Paracatadioptric camera calibration

For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they intersect at a common point, are more “powerful” than a set of parallel lines. In particular, we prove that every such set of lines supports outerpaths, lobsters, and squids, none of which are supported by any set of parallel lines. On the negative side, we prove that no set of n lines that intersect in a common point supports all n-vertex planar graphs. Finally, we show that there exists a set of n lines in general position that does not support all n-vertex planar graphs.

Theoretical and experimental investigation of the influence of the snow cover on the surfaces of reflector, in particular, parabolic reflector antennas on parameters of these antennas is performed. In the physical-Optics approximation, design relationships allowing one to estimate degradation of the antenna parameters were derived. It was experimentally confirmed that, depending on the dimensions and shape of the snow layer on the surface of a parabolic reflector, it may lower the antenna gain by 4–14 dB, increase sidelobes of the antenna pattern by 10–15 dB, and narrow down the main lobe width almost by a factor of two.

A previous field experiment demonstrated that the interface between an air‐water mixture of low fractional air volume (say, 0.005) and air‐free water is an effective reflector of acoustic waves, suggesting that acoustic waves in water might be beamed by placing an energy source at the focus of a paraboloidal interface between an air‐water mixture and air‐free water. When this interface is concave downward, wave energy traveling upward and outward from the source at the focus is reflected downward and the surface reflection (ghost) is eliminated. Accordingly, a paraboloid reflector consisting of perforated circular air pipes was constructed and tested with a small water gun at its focus. The structure, suspended from its apex, had a height of 4 ft (1.2 m), a base diameter of 8 ft (2.4 m), and a focus 1 ft (0.3 m) below the apex. The wave field, measured with an air‐bubble stream emanating from the perforated pipes, displays a beam with a nearly constant half‐width of 22 ft (6.7 m) created by the paraboloid reflector. Signal amplitudes directly below the paraboloid on an extension of its axis are as much as 9 dB above, and off‐axis amplitudes are as much as 17 dB below, signal amplitudes for no air‐bubble stream. The source signal’s amplitude spectrum, extending to about 1.5 kHz, is skewed toward higher frequencies by the paraboloid reflector, resulting in a dominant peak frequency of about 1210 Hz. The ghost is not evident. Theoretical wave fields of beamed monofrequency source signals demonstrate that the paraboloid reflector behaves as a high‐cut filter, the band‐pass narrowing as axial distance to the paraboloid decreases and off‐axis distance increases. Axial rates of decrease of the beamed experimental signal with increasing depth, at depths of 20 ft (6.1 m) and greater below the source, compare favorably to those of beamed theoretical continuous sinusoidal signals which are nearly equal at all frequencies within the experimental signal’s frequency band. Additional research is required to determine the complete effect of the paraboloid reflector on water‐gun signal characteristics. The small prototype reflector used in this experiment is not suitable for typical seismic exploration efforts because it produces excessively high‐frequency content. A useful paraboloid reflector may have to be several times the size of this prototype.

Rotational splitting Δω(n,l,m) of the eigenfrequencies of a star rotating with angular velocity Ω(r, θ) about a unique axis can be represented as a weighted integral of Ω over r and θ, (r, θ, φ) being spherical polar coordinates about the axis of rotation. For high-frequency acoustic modes, Δω/m collapses essentially to a function of ω — ω /(l+1/2) and M = m/(l + 1/2) alone, and the weighting kernel K(r,θ) becomes asymptotically degenerate, each factor being of essentially Abel type. Therefore, formally, the splitting integral can be inverted, once a procedure has been found for extending Δω over the domain of (ω, M) such that the turning points (rt,ωt), given by (c(rt)/rt, sinωt) = (ω, M) where c is sound speed, span the star. Obtaining that representation is the most difficult stage of the inversion. We report on a procedure that treats the inverted two-dimensional Abel integral as a repeated double integral, representing the data successively along a set of parallel lines M =constant. The method is illustrated by an inversion of artificial data which is compared with the angular velocity from which those data were computed.

The structure of a strange attractor

The desire to increase the amount of information that can be encoded onto a single photon has driven research into many areas of optics. One such area is optical orbital angular momentum (OAM) [1]. These beams have helical phasefronts and carry an orbital angular momentum of mbar per photon, where the integer m is unbounded, giving a large state space in which to encode information. We recently developed a telescope system comprising two bespoke refractive optical elements to transform OAM states into transverse momentum states [2]. This is achieved by mapping the azimuthal position of the input plane to the lateral position in the output [3]. A mapping of this type transforms a set of concentric rings at the input plane into a set of parallel lines in the output plane. A lens can then separate the resulting transverse momentum states into specified lateral positions, allowing for the efficient measurement of multiple OAM states simultaneously. Separating OAM states in this way presents an opportunity for this larger alphabet to improve the data capacity of a free space link and has potential application in both the classical and quantum regimes. We will present our latest design, increasing the bandwidth of measurable states to over 50 OAM modes. In such a system we study the crosstalk introduced by a thin phase turbulence, showing that turbulence similarly degrades the purity of all the modes within this range.

Synthesis, physico-chemical and DNA interaction studies of homo- and hetero-trinuclear complexes

The electrostatic potential in an ionic crystal is presented in terms of the zeroth-order MacDonald function by means of decomposition of the crystal lattice into sets of parallel lines with the periodic charge distribution with the zero net charge within a period. The method is applied to the calculation of the Madelung constants of a series of standard cubic lattices, doped fullerides and idealized Y-Ba-Cu-O crystals.

Determining object shape from local velocity measurements

With a still developing and largely unpoliced code of ethics, the Internet forces users to renegotiate continually the boundaries and registers of publicity and privacy, and thus, it is the technic that constellates the ideal conditions for gossip, quite apart from its speed and efficiency in circulating tittle-tattle. Proceeding from observations about how the Internet challenges definitional certitudes about the practice and performance of gossip, this article considers the queer performances of Stephen Karam's darkly comic play Speech & Debate, in which three high-school misfits meet and bond over shared sexual secrets that begin to circulate online. Karam's representation suggests how the new platforms or stages for gossip that develop out of networking sites and technologies may create new counter-publics, capable, in their turn, of occasioning new forms of counter-intimacy. These platforms offer not only new potentialities for intertextual citation and public discourse but also mechanisms for self-promotion and, in this way, raise questions about the distinction between confession and gossip and between intimacy and publicity: two sets of parallel lines that have begun to bend toward one another.

Given an arbitrary simple polygon with N vertices we present an algorithm for shading the interior of the polygon with a set of parallel lines where the slope and the distance between lines are prespecified. If the number of shading line segments is M, the algorithm described in the paper runs in 0(N log N + M) time. The algorithm is generalizable to shade any region or regions of an arbitrary planar subdivision.

The algorithm of combining a real image with a virtual model was proposed to increase the reality of synthesized images. Currently, synthesizing a real image with a virtual model facilitated the surface reflection model and various geometric techniques. In the current methods, the characteristics of various illuminants in the real image are not sufficiently considered. In addition, despite the chromatic adaptation plays a vital role for accommodating different illuminants in the two media viewing conditions, it is not taken into account in the existing methods. Thus, it is hardly to get high-quality synthesized images. In this paper, we proposed the two-phase image synthesis algorithm. First, the surface reflectance of the maximum high-light region (MHR) was estimated using the three eigenvectors obtained from the principal component analysis (PCA) applied to the surface reflectances of 1269 Munsell samples. The combined spectral value, i.e., the product of surface reflectance and the spectral power distributions (SPDs) of an illuminant, of MHR was then estimated using the three eigenvectors obtained from PCA applied to the products of surface reflectances of Munsell 1269 samples and the SPDs of four CIE Standard Illuminants (A, C, D50, D65). By dividing the average combined spectral values of MHR by the average surface reflectances of MHR, we could estimate the illuminant of a real image. Second, the mixed chromatic adaptation (S-LMS) using an estimated and an external illuminants was applied to the virtual-model image. For evaluating the proposed algorithm, experiments with synthetic and real scenes were performed. It was shown that the proposed method was effective in synthesizing the real and the virtual scenes under various illuminants.

A new technique is proposed for calibrating a 3D modeling system with variable zoom based on multi-view stereo image analysis. The 3D modeling system uses a stereo camera with variable zoom setting and a turntable for rotating an object. Given an object whose complete 3D model (mesh and texture-map) needs to be generated, the object is placed on the turntable and stereo images of the object are captured from multiple views by rotating the turntable. Partial 3D models generated from different views are integrated to obtain a complete 3D model of the object. Changing the zoom to accommodate objects of different sizes and at different distances from the stereo camera changes several internal camera parameters such as focal length and image center. Also, the parameters of the rotation axis of the turntable changes. We present camera calibration techniques for estimating the camera parameters and the rotation axis for different zoom settings. The Perspective Projection Matrices (PPM) of the cameras are calibrated at a selected set of zoom settings. The PPM is decomposed into intrinsic parameters, orientation angles, and translation vectors. Camera parameters at an arbitrary intermediate zoom setting are estimated from the nearest calibrated zoom positions through interpolation. A performance evaluation of this technique is presented with experimental results. We also present a refinement technique for stereo rectification that improves partial shape recovery. And the rotation axis of multi-view at different zoom setting is estimated without further calibration. Complete 3D models obtained with our techniques are presented.

This paper describes a new approach to color image rendering for mixed reality applications. The approach has two steps. The first uses neural network based photometric stereo to obtain both a 3D shape model and color reflectance factors simultaneously. The second uses neural network based image rendering to generate realistic virtual images for arbitrary viewpoint and direction of light source. The proposed approach achieves high quality 3D modeling of real objects and subsequent virtual image rendering based on empirical measurements obtained in a simple experimental environment. The approach is empirical using only a standard digital camera and light sources. Assumptions about surface reflectance are reasonably generic. Experiments using real data are demonstrated.

Detecting and finding people are complex tasks when visibility is reduced. This happens, for example, if a fire occurs. In these situations, heat sources and large amounts of smoke are generated. Under these circumstances, locating survivors using thermal or conventional cameras is not possible and it is necessary to use alternative techniques. The challenge of this work was to analyze if it is feasible the integration of an acoustic camera, developed at the University of Valladolid, on an unmanned aerial vehicle (UAV) to locate, by sound, people who are calling for help, in enclosed environments with reduced visibility. The acoustic array, based on MEMS (micro-electro-mechanical system) microphones, locates acoustic sources in space, and the UAV navigates autonomously by closed enclosures. This paper presents the first experimental results locating the angles of arrival of multiple sound sources, including the cries for help of a person, in an enclosed environment. The results are promising, as the system proves able to discriminate the noise generated by the propellers of the UAV, at the same time it identifies the angles of arrival of the direct sound signal and its first echoes reflected on the reflective surfaces.