Automatic detection of asteroids on the CCD-images. Software description.
The present software input data is represented by series of CCD-images showing a part of celestial sphere and stellar catalog. The intraframe processing module checks defective (“bad” and “hot”) pixels of CCD matrix; splitting frames for subseries with the basic frame detection; subseries frames combining with accumulation of signals coming from moving object, receiving superframes based on “areal approach” and digital smoothing filter application; preliminary selection of celestial objects’ signals on superframes, based upon comparison with spatial convolution criteria of received flux (in the vicinity of image peak) with form of estimated signal. Then the module of intraframe processing evaluates coordinates and signals amplitudes on the superframes (marks formation) based on tabulated samplings using model of noise photons’ decline coordinates like flat substrate; combination of superframes from same subseries received for different hypothetic velocities of objects’ apparent movement; evaluation of equatorial coordinates of objects using astrometric reduction which is done by generalized least squares estimation of coefficients of plate constants with following single-valued conversion of ideal coordinates to equatorial and with even reference stars selection and carrying out of iteration evaluation by least-squares method (LSM), rejecting abnormal observation on each iteration. Plus under the formation of weighting generic LSM matrix of measurement’s errors, it also consider dependence of errors’ value in evaluation of equatorial coordinates on objects’ apparent brightness level and their coordinates in CCD-frames coordinate system (CS). Obtained results are represented as set of marks. Each mark is a formalized determination of celestial object’s existence, done during intraframe processing of initial astronomic data. These marks include evaluation of estimated celestial objects’ amplitude and equatorial coordinates, as well as evaluation of present objects’ coordinates in CS of basic frame’s CCD-matrix. Plus, an array of the model of plate constants’ coefficients and adjusted equatorial coordinates of the base frame’s center will be formed according to the block’s work.
The objects still on series of frames are rejected in module of inside catalogue of still objects’ formation (inside catalogue) and will be identified with stellar catalog in the block of marks’ identification.
Still objects’ marks are identified with objects from stellar catalog in identification module, by resolving a problem (using Hungarian method) of setting on bigraph, one part of which represents frame’s marks while another one — objects from star catalog.
The module of objects’ apparent brightness evaluation performs LSM factors’ evaluation of double-band, piecewise-linear module representing dependence of asteroid’s apparent brightness’ value on its signal’s amplitude on the CCD-frame (model of photometric conversion), based on objects from inside catalogue, identified with stars; objects’ apparent brightness evaluation matching the marks of the present series of CCD-frames according to the model of photometric conversion’s obtained coefficients; formation of rejection criteria based on apparent brightness. The launch of the present model is stimulated by the fact, that the application of linear single-band model of photometric scaling for a wide range of amplitude values reduces precision of apparent brightness evaluation for small amplitudes (appropriate to the asteroids’ signal), while the application of quadratic single-band model of photometric scaling doesn’t increase the precision rate as The module of rejection based on apparent brightness preserves only marks with apparent brightness evaluation that doesn’t exceed the set rejection criteria.
In the module of preliminary tracks indication, the tracks are discovered on the statistics accumulation basis proportional to the signal energy along the possible tracks of the object motion (by method of light collection). The present signal accumulation is provided due to implementation of multiple-valued transformation of object coordinates allowing multistage implementation. Multiple-valued transformation also allows accumulating signals along all the possible motion tracks of celestial bodies. Physically observed area according to the accepted motion model will be divided into crossing spatio-temporal areas (spatial areas shifting from one frame to another) in a way that an object remains inside one during the detection period. Each area will have a storage and celestial objects’ signals will be stored in all corresponding storages of areas. During the method’s application, the model of rectilinear and uniform motion of objects in the plain will be used as a model of object’s apparent motion.
In the initial stage, separate tracks will be merged in classes (one class comprises all tracks of one straight line) and corresponding areas will be studied. The second stage – study of spatio-temporal areas on a marked straight line – will be used in order to accept the existence of celestial body on one of studied straight lines. In the initial stage of the present realization of multivalued conversion of objects’ coordinates which allows multistage realization, statistics’ accumulation will be carried out in the space “traverse angle – traverse distance” of the track, in the second stage it will be done in the space “initial position – velocity”.
Valuation of apparent magnitude of the object is used as flux statistics. The present method assures the possibility (which is advisable because of the realization of the whole covering of observation area using error evaluations of objects’ coordinates) of signal mark’s getting into two or three strobes according to the traverse distance and initial position.
The collection of marks which belong to one object with nonzero apparent motion is formed in the result of module operation. Only those marks which were not rejected according to the valuation of apparent magnitude are used for it.
In the module of amplitude and coordinate detection the OLS-evaluation of parameters of the discovered tracks is provided and the decision about tracks formed by asteroids is made. Decision rule (DR) of asteroid detection on each frame chooses “the best” mark for extension of the track. “The best” mark should have little deviation (kinematic constituent) from asteroid’s track, while the amplitude value of “the best” mark (valuation of the apparent brightness of the object relevant to the mark) should not be very different from the amplitude of the other marks which belong to the given track (amplitude constituent). Application of this amplitude constituent in DR is connected with big amplitude variation of signals from asteroids by rapid change of observation conditions within the time of observation.
Tracks presumably formed by asteroids (decision is made according to the amplitude-coordinates detector’s work) are identified with the tracks of the known asteroids, in the identification module by resolving a problem (using Hungarian method) of setting on bigraph, one part of which represents tracks’ parameters presumably formed by asteroids, while another one is formed by tracks’ parameters of known asteroids. Data of known asteroids is received from the base of parameters of asteroid orbits or from the server of Minor Planet Center (MPC) with the help of the checker module.
Requests for the local base of orbits or Web server of orbits will be formed in the checker block and the answers for them will be received by the block of tracks’ identification. The range of tracks identified with known asteroids and preliminarily accepted as newly discovered asteroids will be formed as a result of work done by the block of tracks’ identification.
In the visual control module the observer has the opportunity to make the final decision whether the track belongs to the asteroid or false-detection by using the blinking method. Data of detected asteroids is used to make the MPC-report. Observer sends the generated report with measurements to the MPC sever via email.