7027764
Optimization Criteria, Sensitivity and Robustness of Motion and Structure Estimation
The prevailing efforts to study the standard formulation of motion and structure recovery have been recently focused on issues of sensitivity and robustness of existing techniques. While many cogent observations have been made and verified experimentally, many statements do not hold in general settings and make a comparison of existing techniques difficult. With an ultimate goal of clarifying these issues we study the main aspects of the problem: the choice of objective functions, optimization techniques and the sensitivity and robustness issues in the presence of noise. 
 
We clearly reveal the relationship among different objective functions, such as "(normalized) epipolar constraints", "reprojection error" or "triangulation", which can all be be unified in a new "optimal triangulation" procedure formulated as a constrained optimization problem. Regardless of various choices of the objective function, the optimization problems all inherit the same unknown parameter space, the so called "essential manifold", making the new optimization techniques on Riemanian manifolds directly applicable. 
 
Using these analytical results we provide a clear account of sensitivity and robustness of the proposed linear and nonlinear optimization techniques and study the analyticaland practical equivalence of different objective functions. The geometric characterization of critical points of a function defined on essential manifold and the simulation results clarify the difference between the effect of bas relief ambiguity and other types of local minima leading to a consistent interpretations of simulation results over large range of signal-to-noise ratio and variety of configurations.
354989
Symmetry-based photo editing
Based on high-level geometric knowledge, especially symmetry, imposed upon objects in images, we demonstrate how to edit images in terms of correct 3-D shape and relationships of the objects, without explicitly performing full 3-D reconstruction. Symmetry is proposed as the central notation that unifies both conceptually and algorithmically all types of geometric regularities such as parallelism, orthogonality, and similarity. The methods are extremely simple, accurate and easy to implement, and they demonstrate the power of applying scene knowledge.
696914
Generalized principal component analysis (GPCA)
This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high-dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as k-subspaces and expectation maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.
13369249
Reconstruction of 3-D Symmetric Curves from Perspective Images without Discrete Features
The shapes of many natural and man-made objects have curved contours. The images of such contours usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. This paper shows that both the shape of curves in 3-D space and the camera poses can be accurately reconstructed from their perspective images with unknown point correspondences given that the curves have certain invariant properties such as symmetry. We show that in such cases the minimum number of views needed for a solution is remarkably small: one for planar curves and two for nonplanar curves (of arbitrary shapes), which is significantly less than what is required by most existing algorithms for general curves. Our solutions rely on minimizing the L 2-distance between the shapes of the curves reconstructed via the “epipolar geometry” of symmetric curves. Both simulations and experiments on real images are presented to demonstrate the effectiveness of our approach.
8131766
Segmentation of a piece-wise planar scene from perspective images
We study and compare two novel embedding methods for segmenting feature points of piece-wise planar structures from two (uncalibrated) perspective images. We show that a set of different homographies can be embedded in different ways to a higher-dimensional real or complex space, so that each homography corresponds to either a complex bilinear form or a real quadratic form. Each embedding reveals different algebraic properties and relations of homographies. We give a closed-form segmentation solution for each case by utilizing these properties based on subspace-segmentation methods. These theoretical results show that one can intrinsically segment a piece-wise planar scene from 2-D images without explicitly performing any 3-D reconstruction. The resulting segmentation may make subsequent 3-D reconstruction much better-conditioned. We demonstrate the proposed methods with some convincing experimental results.
36567578
Euclidean reconstruction and reprojection up to subgroups
The necessary and sufficient conditions for being able to estimate scene structure, motion and camera calibration from a sequence of images are very rarely satisfied in practice. What exactly can be estimated in sequences of practical importance, when such conditions are not satisfied? In this paper we give a complete answer to this question. For every camera motion that fails to meet the conditions, we give explicit formulas for the ambiguities in the reconstructed scene, motion and calibration. Such a characterization is crucial both for designing robust estimation algorithms (that do not try to recover parameters that cannot be recovered), and for generating novel views of the scene by controlling the vantage point. To this end, we characterize explicitly all the vantage points that give rise to a valid Euclidean reprojection regardless of the ambiguity in the reconstruction. We also characterize vantage points that generate views that are altogether invariant to the ambiguity. All the results are presented using simple notation that involves no tensors nor complex projective geometry, and should be accessible with basic background in linear algebra.
7391513
Asymptotic performance of hybrid-selection/maximal-ratio combining over fading channels
In this letter, we study the asymptotic performance of hybrid-selection/maximal-ratio combining (HS/MRC) and postdetection HS/equal-gain combining (HS/EGC) over generalized fading channels for large average signal-to-noise ratios (ASNRs). By evaluating the asymptotic moment generating function of the HS/MRC output SNR at high ASNR, we derive the diversity and coding gains for HS/MRC for a large class of modulation formats and versatile fading conditions, including different types of fading channels and nonidentical SNR statistics across diversity branches. Our analytical results reveal that the diversity gains of HS/MRC and HS/EGC are equivalent to that of MRC, and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter. Some new analytical results about effects of the number of combined branches for HS/MRC and noncoherent combining loss of HS/EGC are also provided.
47404061
Diversity and Multiplexing Tradeoff in General Fading Channels
The optimal tradeoff between diversity gain and multiplexing gain for multiple-inputmultiple-output (MIMO) channels has been studied recently under the independent and identically distributed (i.i.d.) Rayleigh-fading assumption. In this correspondence, this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions, including different fading types, nonidentical fading distributions, spatial correlation, and nonzero channel means. Our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance
5996048
Scaling up all pairs similarity search
Given a large collection of sparse vector data in a high dimensional space, we investigate the problem of finding all pairs of vectors whose similarity score (as determined by a function such as cosine distance) is above a given threshold. We propose a simple algorithm based on novel indexing and optimization strategies that solves this problem without relying on approximation methods or extensive parameter tuning. We show the approach efficiently handles a variety of datasets across a wide setting of similarity thresholds, with large speedups over previous state-of-the-art approaches.
1012168
SAT: Spatial Awareness from Textual Input
Recent events (WTC attacks, Southeast Asia Tsunamis, Hurricane Katrina, London bombings) have illustrated the need for accurate and timely situational awareness tools in emergency response. Developing effective situational awareness (SA) systems has the potential to radically improve decision support in crises by improving the accuracy and reliability of the information available to the decision-makers. In an evolving crisis, raw situational information comes from a variety of sources in the form of situational reports, live radio transcripts, sensor data, video streams. Much of the data resides (or can be converted) in the form of free text, from which events of interest are extracted. Spatial or location information is one of the fundamental attributes of the events, and is useful for a variety of situational awareness (SA) tasks.
33501253
A design analysis model for developing world wide web sites
This study applies reader-response criticism to examine the relationship between and among designers, text, and users of the Galter Health Sciences Library Web site. It asks such questions as "How do Web site designers construct their subject?" or, "whom do the web designers think their users are?" The study ascertains the intentions of the designers of the GHSL Web site; examines the meanings made by the users through interviews; compares the similarities and differences of designers' intentions with their organization of knowlege represented in the GHSL Web site; and compares the similarities and differences between the designers' intentions and views of the users.