The Discrete Cosine Maximum Ignorance Assumption

2021 ◽  
Vol 2021 (29) ◽  
pp. 13-18
Author(s):  
Graham D. Finlayson ◽  
Javier Vazquez-Corral ◽  
Fufu Fang

The performance of colour correction algorithms are dependent on the reflectance sets used. Sometimes, when the testing reflectance set is changed the ranking of colour correction algorithms also changes. To remove dependence on dataset we can make assumptions about the set of all possible reflectances. In the Maximum Ignorance with Positivity (MIP) assumption we assume that all reflectances with per wavelength values between 0 and 1 are equally likely. A weakness in the MIP is that it fails to take into account the correlation of reflectance functions between wavelengths (many of the assumed reflectances are, in reality, not possible). In this paper, we take the view that the maximum ignorance assumption has merit but, hitherto it has been calculated with respect to the wrong coordinate basis. Here, we propose the Discrete Cosine Maximum Ignorance assumption (DCMI), where all reflectances that have coordinates between max and min bounds in the Discrete Cosine Basis coordinate system are equally likely. Here, the correlation between wavelengths is encoded and this results in the set of all plausible reflectances 'looking like' typical reflectances that occur in nature. This said the DCMI model is also a superset of all measured reflectance sets. Experiments show that, in colour correction, adopting the DCMI results in similar colour correction performance as using a particular reflectance set.

2021 ◽  
Vol 976 (10) ◽  
pp. 2-12
Author(s):  
A.P. Karpik ◽  
V.I. Obidenko ◽  
N.S. Kosarev ◽  
N.K. Shendrik

The results of studies on the SSC-2011 coordinate base homogeneity carried out in the process of linking a special-purpose geodetic network’s points to this coordinate system are presented. The research consisted of multiple determinations of the differential geodetic stations (DGS) coordinates in GSK-2011 from different types of the coordinate base of this system. In the first version, they were obtained through their binding to the nearest points of the SGN with known coordinates in the SSC-2011. In the second one, the DGS was linked to SSC-2011 by GNSS vectors to four FAGS points. In the third variant, in order to obtain these coordinates in SSC-2011 the reference were four points of the IGS network. The grid coordinates of the DGS determined in GSK-2011 from the FAGS and IGS points coincided within 1,3 cm. Those of the DGS in SSC-2011, from points of the SGN, differ from the ones obtained in the FAGS and IGS by maximum values up to 21,8 cm, 22,2 cm, 27,2 cm in the abscissa, ordinate, and position, respectively. The derived data on the degree of heterogeneity of the SGN in SSC-2011 enable concluding the impracticality of using it as the coordinate basis of this system at carrying out works, requiring positioning accuracy at the level of several centimeters.


1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.


1975 ◽  
Vol 26 ◽  
pp. 21-26

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.


2013 ◽  
Vol 50 (10) ◽  
pp. 840-844
Author(s):  
Yukiya INOUE ◽  
Mayumi KIHARA ◽  
Junko YOSHIMURA ◽  
Naoki YOSHIDA ◽  
Kenji MATSUMOTO ◽  
...  

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