4,106 research outputs found
Calibration by correlation using metric embedding from non-metric similarities
This paper presents a new intrinsic calibration method that allows us to calibrate a generic single-view point camera just
by waving it around. From the video sequence obtained while the camera undergoes random motion, we compute the pairwise time
correlation of the luminance signal for a subset of the pixels. We show that, if the camera undergoes a random uniform motion, then
the pairwise correlation of any pixels pair is a function of the distance between the pixel directions on the visual sphere. This leads to
formalizing calibration as a problem of metric embedding from non-metric measurements: we want to find the disposition of pixels on
the visual sphere from similarities that are an unknown function of the distances. This problem is a generalization of multidimensional
scaling (MDS) that has so far resisted a comprehensive observability analysis (can we reconstruct a metrically accurate embedding?)
and a solid generic solution (how to do so?). We show that the observability depends both on the local geometric properties (curvature)
as well as on the global topological properties (connectedness) of the target manifold. We show that, in contrast to the Euclidean case,
on the sphere we can recover the scale of the points distribution, therefore obtaining a metrically accurate solution from non-metric
measurements. We describe an algorithm that is robust across manifolds and can recover a metrically accurate solution when the metric
information is observable. We demonstrate the performance of the algorithm for several cameras (pin-hole, fish-eye, omnidirectional),
and we obtain results comparable to calibration using classical methods. Additional synthetic benchmarks show that the algorithm
performs as theoretically predicted for all corner cases of the observability analysis
Comparison and contrast in perceptual categorization
People categorized pairs of perceptual stimuli that varied in both category membership and pairwise similarity. Experiments 1 and 2 showed categorization of 1 color of a pair to be reliably contrasted from that of the other. This similarity-based contrast effect occurred only when the context stimulus was relevant for the categorization of the target (Experiment 3). The effect was not simply owing to perceptual color contrast (Experiment 4), and it extended to pictures from common semantic categories (Experiment 5). Results were consistent with a sign-and-magnitude version of N. Stewart and G. D. A. Brown's (2005) similarity-dissimilarity generalized context model, in which categorization is affected by both similarity to and difference from target categories. The data are also modeled with criterion setting theory (M. Treisman & T. C. Williams, 1984), in which the decision criterion is systematically shifted toward the mean of the current stimuli
Sparsity prior for electrical impedance tomography with partial data
This paper focuses on prior information for improved sparsity reconstruction
in electrical impedance tomography with partial data, i.e. data measured only
on subsets of the boundary. Sparsity is enforced using an norm of the
basis coefficients as the penalty term in a Tikhonov functional, and prior
information is incorporated by applying a spatially distributed regularization
parameter. The resulting optimization problem allows great flexibility with
respect to the choice of measurement boundaries and incorporation of prior
knowledge. The problem is solved using a generalized conditional gradient
method applying soft thresholding. Numerical examples show that the addition of
prior information in the proposed algorithm gives vastly improved
reconstructions even for the partial data problem. The method is in addition
compared to a total variation approach.Comment: 17 pages, 12 figure
Censored Quantile Regression Redux
Quantile regression for censored survival (duration) data offers a more flexible alternative to the Cox proportional hazard model for some applications. We describe three estimation methods for such applications that have been recently incorporated into the R package quantreg: the Powell (1986) estimator for fixed censoring, and two methods for random censoring, one introduced by Portnoy (2003), and the other by Peng and Huang (2008). The Portnoy and Peng-Huang estimators can be viewed, respectively, as generalizations to regression of the Kaplan-Meier and Nelson-Aalen estimators of univariate quantiles for censored observations. Some asymptotic and simulation comparisons are made to highlight advantages and disadvantages of the three methods.
Universality classes for horizon instabilities
We introduce a notion of universality classes for the Gregory-Laflamme
instability and determine, in the supergravity approximation, the stability of
a variety of solutions, including the non-extremal D3-brane, M2-brane, and
M5-brane. These three non-dilatonic branes cross over from instability to
stability at a certain non-extremal mass. Numerical analysis suggests that the
wavelength of the shortest unstable mode diverges as one approaches the
cross-over point from above, with a simple critical exponent which is the same
in all three cases.Comment: 23 pages, latex2e, 4 figure
Understanding the Random Displacement Model: From Ground-State Properties to Localization
We give a detailed survey of results obtained in the most recent half decade
which led to a deeper understanding of the random displacement model, a model
of a random Schr\"odinger operator which describes the quantum mechanics of an
electron in a structurally disordered medium. These results started by
identifying configurations which characterize minimal energy, then led to
Lifshitz tail bounds on the integrated density of states as well as a Wegner
estimate near the spectral minimum, which ultimately resulted in a proof of
spectral and dynamical localization at low energy for the multi-dimensional
random displacement model.Comment: 31 pages, 7 figures, final version, to appear in Proceedings of
"Spectral Days 2010", Santiago, Chile, September 20-24, 201
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