Fast Random Rotation Matrices

Arvo, James

doi:10.1016/b978-0-08-050755-2.50034-8

Cited by 83 publications

(82 citation statements)

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“…• , since observations could coincide with any point on the precession period. The 3D orientation of the circumbinary system on the sky, with respect to a given observer, was randomised by applying a uniform 3D rotation algorithm by Arvo (1992). We simulated 10 000 randomly drawn systems over four years, and recorded stellar eclipses and planet transits.…”

Section: Impact Of the Observing Timespanmentioning

confidence: 99%

Planets transiting non-eclipsing binaries

Martin

Triaud

2014

A&A

106

141

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The majority of binary stars do not eclipse. Current searches for transiting circumbinary planets concentrate on eclipsing binaries, and are therefore restricted to a small fraction of potential hosts. We investigate the concept of finding planets transiting non-eclipsing binaries, whose geometry would require mutually inclined planes. Using an N-body code we explore how the number and sequence of transits vary as functions of observing time and orbital parameters. The concept is then generalised thanks to a suite of simulated circumbinary systems. Binaries are constructed from radial-velocity surveys of the solar neighbourhood. They are then populated with orbiting gas giants, drawn from a range of distributions. The binary population is shown to be compatible with the Kepler eclipsing binary catalogue, indicating that the properties of binaries may be as universal as the initial mass function. These synthetic systems produce transiting circumbinary planets occurring on both eclipsing and non-eclipsing binaries. Simulated planets transiting eclipsing binaries are compared with published Kepler detections. We find 1) that planets transiting non-eclipsing binaries are probably present in the Kepler data; 2) that observational biases alone cannot account for the observed over-density of circumbinary planets near the stability limit, which implies a physical pile-up; and 3) that the distributions of gas giants orbiting single and binary stars are likely different. Estimating the frequency of circumbinary planets is degenerate with the spread in mutual inclination. Only a minimum occurrence rate can be produced, which we find to be compatible with 9%. Searching for inclined circumbinary planets may significantly increase the population of known objects and will test our conclusions. Their presence, or absence, will reveal the true occurrence rate and help develop circumbinary planet formation theories.

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Section: Impact Of the Observing Timespanmentioning

confidence: 99%

Planets transiting non-eclipsing binaries

Martin

Triaud

2014

A&A

106

141

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“…To generate the poses, we assume no prior information on the rotation and so we generate random rotation matrices according to [Arvo, 1992]. However, we initialise the translation such that the mean of the 3D data is in the centre of the image (which is the case in the synthetic data, and is sufficiently close for the real data) and initialise a random depth within 5% from the ground truth.…”

Section: Methodsmentioning

confidence: 99%

“…The synthetic datasets are the Stanford bunny and Stanford dragon, and the horse and angel from the Large Geometric Models Archive from Georgia Institute of Technology. For the synthetic datasets, textureless images were generated using POV-Ray from a random angle [Arvo, 1992] and fixed translation, using a point light source at the same location as the camera. The two real datasets are the dinosaur and temple from Middlebury's multi-view reconstruction dataset [Seitz et al, 2006].…”

Section: Methodsmentioning

confidence: 99%

“…Therefore, the points are initially aligned according to (5) by SoftPosit and scored according to (6), which is subsequently minimised in Section 3.4. In the current implementation, 50 iterations are carried out from 500 random initial poses, for which random rotation matrices were generated using the method described in [Arvo, 1992]. Further, OpenGL is used to render the 3D model and points that are not visible are not included in the update step.…”

Section: Compute a Matrix Of Weightsmentioning

confidence: 99%

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A Saliency-based Framework for 2D-3D Registration

Brown

Guillemaut

Windridge

2014

Proceedings of the 9th International Conference on Computer Vision Theory and Applications

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Abstract:Here we propose a saliency-based filtering approach to the problem of registering an untextured 3D object to a single monocular image. The principle of saliency can be applied to a range of modalities and domains to find intrinsically descriptive entities from amongst detected entities, making it a rigorous approach to multi-modal registration. We build on the Kadir-Brady saliency framework due to its principled information-theoretic approach which enables us to naturally extend it to the 3D domain. The salient points from each domain are initially aligned using the SoftPosit algorithm. This is subsequently refined by aligning the silhouette with contours extracted from the image. Whereas other point based registration algorithms focus on corners or straight lines, our saliency-based approach is more general as it is more widely applicable e.g. to curved surfaces where a corner detector would fail. We compare our salient point detector to the Harris corner and SIFT keypoint detectors and show it generally achieves superior registration accuracy.

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“…Our first approach was to use evenly distributed sets of the three rotational angles, however, this leads to a very uneven sampling and is highly inefficient since some areas are heavily oversampled. We therefore used a simple, more promising approach, random sample generation [7]. Deterministic sample generation with good properties is challenging and application of existing results could be a topic of further research.…”

Section: Introductionmentioning

confidence: 99%

Local approximate 3D matching of proteins in viral cryo-EM density maps

Burkhardt

Fredriksson

Ojamies

et al.

Proceedings. 2nd International Symposium on 3D Data Processing, Visualization and Transmission, 2004. 3DPVT 2004.

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Abstract-Experimental structure analysis of biological molecules (e.g, proteins) or macromolecular complexes (e.g, viruses) can be used to generate three-dimensional density maps of these entities. Such a density map can be viewed as a three-dimensional gray-scale image where space is subdivided in voxels of a given size. The focus of this paper is the analysis of virus density maps. The hull of a virus consists of many copies of one or several different proteins. An important tool for the study of viruses is cryo-electron microscopy (cryo-EM), a technique with insufficient resolution to directly determine the arrangement of the proteins in the virus. We therefore created a tool that locates proteins in the three-dimensional density map of a virus. The goal is to fully determine the locations and orientations of the protein(s) in the virus given the virus' three-dimensional density map and a database of density maps of one or more protein candidates.

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Fast Random Rotation Matrices

Cited by 83 publications

References 0 publications

Planets transiting non-eclipsing binaries

Planets transiting non-eclipsing binaries

A Saliency-based Framework for 2D-3D Registration

Local approximate 3D matching of proteins in viral cryo-EM density maps

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