# Light and Color Models ## Spectral power distribution Plot of Wavelength vs Engergy of electromagnetic waves. We can use it to interpret: - Hue: dominant wavelength of the curve: EH - Saturation: purity of the color: EH-EW - Intensity: brightness of the color: EW (area of the curve) ![[Spectral Power Distribution.jpg]] ## Light sources and illuminants Light sources: sun, candle, lamps ![[illuminant SPD.jpg]] Illuminants: - illuminant A - Average Daylight (D65) - Determined as the color of temperature at 6500 K - illuminant C ![[source SPD.jpg]] ## Colour Constancy Aim for colour constancy algorithms is first to estimate the illuminance of the light source, and then correct the image so that the corrected image appeas to be taken under a canonical (white light source). This is done by automatic white balance (AWB) in digital cameras to make the images look as natural as possible. ![[Screenshot 2020-09-13 at 10.28.23 AM.jpg]] Assumption above don't always work. ![[Screenshot 2020-09-13 at 10.30.07 AM.jpg]] ## Object colours ![[object-colors.jpg]] ## Observer Human Eyes - Retina contains light sensitive cells that convert light energy into electrical impulses that travel through nerves to the brain. - Brain interprets the electrical signals to form images. - Retina - Cone cells: cone-shaped, less sensitive, operate in high light color vision - Rod cells: highly sentitive, operate at night, gray-scale vision - Ganglion cells - output neurons of the retina, aggregates information from rods and cones. They have roational invariance. They respond to edges and higher level features. Theories: - Tri-chromacy theory - Opponent theory - Retinex theory ## Tristimulus of Color Theory Determines object color by Spectral-response functions of each of the three types of cones. - Color matching function based on RGB. Observer matches R,G,B knobs to match the target color. ![[color-matching-functions.jpg]] Light source can be identified with spectral power distribution, whereas color of the object can be determined by reflectance curve. ## CIE XYZ-system To standarize precieved colors for any human observer, we use XYZ system, defined as $ \begin{align} X=\int_{\lambda} e(\lambda) \rho(\lambda) \bar{x}(\lambda) d \lambda \\ Y=\int_{\lambda} e(\lambda) \rho(\lambda) \bar{y}(\lambda) d \lambda\\ Z=\int_{\lambda} e(\lambda) \rho(\lambda) \bar{z}(\lambda) d \lambda \end{align} $ where $e(\lambda)$ is light source, $\rho(\lambda)$ is reflectance curve and $\bar{x}, \bar{y}, \bar{z}$ are spectral color matching functions for R, G and B respectively. With this system, you can measure what color a standard human observer will percieve under D65 light source. ![[XYZcolors.jpg]] To get the spectral color values, chromaticity diagram is obtained by normalizing X, Y and Z values: $ \begin{array}{l} x=\frac{X}{X+Y+Z} \\ y=\frac{Y}{X+Y+Z} \\ z=\frac{Z}{X+Y+Z} \end{array} $ ![[chromaticity diagram.jpg]] --- ## References