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3.7.2. LIMITATION OF BRIGHTNESS RANGE

Lecture



Most natural images are created by light reflected from opaque objects or transmitted through transparent media. The range of variation in the brightness of such a non-luminous object is limited and depends on its color. Mac-Adam [23, 24] proved that the color body of maximum volume is realized in the case when objects have reflection or transmission coefficients shown in Fig. 3.7.3. Such objects do not physically exist; therefore, the color body of real objects has a smaller volume. We explain this by limiting for simplicity only the case of objects reflecting light. The same reasoning will remain fair in the case of transparent objects.

Consider the color   3.7.2.  LIMITATION OF BRIGHTNESS RANGE given by color coordinates

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE (3.7.3a)

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE , (3.7.3b)

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE , (3.7.3в)

Where   3.7.2.  LIMITATION OF BRIGHTNESS RANGE - spectral reflection coefficient,   3.7.2.  LIMITATION OF BRIGHTNESS RANGE - the spectral density of the radiation of light falling on the object,   3.7.2.  LIMITATION OF BRIGHTNESS RANGE - addition function. Visual efficiency   3.7.2.  LIMITATION OF BRIGHTNESS RANGE defined as the ratio of the brightness of the object with the reflection coefficient   3.7.2.  LIMITATION OF BRIGHTNESS RANGE to the brightness of the object with a unitary reflection coefficient, i.e.

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE (3.7.4)

If the object has a reflection coefficient of the type shown in Fig. 3.7.3, and, its brightness is equal

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE (3.7.5)

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE

Fig. 3.7.3. Optimal spectral coefficients of reflection or transmission of non-luminous objects.

Suppose the spectral density is known   3.7.2.  LIMITATION OF BRIGHTNESS RANGE energy of incident light. Then you can calculate the brightness of the subject, if you know the value of visual efficiency   3.7.2.  LIMITATION OF BRIGHTNESS RANGE . For a given minimum wavelength   3.7.2.  LIMITATION OF BRIGHTNESS RANGE maximum value   3.7.2.  LIMITATION OF BRIGHTNESS RANGE can be found numerically from the equation

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE (3.7.6)

Using the found value   3.7.2.  LIMITATION OF BRIGHTNESS RANGE can calculate color coordinates   3.7.2.  LIMITATION OF BRIGHTNESS RANGE :

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE (3.7.7)

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE (3.7.8)

Chromaticity coordinates   3.7.2.  LIMITATION OF BRIGHTNESS RANGE and   3.7.2.  LIMITATION OF BRIGHTNESS RANGE can be found by color coordinates. If this procedure is repeated for all possible values   3.7.2.  LIMITATION OF BRIGHTNESS RANGE for given values ​​of visual efficiency   3.7.2.  LIMITATION OF BRIGHTNESS RANGE , it is possible to obtain a surface that bounds the body of possible colors of objects, in color coordinates or color and brightness coordinates. In fig. 3.7.4 shows such a surface in terms of chromaticity and brightness when illuminating objects with a source of white light. Note that the maximum brightness corresponds to the white surface.

  3.7.2.  LIMITATION OF BRIGHTNESS RANGE

Fig. 3.7.4. Color body of objects in chromaticity and brightness coordinates   3.7.2.  LIMITATION OF BRIGHTNESS RANGE [23].


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Digital image processing

Terms: Digital image processing