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

Rectification from Radially-Distorted Scales

This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from repetitions of rigidly transformed coplanar local features. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle images that contain nearly any type of coplanar repeated content. We demonstrate a principled approach to generating stable minimal solvers by the Grobner basis method, which is accomplished by sampling feasible monomial bases to maximize numerical stability. Synthetic and real-image experiments confirm that the solvers give accurate rectifications from noisy measurements when used in a RANSAC-based estimator. The proposed solvers demonstrate superior robustness to noise compared to the state-of-the-art. The solvers work on scenes without straight lines and, in general, relax the strong assumptions on scene content made by the state-of-the-art. Accurate rectifications on imagery that was taken with narrow focal length to near fish-eye lenses demonstrate the wide applicability of the proposed method. The method is fully automated, and the code is publicly available at https://github.com/prittjam/repeats.Comment: pre-prin

Radially-Distorted Conjugate Translations

This paper introduces the first minimal solvers that jointly solve for affine-rectification and radial lens distortion from coplanar repeated patterns. Even with imagery from moderately distorted lenses, plane rectification using the pinhole camera model is inaccurate or invalid. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle imagery, which is now common from consumer cameras. The solvers are derived from constraints induced by the conjugate translations of an imaged scene plane, which are integrated with the division model for radial lens distortion. The hidden-variable trick with ideal saturation is used to reformulate the constraints so that the solvers generated by the Grobner-basis method are stable, small and fast. Rectification and lens distortion are recovered from either one conjugately translated affine-covariant feature or two independently translated similarity-covariant features. The proposed solvers are used in a \RANSAC-based estimator, which gives accurate rectifications after few iterations. The proposed solvers are evaluated against the state-of-the-art and demonstrate significantly better rectifications on noisy measurements. Qualitative results on diverse imagery demonstrate high-accuracy undistortions and rectifications. The source code is publicly available at https://github.com/prittjam/repeats

The quest for companions to post-common envelope binaries: III. A reexamination of HW Virginis

We report new mid-eclipse times of the short-period sdB/dM binary HW Vir, which differ substantially from the times predicted by a previous model. The proposed orbits of the two planets in that model are found to be unstable. We present a new secularly stable solution, which involves two companions orbiting HW VIr with periods of 12.7 yr and 55 +/-15 yr. For orbits coplanar with the binary, the inner companion is a giant planet with mass M_3 sin i_3 = 14 M_Jup and the outer one a brown dwarf or low-mass star with a mass of M_4 sin i_4 = 30-120 M_Jup. Using the mercury6 code, we find that such a system would be stable over more than 10^7 yr, in spite of the sizeable interaction. Our model fits the observed eclipse-time variations by the light-travel time effect alone, without invoking any additional process, thereby providing support for the planetary hypothesis of the eclipse-time variations in close binaries. The signature of non-Keplerian orbits may be visible in the data.Comment: accepted by A&

Preliminary capture trajectory design for Europa tomography probe

The objective of this work is the preliminary design of a low-DV transfer from an initial elliptical orbit around Jupiter into a final circular orbit around the moon Europa. This type of trajectory represents an excellent opportunity for a low-cost mission to Europa, accomplished through a small orbiter, as in the proposed Europa Tomography Probe mission, a European contribution to NASA’s Europa Multiple-Flyby Mission (or Europa Clipper). The mission strategy is based on the v-infinity leveraging concept, and the use of resonant orbits to exploit multiple gravity-assist from the moon. Possible sequences of resonant orbits are selected with the help of the Tisserand graph. Suitable trajectories are provided by an optimization code based on the parallel running of several differential evolution algorithms. Different solutions are finally compared in terms of propellant consumption and flight time