Coplanar Repeats by Energy Minimization

This paper proposes an automated method to detect, group and rectify arbitrarily-arranged coplanar repeated elements via energy minimization. The proposed energy functional combines several features that model how planes with coplanar repeats are projected into images and captures global interactions between different coplanar repeat groups and scene planes. An inference framework based on a recent variant of $\alpha$-expansion is described and fast convergence is demonstrated. We compare the proposed method to two widely-used geometric multi-model fitting methods using a new dataset of annotated images containing multiple scene planes with coplanar repeats in varied arrangements. The evaluation shows a significant improvement in the accuracy of rectifications computed from coplanar repeats detected with the proposed method versus those detected with the baseline methods.Comment: 14 pages with supplemental materials attache

Planarizable Supersymmetric Quantum Toboggans

In supersymmetric quantum mechanics the emergence of a singularity may lead to the breakdown of isospectrality between partner potentials. One of the regularization recipes is based on a topologically nontrivial, multisheeted complex deformations of the line of coordinate $x$ giving the so called quantum toboggan models (QTM). The consistent theoretical background of this recipe is briefly reviewed. Then, certain supersymmetric QTM pairs are shown exceptional and reducible to doublets of non-singular ordinary differential equations a.k.a. Sturm-Schr\"odinger equations containing a weighted energy $E\to EW(x)$ and living in single complex plane

Self-calibration and motion recovery from silhouettes with two mirrors

LNCS v. 7724-7727 (pts. 1-4) entitled: Computer vision - ACCV 2012: 11th Asian Conference on Computer Vision ... 2012: revised selected papersThis paper addresses the problem of self-calibration and motion recovery from a single snapshot obtained under a setting of two mirrors. The mirrors are able to show five views of an object in one image. In this paper, the epipoles of the real and virtual cameras are firstly estimated from the intersection of the bitangent lines between corresponding images, from which we can easily derive the horizon of the camera plane. The imaged circular points and the angle between the mirrors can then be obtained from equal angles between the bitangent lines, by planar rectification. The silhouettes produced by reflections can be treated as a special circular motion sequence. With this observation, technique developed for calibrating a circular motion sequence can be exploited to simplify the calibration of a single-view two-mirror system. Different from the state-of-the-art approaches, only one snapshot is required in this work for self-calibrating a natural camera and recovering the poses of the two mirrors. This is more flexible than previous approaches which require at least two images. When more than a single image is available, each image can be calibrated independently and the problem of varying focal length does not complicate the calibration problem. After the calibration, the visual hull of the objects can be obtained from the silhouettes. Experimental results show the feasibility and the preciseness of the proposed approach. © 2013 Springer-Verlag.postprin

Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory

A few recent innovations of applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly broadened four-Hilbert-space update. Among applications involving several new scattering and bound-state problems the central role is played by the models using apparently non-Hermitian ("crypto-Hermitian") Hamiltonians with real spectra. The formalism (originally inspired by the topical need of mathematically consistent description of tobogganic quantum models) is shown to admit certain unusual nonlocal and/or "moving-frame" representations of the standard physical Hilbert space of wave functions.Comment: 10 pages, talk, int. conf. "Selected Topics in Mathematical and Particle Physics" (Prague, 5-7 May 2009, http://www.km.fjfi.cvut.cz/conference/st2009/

Non-parametric Models of Distortion in Imaging Systems.

Traditional radial lens distortion models are based on the physical construction of lenses. However, manufacturing defects and physical shock often cause the actual observed distortion to be different from what can be modeled by the physically motivated models. In this work, we initially propose a Gaussian process radial distortion model as an alternative to the physically motivated models. The non-parametric nature of this model helps implicitly select the right model complexity, whereas for traditional distortion models one must perform explicit model selection to decide the right parametric complexity. Next, we forego the radial distortion assumption and present a completely non-parametric, mathematically motivated distortion model based on locally-weighted homographies. The separation from an underlying physical model allows this model to capture arbitrary sources of distortion. We then apply this fully non-parametric distortion model to a zoom lens, where the distortion complexity can vary across zoom levels and the lens exhibits noticeable non-radial distortion. Through our experiments and evaluation, we show that the proposed models are as accurate as the traditional parametric models at characterizing radial distortion while flexibly capturing non-radial distortion if present in the imaging system.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120690/1/rpradeep_1.pd