The paper deals with a computational method for detection of the solar system minor bodies (SSOs), whose inter-frame shifts in series of CCD-frames during the observation are commensurate with the errors in measuring their positions. These objects have velocities of apparent motion between CCD-frames not exceeding three rms errors (3σ) of measurements of their positions. About 15% of objects have a near-zero apparent motion in CCD-frames, including the objects beyond the Jupiter's orbit as well as the asteroids heading straight to the Earth. The proposed method for detection of the object's near-zero apparent motion in series of CCD-frames is based on the Fisher f -criterion instead of using the traditional decision rules that are based on the maximum likelihood criterion. We analyzed the quality indicators of detection of the object's near-zero apparent motion applying statistical and in situ modeling techniques in terms of the conditional probability of the true detection of objects with a near-zero apparent motion. The efficiency of method being implemented as a plugin for the Collection Light Technology (CoLiTec) software for automated asteroids and comets detection has been demonstrated. Among the objects discovered with this plugin, there was the sungrazing comet C/2012 S1 (ISON). Within 26 min of the observation, the comet's image has been moved by three pixels in a series of four CCD-frames (the velocity of its apparent motion at the moment of discovery was equal to 0.8 pixels per CCD-frame; the image size on the frame was about five pixels). Next verification in observations of asteroids with a near-zero apparent motion conducted with small telescopes has confirmed an efficiency of the method even in bad conditions (strong backlight from the full Moon). So, we recommend applying the proposed method for series of observations with four or more frames.
We describe a new iteration method to estimate asteroid coordinates, which is based on the subpixel Gaussian model of a discrete object image. The method operates by continuous parameters (asteroid coordinates) in a discrete observational space (the set of pixels potential) of the CCD frame. In this model, a kind of the coordinate distribution of the photons hitting a pixel of the CCD frame is known a priori, while the associated parameters are determined from a real digital object image. The developed method, being more flexible in adapting to any form of the object image, has a high measurement accuracy along with a low calculating complexity due to a maximum likelihood procedure, which is implemented to obtain the best fit instead of a least-squares method and Levenberg-Marquardt algorithm for the minimisation of the quadratic form.Since 2010, the method was tested as the basis of our CoLiTec (Collection Light Technology) software, which has been installed at several observatories of the world with the aim of automatic discoveries of asteroids and comets on a set of CCD frames. As the result, four comets (C/2010 X1 (Elenin), P/2011 NO1(Elenin), C/2012 S1 (ISON), and P/2013 V3 (Nevski)) as well as more than 1500 small Solar System bodies (including five NEOs, 21 Trojan asteroids of Jupiter, and one Centaur object) were discovered. We discuss these results that allowed us to compare the accuracy parameters of a new method and confirm its efficiency.In 2014, the CoLiTec software was recommended to all members of the Gaia-FUN-SSO network for analysing observations as a tool to detect faint moving objects in frames.
In this article we described CoLiTec software for full automated frames processing. CoLiTec software allows processing the Big Data of observation results as well as processing of data that is continuously formed during observation. The scope of solving tasks includes frames brightness equalization, moving objects detection, astrometry, photometry, etc. Along with the high efficiency of Big Data processing CoLiTec software also ensures high accuracy of data measurements. A comparative analysis of the functional characteristics and positional accuracy was performed between CoLiTec and Astrometrica software. The benefits of CoLiTec used with wide field and low quality frames were observed. The efficiency of the CoLiTec software was proved by about 700.000 observations and over 1.500 preliminary discoveries.
A computational method for the automated formation of a typical form of a digital image of the investigated objects on a series of digital frames has been developed. Due to the imperfection of the mounting of digital cameras, as well as their automated mounts, their immobility at shooting during exposure time can be disturbed, which leads to the formation of "blurred" images of objects of various forms. Due to such inaccuracies in the tracking of objects on digital frames, even in one series, the typical form of the image of objects can vary from frame to frame. This fact of the difference in the standard form significantly complicates the execution of various image processing tasks. In order to simplify the evaluation of the image parameters of objects in a series of digital frames, it has been proposed to use a typical image on a digital frame corresponding to the average image of objects as a model of object images. In this case, the appearance of the image of the object, its form, the distribution of brightness in the image will be determined only by the typical image. This paper proposes a computational method for the automated formation and evaluation of the typical form of the image of an object in a digital frame based on the initial data – the actual given digital frame. This computational method is based on the selection of single images of objects and the formation of their rectangular area. Next, the offset is evaluated, and the selected single images of objects are normalized to calculate the typical form of the object image. Using the method makes it possible to highlight objects against the background of noise and reduce the number of false detections. It is recommended to apply the method only in the case when the frames have defects and "blurs" during the shooting, otherwise there will be unreasonable additional computational costs. The developed computational method was successfully tested in practice within the framework of the CoLiTec project and implemented in the intraframe processing unit of the Lemur software.
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