3D shape models for describing monolithic asteroids and meteoroids

YORP-Induced Long-Term Evolution of the Spin State of Small Asteroids and Meteoroids: Rubincam's Approximation

Spin states of asteroids in the Eos collisional family

Three-dimensional (3D) shape models have recently been used in various fields including machine designing, internet mall, and medical application. Therefore, efficient management and reuse of 3D shape models is becoming important with research on object searching of 3D shape models. 3D shape model searching requires taking into consideration rotation, scaling, and translation of models. This paper proposes a method to search 3D objects to include and account for the above conditions. The proposed method acquires 2D range images by rendering a 3D object from many viewpoints, and discretely approximating two of the three degrees of rotational freedom by a finite number of viewpoints. Using the phase correlation method on the range image one can estimate the rotation around one axis, include scaling and translation, and compare the similarities between the input with models in a dictionary. Experimental results show that whether models match or not match can be distinguished even when the supposed viewpoints are limited to a finite number.

Very small asteroids with diameters smaller than around 200 m, although they constitute the majority of objects in the immediate vicinity of the Earth, we still know little about their mineralogical composition (important for assessing impact hazards and better understanding larger asteroids - rubble piles as their potential building blocks) and the behaviour of their rotation axes (being small and relatively close to the Sun, they are good candidates for testing theories of non-gravitational effects such as the YORP and Yarkovsky effects).Since 2015, we have been conducting campaigns of photometric observations of very small near-Earth asteroids, especially with a very long observation arc in order to determine their physical properties from a single near-Earth flyby. We determine the rotation periods, colour indices, taxonomic types, absolute brightnesses from the phase curves, effective diameters, and spin axis. Examples of our results:[1],[2],[3].Between 2024-10-01 and 2024-10-12 we observed a very small asteroid 2020~WG (H=21.64 +/- 0.40 mag [4]). The work is still in progress. Here we want to present some of the preliminary results.We used observations in griz filters to determine the taxonomic type. The first such observations were made by the 0.6-m REM telescope in La Silla (Chile). It is one of the few telescopes that can simultaneously observe in 4 filters. Comparison of brightnesses made simultaneously eliminates the influence of rotation and change of observation geometry on the colour index results. Unfortunately, we obtain only a few useful observation points, hence the relatively high measurement uncertainty, see Table 1.Our main instrument, the 0.7-m RBT telescope in Arizona, made 30-s exposures. Observations were divided into 3 blocks to determine g-r, g-i, and g-z, respectively. In each block, exposures were alternately made in the g filter and one of the other filters. This technique minimizes the influence of rotation and changes in the observation geometry on the obtained results. We obtained the shifts of the lightcurves in the different bands by compositing the lightcurves using the PerFit program[5]. For an example of a composite lightcurve, see Fig.1.We also collected data from the 1.88-meter telescope of the Kottamia Astronomical Observatory (KAO) in Egypt. Since we did not have the possibility of rapid alternating filter changes, we used 5-s exposures in 15-min blocks. Block sequence: g,z,g,z,g,z,g,i,g,i,g,r,g,r,g. We determined the color indices in the same way as for the RBT data. The SDSS colour indices for each data set are presented in Table 1. We assumed the mean value of the colour indices to be a weighted average, where the weights were the inverse squares of the uncertainties.Following the publication by [6], we converted the colour indices to reflectance values and then compared them with the reflectance values for the taxonomic classes. In this case, the taxonomic class cannot be determined unambiguously. Fig. 2 shows three probable taxonomic classes compared to our results: Xe, K, Cg. We consider Xe as the most probable for which albedo pv=0.15 +/- 0.041 [7]. With this albedo value and H=21.64 +/- 0.40 mag [4], the asteroid's effective diameter is D=0.161 +/- 0.036 km. Due to the very similar albedo for K class (pv=0.14 +/- 0.02) [6], the diameter D=0.167 +/- 0.032 km, is essentially the same within uncertainty. It should be noted that for the Cg type, the asteroid may be larger (pv=0.076 +/- 0.034) [7], D= 0.227 +/- 0.064.Fig. 1. Example of composite lightcurve. Data from RBT telescope, 2024-10-28. Blue dots - observation in g band, orange crosess - i band. The lightcurve in i band was shifted to the lightcurve in the g band. The synodical rotation period P is 35.64 +/- 0.01 minutes.UTC date, telescope g-r g-i g-z 2024-10-26 REM 0.572 +/- 0.054 0.702 +/- 0.068 0.684 +/- 0.061 2024-10-28 RBT 0.560 +/- 0.009 0.704 +/- 0.009 0.699 +/- 0.012 2024-10-29 RBT 0.567 +/- 0.009 0.701 +/- 0.087 0.705 +/- 0.013 2024-10-29 KAO 0.577 +/- 0.008 0.729 +/- 0.010 0.718 +/- 0.012 average 0.569 +/- 0.005 0.715 +/- 0.007 0.707 +/- 0.007 Tab. 1. Colour indices in SDSS bandsFig. 2. Reflectance values obtained from the colour indices of asteroid 2020 WG compared to the three most probable taxonomic classes. Data for taxonomictypes from [6].AcknowledgementsThis research was funded in whole or in part by the National Science Centre, Poland, Grant No. 2021/41/N/ST9/04259. These results are part of a project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 101004719. We would like to thank the REM telescope team for their help in observations.

The distribution of rotation rates of small (D = 3–15 km) main-belt asteroids is analyzed in the context of the probable influence of solar radiation on the rotation of asteroids (YORP effect). It is demonstrated that the evolution of this distribution with heliocentric distance (i.e., the presence of well-marked slow and fast rotation excesses in the inner part of the belt, which become less noticeable in the middle part and are almost indistinguishable in the outer part) is well accounted for by the YORP effect. The influence of this effect on the studied asteroid population is rather weak compared to its influence on near-Earth asteroids, which are 3–4 times smaller on average and with ~3 times more intense solar irradiation; however, it is still sufficiently significant to be identified reliably in the available observational data.

We propose a markerless end-to-end training framework for parametric 3D human shape models. The training of statistical 3D human shape models with minimal supervision is an important problem in computer vision. Contrary to prior work, the whole training process (i) uses a differentiable shape model surface and (ii) is trained end-to-end by jointly optimizing all parameters of a single, self-contained objective that can be solved with slightly modified off-the-shelf non-linear least squares solvers. The training process only requires a compact model definition and an off-the-shelf 2D RGB pose estimator. No pre-trained shape models are required. For training (iii) a medium-sized dataset of approximately 1000 low-resolution human body scans is sufficient to achieve competitive performance on the challenging FAUST surface correspondence benchmark. The training and evaluation code will be made available for research purposes to facilitate end-to-end shape model training on novel datasets with minimal setup cost.

We present an autonomous visual landmark recognition and pose estimation algorithm designed for use in navigation of spacecraft around small asteroids. Landmarks are selected as generic points on the asteroid surface that produce strong Harris corners in an image under a wide range in viewing and illumination conditions; no particular type of morphological feature is required. The set of landmarks is triangulated to obtain a tightly fitting mesh representing an optimal low resolution model of the natural asteroid shape, which is used onboard to determine the visibility of each landmark and enables the algorithm to work with highly concave bodies. The shape model is also used to estimate the centre of brightness of the asteroid and eliminate large translation errors prior to the main landmark recognition stage. The algorithm works by refining an initial estimate of the spacecraft position and orientation. Tests with real and synthetic images show good performance under realistic noise conditions. Using simulated images, the median landmark recognition error is 2m, and the error on the spacecraft position in the asteroid body frame is reduced from 45m to 21m at a range of 2km from the surface. With real images the translation error at 8km to the surface increases from 107m to 119m, due mainly to the larger range and lack of sensitivity to translations along the camera boresight. The median number of landmarks detected in the simulated and real images is 59 and 44 respectively. This algorithm was partly developed and tested during industrial studies for the European Space Agency’s Marco Polo-R asteroid sample return mission.

Shape model and surface properties of the OSIRIS-REx target Asteroid (101955) Bennu from radar and lightcurve observations

One of the major goals of computer vision is the development of flexible and efficient methods for shape representation. This is true, especially for non-rigid 3D shapes where a great variety of shapes are produced as a result of deformations of a non-rigid object. Modeling these non-rigid shapes is a very challenging problem. Being able to analyze the properties of such shapes and describe their behavior is the key issue in research. Also, considering photometric features can play an important role in many shape analysis applications, such as shape matching and correspondence because it contains rich information about the visual appearance of real objects. This new information (contained in photometric features) and its important applications add another, new dimension to the problem's difficulty. Two main approaches have been adopted in the literature for shape modeling for the matching and retrieval problem, local and global approaches. Local matching is performed between sparse points or regions of the shape, while the global shape approaches similarity is measured among entire models. These methods have an underlying assumption that shapes are rigidly transformed. And Most descriptors proposed so far are confined to shape, that is, they analyze only geometric and/or topological properties of 3D models. A shape descriptor or model should be isometry invariant, scale invariant, be able to capture the fine details of the shape, computationally efficient, and have many other good properties. A shape descriptor or model is needed. This shape descriptor should be: able to deal with the non-rigid shape deformation, able to handle the scale variation problem with less sensitivity to noise, able to match shapes related to the same class even if these shapes have missing parts, and able to encode both the photometric, and geometric information in one descriptor. This dissertation will address the problem of 3D non-rigid shape representation and textured 3D non-rigid shapes based on local features. Two approaches will be proposed for non-rigid shape matching and retrieval based on Heat Kernel (HK), and Scale-Invariant Heat Kernel (SI-HK) and one approach for modeling textured 3D non-rigid shapes based on scale-invariant Weighted Heat Kernel Signature (WHKS). For the first approach, the Laplace-Beltrami eigenfunctions is used to detect a small number of critical points on the shape surface. Then a shape descriptor is formed based on the heat kernels at the detected critical points for different scales. Sparse representation is used to reduce the dimensionality of the calculated

Against the biases in spins and shapes of asteroids

I propose novel 3D shape analysis and modeling algorithm for active contours using variational scheme. The proposed algorithm utilizes an unknown surface of 3D shape by normal to 3D shape analysis and modeling. It would be used to get high quality reconstruction's results from many dimensions' data. I give it by utilizing continuous anisotropism weights would finish comparable ameliorate to surface reconstruction.

view Abstract Citations (88) References (28) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Optical Properties of Cometary Nuclei and a Preliminary Comparison with Asteroids Jewitt, D. C. ; Meech, K. J. Abstract Direct CCD observations of cometary nuclei are used to make a preliminary physical comparison with main-belt asteroids of comparable size. The nuclei have been studied within the past 2 yr using charge-coupled devices; the observations of P/Neujmin 1 and P/Tempel 2 are presented here for the first time. The photometric ranges of the nuclei are found to be larger than the ranges of typical main-belt asteroids of similar size, suggesting a systematic shape difference between the nuclei and the small asteroids. The shape difference may be a result of the different collisional histories of the nuclei and asteroids or of anisotropic sublimation of the nuclei. These and other possibilities are briefly discussed. From the scant available information it is suspected that the shapes of the nuclei may be more similar to the shapes of earth-crossing asteroids than to the shapes of main-belt asteroids, consistent with, but not proving, a common origin for the cometary nuclei and the earth-crossing asteroids. Publication: The Astrophysical Journal Pub Date: May 1988 DOI: 10.1086/166351 Bibcode: 1988ApJ...328..974J Keywords: Asteroid Belts; Charge Coupled Devices; Comet Nuclei; Comet Tails; Cross Sections; Physical Properties; COMETS; NUCLEI; OPTICAL PROPERTIES; COMPARISONS; CCD METHODS; ASTEROIDS; PHYSICAL PROPERTIES; NEUJMIN 1; TEMPEL 2; PHOTOMETRY; SIZE; SHAPE; EARTH-BASED OBSERVATIONS; COLLISIONS; SUBLIMATION; EARTH-CROSSERS; TELESCOPE METHODS; CALCULATIONS; HYPOTHESES; FORMATION; DENSITY; Astrophysics; Comets; ASTEROIDS; COMETS full text sources ADS |

<p>The recently developed Unistellar’s eVscope/eVscope2 and eQuinox telescopes have been delivered to more than 5,000 customers around the globe. These telescope owners already represent the largest worldwide network of potential citizen astronomers. Due to the unified design and user-friendly operation via a smartphone app, several types of useful scientific observations are enabled and supported by Unistellar.</p> <p>Each individual frame is stored in the telescope and can be accessed in 12-bit TIFF format by the user for the following data processing and analysis. Moreover, the user can upload the data to Unistellar for further processing, which is the main concept of the campaign mode: Any owner of an eVscope can receive notifications on their smartphone of transient events visible in the sky, such as comets, supernovae, asteroid flybys, stellar occultations by asteroids, or other targets of interest, perform the observations and upload the data to Unistellar’s server.</p> <p>In this contribution, we focus on</p> <p>(i) light curve observations of asteroids, and</p> <p>(ii) stellar occultations by asteroids.</p> <p>Light curves represent the temporal changes of asteroids' brightness within the typical night observational window, which takes usually several hours. Light curve observations allow us to study asteroidal physical properties - rotation period, rotation axis, and the 3D shape model.</p> <p>During the stellar occultation, the asteroid is passing in front of a bright star, which is occulted, the duration of this event is directly related to the asteroid's dimension. Various observers distributed on the ground can sample different parts of the asteroid, which can lead to an accurate size estimate, and possibly even to a shape model refinement.</p> <p>In 2021 and 2022, we initiated several observing campaigns aiming at obtaining light curve data of several near-Earth asteroids (NEA) that were having close approaches to the Earth - e.g., NEAs 1999 AP10 and 2000 PQ9. Dozens of citizen scientists provided their observations. Here we show the initial results obtained by analyzing these optical data. We will also discuss the quality of the photometric data and the significance and potential of the eVscope network for the study of the physical properties of asteroids.</p> <p>We selected asteroids that get bright enough for at least one month, which provides a sufficiently wide window of opportunity for the eVscope users that are often limited by the weather conditions. Also, these targets have unknown or poorly constrained physical properties, which results in the opportunity to contribute to the better characterization and understanding of the population of asteroids.</p> <p>Within the Unistellar's eVscope network of citizen astronomers, we are targeting stellar occultations in order to estimate their dimensions with an accuracy non-achievable by commonly used techniques such as thermal modeling. This task is quite challenging, however, we will report the first successful observations of these events.</p> <p><strong><span dir="ltr" role="presentation">Acknowledgments</span></strong></p> <p><span dir="ltr" role="presentation">The work of JH and JD has been supported by the Czech </span><span dir="ltr" role="presentation">Science Foundation through grant 22-17783S.<br /></span></p>

Example-based statistical framework for parametric modeling of human body shapes

Context.We assess statistical inversion of asteroid rotation periods, pole orientations, shapes, and phase curve parameters from photometric lightcurve observations, here sparse data from the ESAGaiaspace mission (Data Release 2) or dense and sparse data from ground-based observing programs.Aims.Assuming general convex shapes, we develop inverse methods for characterizing the Bayesian a posteriori probability density of the parameters (unknowns). We consider both random and systematic uncertainties (errors) in the observations, and assign weights to the observations with the help of Bayesian a priori probability densities.Methods.For general convex shapes comprising large numbers of parameters, we developed a Markov-chain Monte Carlo sampler (MCMC) with a novel proposal probability density function based on the simulation of virtual observations giving rise to virtual least-squares solutions. We utilized these least-squares solutions to construct a proposal probability density for MCMC sampling. For inverse methods involving triaxial ellipsoids, we update the uncertainty model for the observations.Results.We demonstrate the utilization of the inverse methods for three asteroids withGaiaphotometry from Data Release 2: (21) Lutetia, (26) Proserpina, and (585) Bilkis. First, we validated the convex inverse methods using the combined ground-based andGaiadata for Lutetia, arriving at rotation and shape models in agreement with those derived with the help of Rosetta space mission data. Second, we applied the convex inverse methods to Proserpina and Bilkis, illustrating the potential of theGaiaphotometry for setting constraints on asteroid light scattering as a function of the phase angle (the Sun-object-observer angle). Third, with the help of triaxial ellipsoid inversion as applied toGaiaphotometry only, we provide additional proof that the absoluteGaiaphotometry alone can yield meaningful photometric slope parameters. Fourth, for (585) Bilkis, we report, with 1-σuncertainties, a refined rotation period of (8.5750559 ± 0.0000026) h, pole longitude of 320.6° ± 1.2°, pole latitude of − 25.6° ± 1.7°, and the first shape model and its uncertainties from convex inversion.Conclusions.We conclude that the inverse methods provide realistic uncertainty estimators for the lightcurve inversion problem and that theGaiaphotometry can provide an asteroid taxonomy based on the phase curves.