method;surface, modeling;Boltzmann, models;surface, MOSFET, MOSFET;Poisson, pair, potential;hole, recombination;electrostatic, recombination;hole, scattering;, scattering;two-dimensional, simulation, solution;spherical, submicron, temperature;electron-hole, transport},
	isbn = {0018-9383},
	doi = {10.1109/16.557713},
	author = {Liang,Wenchao and Goldsman,N. and Mayergoyz, Issak D and Oldiges,P.J.}
}
@article {14890,
	title = {The space requirements of indexing under perspective projections},
	journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
	volume = {18},
	year = {1996},
	month = {1996/03//},
	pages = {330 - 333},
	abstract = {Object recognition systems can be made more efficient through the use of table lookup to match features. The cost of this indexing process depends on the space required to represent groups of model features in such a lookup table. We determine the space required to perform indexing of arbitrary sets of 3D model points for lookup from a single 2D image formed under perspective projection. We show that in this case, one must use a 3D surface to represent model groups, and we provide an analytic description of such a surface. This is in contrast to the cases of scaled-orthographic or affine projection, in which only a 2D surface is required to represent a group of model features. This demonstrates a fundamental way in which the recognition of objects under perspective projection is more complex than is recognition under other projection models},
	keywords = {2D, complexity;feature, complexity;table, extraction;image, hashing;indexing, image, images;3D, lookup;, lookup;computational, matching;geometric, matching;indexing;object, model, points;feature, process;invariants;object, processing;table, projections;space, recognition;perspective, recognition;stereo},
	isbn = {0162-8828},
	doi = {10.1109/34.485561},
	author = {Jacobs, David W.}
}
@article {15374,
	title = {A parallel-in-time method for the transient simulation of SOI devices with drain current overshoots},
	journal = {Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on},
	volume = {13},
	year = {1994},
	month = {1994/08//},
	pages = {1035 - 1044},
	abstract = {This paper presents a new parallel-in-time algorithm for the two dimensional transient simulation of SOI devices. With this approach, simulation in both space and time domains is performed in parallel As a result, the CPU time is reduced significantly from the conventional serial-in-time method. This new approach fully exploits the inherent parallelism of the finite difference formulation of the basic semiconductor device equations and the massively parallel architecture of SIMD computers. The space domain computations are inherently parallel due to the nature of our technique of solving the finite-difference equations. Time domain parallelism is achieved by shifting the potentials from previous time points to subsequent points one-step forward along the time axis with each Gummel iteration. This algorithm employs a fixed-point iteration technique, therefore a direct solution of matrix equations is avoided. The algorithm is especially suitable for the transient simulation of SOI devices that exhibit transient drain current overshoot. Numerical experiments show that the new parallel-in-time method is up to eight times faster than the conventional serial-in-time method in SOI transient simulations. The program is coded in CM Fortran for the Connection Machine},
	keywords = {2D, algorithms;semiconductor, analysis;transient, architecture;parallel-in-time, boundaries;silicon;time-domain, computations;time, computers;SOI, computing;finite, current, device, devices;drain, devices;parallel, difference, dimensional, domain, effect, engineering, equations;fixed-point, equations;space, field, Fortran;CPU, gate, iteration, iteration;SIMD, Machine;Gummel, method;semiconductor, methods;insulated, methods;metal-insulator-semiconductor, models;semiconductor-insulator, overshoots;finite-difference, Parallel, parallelism;transient, response;, simulation;CM, simulation;digital, simulation;electronic, simulation;two, technique;massively, time;Connection, transistors;iterative},
	isbn = {0278-0070},
	doi = {10.1109/43.298039},
	author = {Tai,G.-C. and Korman,C.E. and Mayergoyz, Issak D}
}
@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 {13571,
	title = {Image based typographic analysis of documents},
	booktitle = {Document Analysis and Recognition, 1993., Proceedings of the Second International Conference on},
	year = {1993},
	month = {1993/10//},
	pages = {769 - 773},
	abstract = {An approach to image based typographic analysis of documents is provided. The problem requires a spatial understanding of the document layout as well as knowledge of the proper syntax. The system performs a page synthesis from the stream of formatting commands defined in a DVI file. Since the two-dimensional relationships between document components are not explicit in the page language, the authors develop a representation which preserves the two-dimensional layout, the read-order and the attributes of document components. From this hierarchical representation of the page layout we extract and analyze relevant typographic features such as margins, line and character spacing, and figure placement},
	keywords = {2D, analysis;, attributes;, based, character, commands;, component, data, description, document, DVI, extraction;, feature, figure, file;, formatting, hierarchical, image, language;, languages;, layout;, line, margins;, page, placement;, processing;, read-order;, relationships;, representation;, spacing;, spatial, structures;, syntax;, synthesis;, typographic, understanding;},
	doi = {10.1109/ICDAR.1993.395624},
	author = {David Doermann and Furuta,R.}
}
@article {14888,
	title = {Space and time bounds on indexing 3D models from 2D images},
	journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
	volume = {13},
	year = {1991},
	month = {1991/10//},
	pages = {1007 - 1017},
	abstract = {Model-based visual recognition systems often match groups of image features to groups of model features to form initial hypotheses, which are then verified. In order to accelerate recognition considerably, the model groups can be arranged in an index space (hashed) offline such that feasible matches are found by indexing into this space. For the case of 2D images and 3D models consisting of point features, bounds on the space required for indexing and on the speedup that such indexing can achieve are demonstrated. It is proved that, even in the absence of image error, each model must be represented by a 2D surface in the index space. This places an unexpected lower bound on the space required to implement indexing and proves that no quantity is invariant for all projections of a model into the image. Theoretical bounds on the speedup achieved by indexing in the presence of image error are also determined, and an implementation of indexing for measuring this speedup empirically is presented. It is found that indexing can produce only a minimal speedup on its own. However, when accompanied by a grouping operation, indexing can provide significant speedups that grow exponentially with the number of features in the groups},
	keywords = {2D, bounds;time, bounds;visual, extraction;grouping, features;model, features;model-based, images;3D, indexing;feature, model, operation;image, pattern, picture, processing;, recognition, recognition;computerised, recognition;space, systems;computerised},
	isbn = {0162-8828},
	doi = {10.1109/34.99235},
	author = {Clemens,D. T and Jacobs, David W.}
}
@article {15011,
	title = {Parallel algorithms for planar graph isomorphism and related problems},
	journal = {Circuits and Systems, IEEE Transactions on},
	volume = {35},
	year = {1988},
	month = {1988/03//},
	pages = {304 - 311},
	abstract = {Parallel algorithms for planar graph isomorphism and several related problems are presented. Two models of parallel computation are considered: the CREW-PRAM model and the two-dimensional array of processors. The results include <e1>O</e1>( radic;<e1>n</e1>)-time mesh algorithms for finding a good separating cycle and the triconnected components of a planar graph, and for solving the single-function coarsest partitioning problem},
	keywords = {2D, algorithms;, algorithms;parallel, array;computational, array;CREW-PRAM, coarsest, complexity;graph, components;two-dimensional, COMPUTATION, graph, graph;planar, isomorphism;single-function, model;mesh, models;planar, partitioning, problem;triconnected, processor, theory;parallel},
	isbn = {0098-4094},
	doi = {10.1109/31.1743},
	author = {JaJa, Joseph F. and Kosaraju,S.R.}
}
