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Taking into account the features of human perception

The necessity of taking into account the psychophysiological factors of human perception of the appearance of a diamond has changed the modeling methods used in gemological studies. In particular, a number of special functions, such as subjective brightness, subjective grading, and weighed geometric average, have been introduced.
 
1. Subjective brightness function. If an observer is provided with a number of grayscale color samples and asked to select such a gray tone that equally differs from white and from black, he faces a considerable difficulty, because estimating the relative value of two considerable color differences is based solely on a subjective impression.

However, the required gray tone can be determined by averaging the subjective estimations of a few observers. Then, the same method can be applied to the two color ranges obtained (the first is from black to middle-gray; the second is from middle-gray to white). As a result, a uniform-contrast scale of luminosity (subjective brightness) can be built. 
 
Special  developed special formulas to estimate the brilliance of a diamond and leakage of light in it.
 
2. Subjective grading function. People usually grade various phenomena using a discrete set of categories (such as "bad", "good", "perfect", etc.) rather than percent scale or another continuous measure. One can say that people have natural bias towards discrete grading of phenomena, even if the physical characteristics of these phenomena change continuously. Special functions have been introduced as a measure of human rating of this phenomena.
 
3. Weighed geometric average function. When modeling a grading procedure of a cut diamond, it is not enough to take into account only a single static position of the stone. This is because a real observer would view the diamond from different sides. Therefore, all the necessary computations are performed for 15 orientations of the stone (it was rotated by 30 degrees around its axis) and then used weighed geometric averaging. The latter procedure reflects human perception more adequately than arithmetical averaging does. The geometrical averaging takes into account two key features of human perception.
 
The first feature is highlighting some bad views of the stone under study. This means that if the observer notices a bad perspective while changing the stone orientation, the negative impression may last even after the perspective is changed to a more advantageous one. The human perception tends to grade this stone as bad. So, the geometric averaging makes it possible to adequately grade those stones looking bad in some orientations and prevents the negative rating from being compensated by advantageous perspectives. Such compensation may easily occur if one uses arithmetical averaging.
 
The second key feature of human perception is that when grading a stone the observer pay more attention to the "crown up" position. The larger the deviation of the stone orientation from the position when the crown looks exactly towards the observer, the less the "subjective weight" of this orientation in overall grading. Therefore, we made the geometric averaging weighed by taking into account the deviation angle of the diamond from the "crown towards the observer" orientation.
 

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