Non-rigid Shape Matching Using Geometry and Photometry

International audienceIn this paper, we tackle the problem of finding correspondences between three-dimensional reconstructions of a deformable surface at different time steps. We suppose that (i) the mechanical underlying model imposes time-constant geodesic distances between points on the surface; and that (ii) images of the real surface are available. This is for instance the case in spatio-temporal shape from videos (e.g. multi-view stereo, visual hulls, etc.) when the surface is supposed approximatively unstretchable. These assumptions allow to exploit both geometry and photometry. In particular we propose an energy based formulation of the problem, extending the work of Bronstein et of. [1]. On the one hand, we show that photometry (i) improves accuracy in case of locally elastic deformations or noisy surfaces and (ii) allows to still find the right solution when [1] fails because of ambiguities (e.g. symmetries). On the other hand, using geometry makes it possible to match shapes that have undergone large motion, which is not possible with usual photometric methods. Numerical experiments prove the efficiency of our method on synthetic and real data

Geometric and Photometric Data Fusion in Non-Rigid Shape Analysis

In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fai

KOI-54: The Kepler Discovery of Tidally Excited Pulsations and Brightenings in a Highly Eccentric Binary

Kepler observations of the star HD 187091 (KIC 8112039, hereafter KOI-54) revealed a remarkable light curve exhibiting sharp periodic brightening events every 41.8 days with a superimposed set of oscillations forming a beating pattern in phase with the brightenings. Spectroscopic observations revealed that this is a binary star with a highly eccentric orbit, e = 0.83. We are able to match the Kepler light curve and radial velocities with a nearly face-on (i = 5 degrees.5) binary star model in which the brightening events are caused by tidal distortion and irradiation of nearly identical A stars during their close periastron passage. The two dominant oscillations in the light curve, responsible for the beating pattern, have frequencies that are the 91st and 90th harmonic of the orbital frequency. The power spectrum of the light curve, after removing the binary star brightening component, reveals a large number of pulsations, 30 of which have a signal-to-noise ratio greater than or similar to 7. Nearly all of these pulsations have frequencies that are either integer multiples of the orbital frequency or are tidally split multiples of the orbital frequency. This pattern of frequencies unambiguously establishes the pulsations as resonances between the dynamic tides at periastron and the free oscillation modes of one or both of the stars. KOI-54 is only the fourth star to show such a phenomenon and is by far the richest in terms of excited modes.NASA, Science Mission DirectorateNASA NNX08AR14GEuropean Research Council under the European Community 227224W.M. Keck FoundationMcDonald Observator

Locating the Trailing Edge of the Circumbinary Ring in the KH 15D System

Following two years of complete occultation of both stars by its opaque circumbinary ring, the binary T Tauri star KH 15D has abruptly brightened again during apastron phases, reaching I = 15 mag. Here, we show that the brightening is accompanied by a change in spectral class from K6/K7 (the spectral class of star A) to ~K1, and a bluing of the system in V-I by about 0.3 mag. A radial velocity measurement confirms that, at apastron, we are now seeing direct light from star B, which is more luminous and of earlier spectral class than star A. Evidently, the trailing edge of the occulting screen has just become tangent to one anse of star B's projected orbit. This confirms a prediction of the precession models, supports the view that the tilted ring is self-gravitating, and ushers in a new era of the system's evolution that should be accompanied by the same kind of dramatic phenomena observed from 1995-2009. It also promotes KH 15D from a single-lined to a double-lined eclipsing binary, greatly enhancing its value for testing pre-main sequence models. The results of our study strengthen the case for truncation of the outer ring at around 4 AU by a sub-stellar object such as an extremely young giant planet. The system is currently at an optimal configuration for detecting the putative planet and we urge expedient follow-up observations.Comment: 6 pages, 5 figures, accepted for publication in ApJ Letter

Geometric and photometric affine invariant image registration

This thesis aims to present a solution to the correspondence problem for the registration of wide-baseline images taken from uncalibrated cameras. We propose an affine invariant descriptor that combines the geometry and photometry of the scene to find correspondences between both views. The geometric affine invariant component of the descriptor is based on the affine arc-length metric, whereas the photometry is analysed by invariant colour moments. A graph structure represents the spatial distribution of the primitive features; i.e. nodes correspond to detected high-curvature points, whereas arcs represent connectivities by extracted contours. After matching, we refine the search for correspondences by using a maximum likelihood robust algorithm. We have evaluated the system over synthetic and real data. The method is endemic to propagation of errors introduced by approximations in the system.BAE SystemsSelex Sensors and Airborne System

Construction of Bayesian Deformable Models via Stochastic Approximation Algorithm: A Convergence Study

The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modelling non aligned data affected by various types of geometrical variability. This is especially true in shape modelling in the computer vision community or in probabilistic atlas building for Computational Anatomy (CA). A first coherent statistical framework modelling the geometrical variability as hidden variables has been given by Allassonni\`ere, Amit and Trouv\'e (JRSS 2006). Setting the problem in a Bayesian context they proved the consistency of the MAP estimator and provided a simple iterative deterministic algorithm with an EM flavour leading to some reasonable approximations of the MAP estimator under low noise conditions. In this paper we present a stochastic algorithm for approximating the MAP estimator in the spirit of the SAEM algorithm. We prove its convergence to a critical point of the observed likelihood with an illustration on images of handwritten digits

Young Clusters in the Nuclear Starburst of M 83

We present a photometric catalog of 45 massive star clusters in the nuclear starburst of M 83 (NGC 5236), observed with the Hubble Space Telescope WFPC2, in both broad-band (F300W, F547M, and F814W) and narrow-band (F656N and F487N) filters. By comparing the photometry to theoretical population synthesis models, we estimate the age and mass of each cluster. We find that over 75% of the star clusters more massive than 2*10^4 Msun in the central 300 pc of M 83 are less than 10 Myr old. Among the clusters younger than 10 Myr and more massive than 5*10^3 Msun, 70% are between 5 and 7 Myr old. We list an additional 330 clusters that are detected in our F300W images, but not in the shallower F547M and F814W images. The clusters are distributed throughout a semicircular annulus that identifies the active region in the galaxy core, between 50 and 130 pc from the optical center of M 83. Clusters younger than 5 Myr are preferentially found along the perimeter of the semicircular annulus. We suggest that the 5-7 Myr population has evacuated much of the interstellar material from the active ringlet region, and that star formation is continuing along the edges of the region.Comment: 40 pages, 13 figures, accepted to ApJ