Learning how to be robust: Deep polynomial regression

Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased results when the input data is heavily contaminated by outliers. Moreover, the problem is even harder when outliers have strong structure. Departing from problem-tailored heuristics for robust estimation of parametric models, we explore deep convolutional neural networks. Our work aims to find a generic approach for training deep regression models without the explicit need of supervised annotation. We bypass the need for a tailored loss function on the regression parameters by attaching to our model a differentiable hard-wired decoder corresponding to the polynomial operation at hand. We demonstrate the value of our findings by comparing with standard robust regression methods. Furthermore, we demonstrate how to use such models for a real computer vision problem, i.e., video stabilization. The qualitative and quantitative experiments show that neural networks are able to learn robustness for general polynomial regression, with results that well overpass scores of traditional robust estimation methods.Comment: 18 pages, conferenc

Recursive Estimation of Camera Motion from Uncalibrated Image Sequences

In This memo we present an extension of the motion estimation scheme presented in a previous CDS technical report [14, 16], in order to deal with image sequences coming from an uncalibrated camera. The scheme is based on some results in epipolar geometry and invariant theory which can be found in [6]. Experiments are performed on noisy synthetic images

Proper motions for HST observations in three off-axis bulge fields

Aims. This is the second in a series of papers that attempt to unveil the kinematic structure of the Galactic bulge through studying radial velocities and proper motions. We report here ~15000 new proper motions for three low foreground-extinction off-axis fields of the Galactic bulge. Methods. Proper motions were derived from a combination of Hubble Space Telescope Wide Field Planetary Camera 2 (WFPC2) and Advanced Camera for Surveys (ACS) images taken 8 and 9 years apart, and ACS observations taken 9 and 10 years apart, and they reach accuracies better than 0.9 mas/yr for more than ~10000 objects with magnitudes F814W < 24. Results. The proper motion distributions in these fields are similar to those of Galactic minor axis bulge fields. We observe the rotation of main sequence stars below the turn-off within the Galactic bulge, as in the minor axis fields. Conclusions. Our stellar proper motions measurements show a significant bulge rotation for fields as far from the galactic plane as b=-8.Comment: 14 pages, 14 figures, published in Astronomy & Astrophysic

Recursive estimation of camera motion from uncalibrated image sequences

We describe a method for estimating the motion and structure of a scene from a sequence of images taken with a camera whose geometric calibration parameters are unknown. The scheme is based upon a recursive motion estimation scheme, called the “essential filter”, extended according to the epipolar geometric representation presented by Faugeras, Luong, and Maybank (see Proc. of the ECCV92, vol.588 of LNCS, Springer Verlag, 1992) in order to estimate the calibration parameters as well. The motion estimates can then be fed into any “structure from motion” module that processes motion error, in order to recover the structure of the scene

Stellar Proper Motions in the Galactic Bulge from deep HST ACS/WFC Photometry

We present stellar proper motions in the Galactic bulge from the Sagittarius Window Eclipsing Extrasolar Search (SWEEPS) project using ACS/WFC on HST. Proper motions are extracted for more than 180,000 objects, with >81,000 measured to accuracy better than 0.3 mas/yr in both coordinates. We report several results based on these measurements: 1. Kinematic separation of bulge from disk allows a sample of >15,000 bulge objects to be extracted based on >6-sigma detections of proper motion, with <0.2% contamination from the disk. This includes the first detection of a candidate bulge Blue Straggler population. 2. Armed with a photometric distance modulus on a star by star basis, and using the large number of stars with high-quality proper motion measurements to overcome intrinsic scatter, we dissect the kinematic properties of the bulge as a function of distance along the line of sight. This allows us to extract the stellar circular speed curve from proper motions alone, which we compare with the circular speed curve obtained from radial velocities. 3. We trace the variation of the {l,b} velocity ellipse as a function of depth. 4. Finally, we use the density-weighted {l,b} proper motion ellipse produced from the tracer stars to assess the kinematic membership of the sixteen transiting planet candidates discovered in the Sagittarius Window; the kinematic distribution of the planet candidates is consistent with that of the disk and bulge stellar populations.Comment: 71 pages, 30 figures, ApJ Accepte

The Southern Proper Motion Program III. A Near-Complete Catalog to V=17.5

We present the third installment of the Yale/San Juan Southern Proper Motion Catalog, SPM3. Absolute proper motions, positions, and photographic B,V photometry are given for roughly 10.7 million objects, primarily stars, down to a magnitude of V=17.5. The Catalog covers an irregular area of 3700 square degrees, between the declinations of -20 and -45 degrees, excluding the Galactic plane. The proper-motion precision, for well-measured stars, is estimated to be 4.0 mas/yr. Unlike previous releases of the SPM Catalog, the proper motions are on the International Celestial Reference System by way of Hipparcos Catalog stars, and have an estimated systematic uncertainty of 0.4 mas/yr. The SPM3 Catalog is available via electronic transfer,(http://www.astro.yale.edu/astrom/) As an example of the potential of the SPM3 proper motions, we examine the Galactocentric velocities of a group of metal-poor, main-sequence A stars. The majority of these exhibit thick-disk kinematics, lending support to their interpretation as thick-disk blue stragglers, as opposed to being an accreted component.Comment: 23 pages, 10 figures, accepted for publication in Astronomical Journa

Detection of Extrasolar Planets by Gravitational Microlensing

Gravitational microlensing provides a unique window on the properties and prevalence of extrasolar planetary systems because of its ability to find low-mass planets at separations of a few AU. The early evidence from microlensing indicates that the most common type of exoplanet yet detected are the so-called "super-Earth" planets of ~10 Earth-masses at a separation of a few AU from their host stars. The detection of two such planets indicates that roughly one third of stars have such planets in the separation range 1.5-4 AU, which is about an order of magnitude larger than the prevalence of gas-giant planets at these separations. We review the basic physics of the microlensing method, and show why this method allows the detection of Earth-mass planets at separations of 2-3 AU with ground-based observations. We explore the conditions that allow the detection of the planetary host stars and allow measurement of planetary orbital parameters. Finally, we show that a low-cost, space-based microlensing survey can provide a comprehensive statistical census of extrasolar planetary systems with sensitivity down to 0.1 Earth-masses at separations ranging from 0.5 AU to infinity.Comment: 43 pages. Very similar to chapter 3 of Exoplanets: Detection, Formation, Properties, Habitability, John Mason, ed. Springer (April 3, 2008