COLOUR THEORY - Forsiden

1 COLOUR THEORY INF 5440 - CMOS Image Sensors COLOUR THEORY . Main ref.: Nakamura AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors Response of the eye The human eye has three kinds of cones S, M, and L which is sensitive to different wavelength ranges: Blue, green, red. COLOUR view 108. Retinal Damage Rods has higher sensitivity but for one range only, slightly below the green range. Night 106. vision without COLOUR . Sunlight 104. 102. Indoor light Rod Saturation 1. Moonlight 10-2. Starlight Cone Threshold -4. 10. 10-6. Rod Threshold Ref.: AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors Adaptive and Subtractive COLOUR Mixing Ref.: AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors COLOUR Matching Functions How to quantify colours X( ), Y( ), and Z( ). CIE 1931 standard (Commission Internationale de l'Eclairage).

2 International Commission on Illumination The COLOUR space is associated with the COLOUR sensitivity of the human eye. Ref. Nakamura Ref. Wikipedia AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors COLOUR Matching Functions (cont.). Tristimulus values: X, Y, Z is obtained by weighting the source intensity L( ) and the illuminated object's reflectance R( ) with the COLOUR matching functions x( ), y( ) and z( ). X = L ( )R ( )x ( ) d . Y = L ( )R ( )y ( ) d ( ). Z = L ( )R ( )z ( ) d . Luminance: Y. Chrominance: x, y values is represented in a 2 dimensional space. X Y. x = ------------------------- y = ------------------------- ( ). X+Y+Z X+Y+Z. Converting back to X, Z. Y Y. X = ---- x Z = ---- ( 1 x y ) ( ). y y Ref.: efg'a Computer Lab AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors COLOUR Matching Functions (cont.)

3 Improved geometric uniformity is achieved with the standard CIE 1976: L*u*v* and L*a*b*. Developed for gray background (L*=50). a = 500 ( X n Y n ) b = 200 ( Y n Z n ) ( ). Common L*: where Y 1 3 Y. 116 ------- 16 ------- > . Y0 Y0 X 1 3. ------ X. L = ( ) - ------- > X X0. ------ Y Y 0. - ------- Xn = ( ). Y Y0 X 16. ------ X. 0 - + --------- ------- X 116 X0. 0. u = 13L ( u' u' 0 ) v = 13L ( v' v' 0 ) ( ) Y 1 3. ------ Y. - ------- > ( ). Y0 Y0. where Yn = . Y 16. ------ Y. - + --------- ------- 4X 9Y Y 116 Y0. u' = ---------------------------------- v' = ---------------------------------- ( ) 0. X + 15Y + 3Z X + 15Y + 3Z. Z 1 3. ----- Z. - ------ > Z Z0. 0. Zn = ( ). Z 16. ----- Z. Index 0 represents tristimulus values for white - + --------- ------ Z 116 Z0.

4 0. AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors L*a*b* (CIE1976). 25% Illumination 50% Illumination 75% Illumination Ref.: efg'a Computer Lab AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors L*C*H* (CIECAM02). L* as in ( ). o 2 2 180 b . C ab = ( a + b ) h ab = ----------- atan ------ ( ). a . Ref.: Wikipedia AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors COLOUR temperature of light sources AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors COLOUR temperature of light sources (cont.). Normalised with reference to green Equal COLOUR temperature is not the same as equal spectrum AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors COLOUR Rendering index (CRI). A measure on a light source capability to reproduce COLOUR . 100 is best, 0 is worst The light source is measured against a reference, a filament lamp (blackbody radiation) with CRI=100.

5 A standardized set of colours are illuminated and compared. The reference is daylight for COLOUR temperatures above 5000 K. Average COLOUR rendering index Ra is calculated according to formula 8. 1. R a = --- 8 ( 100 4, 6 Ei ). i=1. Where Ei is the COLOUR deviation in a given COLOUR space, 1964 L*U*V*. 2 2 2. E i = ( L i L i0 ) + ( U i U i0 ) + ( V i V i0 ). Index i gives the COLOUR in the standard set, index 0 represents the reference source. Ref.: Wikipedia AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors COLOUR Rendering index (forts.). AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors Camera COLOUR Properties To generate tristimulus values unlikely, these have to be a linear combination of the camera's sensitivity functions: X=c11Sx +c12Sy +c13Sz Y=c21Sx +c22Sy +c23Sz Z=c31Sx +c32Sy +c33Sz Called the Luther condition.

6 Provided the reflectance has a continuous transitions in the spectrum such that the reflected spectrum can be decomposed into three basic components, an object's tristimulus values can be calculated using any set of sensitivity functions. COLOUR chart for test is made to simulate the reflectance of real objects. The camera COLOUR functions can be generated from the chart. Either an analytical or recursive method. Gretag Macbeth COLOUR checker AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors Camera COLOUR Properties (cont.). The target: Estimated value: Compensation Camera response ( ). Solving for the compensation matrix: AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors Camera COLOUR Properties (cont.). Recursive method to minimize COLOUR differences: n . J = wi E ( Xi, Yi, Zi, Xi, Yi, Zi ) ( ).

7 I=1. Where E is the direct COLOUR difference ( L*a*b). 2 2 2. E ab = ( L 1 L 2 ) + ( a 1 a 2 ) + ( b 1 b 2 ) ( ). J: Visible COLOUR difference (deviation form the object's COLOUR ). wi: Coefficient associated to each COLOUR on the palette. AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors White Balance White act as the reference for the colours, the COLOUR of the light source. The eye adjusts the sensitivity of cones to adapt to the lightning conditions. The question is: What is white in the image? There are several methods. Scene average. Assuming the world is grey and that the average COLOUR is the COLOUR of the light source. The brightest spot is white. Assuming the light that is reflected by the brightest elements represents the light source.

8 Gamut of the scene ( COLOUR space). Assuming the total spectrum has a expected distribution, analyse the spectrum from all part of the scene and move the colours towards the highest correlation between expected and measured distribution. AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors White Balance - Chromatic adaption von Kries model: Images are viewed in a background illumination different form the recording background light. Cone response at background illumination 1, is tristimulus values L1,M1,S1 at the state white = Lw1,Mw1,Sw1. Cone response at background illumination 2, is tristimulus values L2,M2,S2 at the state white = Lw2,Mw2,Sw2. L w2 M w2 S w2. L 2 = ---------- L 1 M 2 = ------------ M 1 S 2 = ---------- S 1. L w1 M w1 S w1. New r' b' g' values is calculated from r g b by: L' w -------- 0 0.

9 Lw r' M' w r L r 1 1. g' = A B 0 ---------- 0 BA b , M = BA g ( ). Mw b' g S b S' w 0 0 -------- Sw A: Sensor RGB -> Tristimulus values XYZ. B: Tristimulus values XYZ -> cone response LMS. AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors White Balance - COLOUR constancy Subjective properties of the eye ensures that an object's COLOUR stays nearly unchanged at varying light conditions (needed for recognition of objects). It is however required that the spectrum of the light has a certain width, that Ra (average COLOUR rendering index) is high. A simple method is to use ( ) with the adaption of B to a standard light source. AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors Perception of COLOUR depend on the COLOUR of the background The pink sheet in top image looks more like white in the bottom image.

10 AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors A is at the same grey level as B? AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors COLOUR Interpolation Sampling of Bayer pattern CFA ( COLOUR Filter Array). Red and blue distance = 2. Green distance = 2. Nyquist frequency is higher for green, in the directions 45 and 135 . AO 10V COLOUR THEORY INF 5440 - CMOS Image Sensors Bilinear Interpolation Interpolation: Insert a new point with values based on averaging of the neighbouring points, spatial low pass filtering of the data. Position 1: G(x1,y1)|R = [R(x1,y1+1) +R(x1,y1-1)]/2. G(x1,y1)|B = [B(x1+1,y1) +B(x1-1,y1)]/2. Position 2: B(x2,y2)|G = [G(x2,y2+1) +G(x2,y2-1)+G(x2+1,y2) +G(x2-1,y2)]/4. B(x2,y2)|R = [G(x2+1,y2+1) +G(x2+1,y2-1)+G(x2-1,y2+1) +G(x2-1,y2-1)]/4.