Object color forma9on

Transcription

1 Color

2 Oject color forma9on The color of an oject is determined y its reflectance ρλ and the visile wavelenghts of the light it is exposed with and angle. Ojects change their color due to different factors: changes in illumina9on intensity, changes of the color of the illumina9on source and condi9ons of interac9on etween light and oject. Two asic components of ρλ are related to material C = m n, s # ody and material surface f C "E"c "d" m s n, reflec9on s, v # terms: f C "E"c s "d" Incident Light ody eflected Light oject colour c " c s " E" n s v f C " ody reflectance " oject material dependent surface aledo scene & viewpoint invariant illumina9on scene dependent oject surface normal oject shape variant illumina9on direc9on scene dependent viewer s direc9on viewpoint variant sensor sensi9vity scene dependent Material surface Surface eflected Light light source colour Material ody Asorption Scattering Colorant

3 cameras Digital images of real world ojects are nowadays otained from photographic digital cameras that use CMOS or CCD sensors to acquire the three color signals. These cameras onen operate with a varia9on of the space in a ayer filter arrangement: green is given twice as many detectors as red and lue ra9o 1:2:1 in order to achieve higher luminance than chrominance resolu9on. The sensor has a grid of red, green, and lue detectors arranged so that the first row is, the next is, and that sequence is repeated in susequent rows. For every channel, missing pixels are otained y interpola9on to uild up the complete image. A pixel only records one color out of three and cannot determine the color of the reflected light. To otain a full color image demosaicing algorithms are used that interpolate a set of complete green, red, lue values at each point. This is done in- camera producing a JPE image.

4 Truecolor is a method of represen9ng and storing graphical image informa9on. Truecolor defines shades of red, green, and lue for each pixel of the digital picture, which results in or 16,777,216 approximately 16.7 million color varia9ons for each pixel. Many low- to medium- end consumer digital cameras and scanners convert the camera measurements into a standard color space referred to as s Color image forma9on, color spaces and color standards are discussed in the following

5 Color Image Forma9on Oserver Camera Ελ Ελ ρλ Incident light eflected light Color image forma9on is determined y the rela9ve radiant power distriu9on of the incident light, the reflec9on of the materials and the characteris9cs of the oserver.

6 Oserver/Sensor f λ Having the light spectrum and the spectral reflectance curve of the oject the appearance of the oject depends on the spectral sensi9vity of the oserver. Considering Tris9mulus, values of camera = Colour * Tris9mulus. Eye esponse Camera esponse

7 Camera spectral integra9on " " " d f E d f E d f E Sin Sin Sin # # # = = = If the spectrum of the light source changes then the colour of the reflected light also changes. " # = # # $ x A i x x i f dx x f / 1 eflected light spectrum is represented y a 3 element vector

8 Color spaces A color space is a three- dimensional defini9on of a color system. The ariutes of the color system are mapped onto the coordinate axes of the color space. Different color spaces exist: each has advantages and disadvantages for color selec9on and specifica9on for different applica9ons: Some color spaces are perceptually linear, i.e. a change in s9mulus will produce the same change in percep9on wherever it is applied. Other colour spaces, e.g. computer graphics color spaces, are not linear. Some color spaces are intui9ve to use, i.e. it is easy for the user crea9ng desired colours from space naviga9on. Other spaces require to manage parameters with astract rela9onships to the perceived colour. Some color spaces are 9ed to specific equipments while others are equally valid on whatever device they are used... CIE Colorimetiric Deviceoriented Deviceoriented and User-oriented Munsell spaces XYZ Non-uniform spaces, YIQ, YCC Uniform spaces L* a* *, L* u* v* HSI, HSV, HSL, I 1 I 2 I 3... Applications Colorimetric calculations Storage, processing, analysis, coding, color TV Color difference evaluation, analysis, color management systems Human color perception, computer graphics Human visual system

9 CIE color matching experiment The first color matching experiment was devised in 1920 to characterize the rela9onship etween the physical spectra and the perceived color, measuring the mixtures of different spectral distriu9ons that are required for human oservers to match colors. The experiments were conducted y using a circular split screen 2 in size the angular size of the cone distriu9on in the human fovea. On one side of the field a test color was projected and on the other side, an oserver- adjustale color was projected, that was a mixture of three monochromac single- wavelength primary colors, each with fixed chroma9city, ut with adjustale rightness. Not all test colors could e matched using this technique. When this was the case, a variale amount of one of the primaries was allowed to add to the test color. The amount of the primary added to the test color was considered to e a nega9ve value.

10 CIE color space In 1931 CIE standardized the color matching func9ons otained using three monochroma9c primaries at wavelengths of 700 nm red, nm green and nm lue. The color matching func9ons are the amounts of primaries needed to match the monochroma9c test primary at the wavelenght shown on the horizontal scale. ather than specifying the rightness of each primary, the curves were normalized scaled to have constant area under them. The CIE color space is one of many color spaces, dis9nguished y a par9cular set of monochroma9c primary colors. The tris9mulus values for a color with a spectral power distriu9on Iλ are given y integra9on of the scaled color matching func9ons. The range of colors represented in such a space gamut is only part of the whole set of colors dis9nguishale y the human eye the triangle in figure. White point

11 CIE XYZ color space Having developed an space of human vision using the CIE matching func9ons, the Commission developed another color space that would relate to the CIE color space y a linear transforma9on such that the new color matching funcons were to e everywhere greater than or equal to zero, and the color matching func9on would e propor9onal to human sensi9vity to luminance i.e. corresponding to the photopic luminous efficiency func9on for the CIE standard oserver. The taulated numerical values of these func9ons are nown as the CIE standard oserver CIE standard oserver. They roughly correspond to colour sensa9ons of red, green and lue. Almost any spectral composi9on can e achieved y a suitaly chosen mix of these three monochroma9c primaries. They yield the CIE XYZ trismulus values X, Y, Z. The XYZ tris9mulus values of a color with spectral distriu9on Eλ are given in terms of the standard oserver and are related to CIE values y a linear transforma9on as Illuminant D65

12 CIE xyy color space The CIE XYZ color space serves as a asis from which other color spaces are defined. y normalizing XYZ i.e. dividing y X Y Z derived values are otained referred to as x,y,z. In that x y z = 1, the chroma9city of a color can e specified y two parameters x y, of the three normalized values. The xy diagram otained y intersec9ng the XYZ space with plane X Y Z = 1 and projec9ng this intersec9on on the x- y plane is referred to as CIE Chroma9city diagram and the xy values are referred to as chroma9city values. They represent all the colors that are visile y the human eye with constant intensity equal to 1. The degree of luminance can e espressed in percentage referring to the Y coordinate of XYZ. The xy Y space is widely used in prac9ce to represent colors.

13 color space The space is usually represented y a cue using non- nega9ve values within a 0 1 range, assigning lac to the origin at the vertex 0, 0, 0, and with increasing intensity values running along the three axes up to white at the vertex 1, 1, 1, diagonally opposite lac. An triplet represents the three- dimensional coordinate of the point of the given color within the cue or its faces or along its edges. This approach allows computa9ons of the color similarity of two given colors y simply calcula9ng the distance etween them: the shorter the distance, the higher the similarity.

14 color spaces color space is hardware dependent. Therefore several color spaces exist. The s color space is the most widely used in prac9ce. Color Space amut White Point Primaries x y x y x y HDTV ITU- T.709, s CT D sc Unlimited signed D OMM Wide D Adoe 98 CT D Apple CT D Standard daylight illuminant White surface illuminated y average midday sun in western Europe/northern Europe s gamut

15 s color space s color space created coopera9vely y HP and MicrosoN in 1996 uses the same primaries as the ITU- T.709 primaries, standardized for studio monitors and HDTV. It is the reference standard used for monitors, printers and on the Internet. LCDs, digital cameras, printers, and scanners all follow the s standard. For this reason, one can generally assume, in the asence of any other informa9on, that any 8- it- per- channel image file or any 8- it- per- channel image API or device interface can e treated as eing in the s color space. The transforma9on etween XYZ and s and viceversa is otained applying a linear transforma9on followed y a second transforma9on as elow: where a = where: linear, linear and linear for in- gamut colors are defined to e in the range [0,1] C linear is linear, linear, or linear, and C srg is srg, srg or srg.

16 The rg color space normalized aims to separate the chroma9c components from the rightness components. It is used to eliminate the influence of varying illumina9on. The red, green and lue channel can e transformed to their normalized counterpart r, g, according to " # $ $ $ $ $ $ $ % & = " # $ $ $ % & g r rg color space One of these normalised channels is redundant since r g = 1. Therefore the normalised space is sufficiently represented y two chroma9c components e.g. r, g and a rightness component.

17 Opponent color space Human percep9on comines, and response of the eye in opponent colours. Opponent colours can e hence expressed in space. Achroma9c ods ed- reen reen cone Yellow lue cone lue- Yellow ed cone l ""#$%&'& % " % $ ' $ ' *, -.& = $ ' $ ' $ ' $ ' /0#, # & # & l l

18 HS HLS - HSV color spaces HSI Hue, Saturaon, Intensity, HLS Hue, Saturaon, Luminance and HSV Hue, Saturaon, Value.. all specify colors using three values: hue the color dominant wavelenght, saturaon how much the color spectral distriu9on is around a certain wavelenght and luminance the amount of gray closely to human percep9on.

19 HSV color space HSV can e represented oth as a cylinder or a cone space depending on whether the term S refers to saturaon colorfulness wrt its own rightness or chroma colorfulness wrt the rightness of another colour which appears white under similar viewing condions. Values can e derived y the values: Max = max,, ; Min = min,, ; V - Value = max,, ; S - Chroma if Max = 0 then Chroma= 0; else Chroma = Max - Min / Max; H - Hue if Max = Min then Hue is undefined achromatic color; otherwise: if Max = & > Hue = 60 * - / Max-Min else if Max = & < Hue = * - / Max - Min else if = Max Hue = 60 * / Max - Min else Hue = 60 * / Max - Min Cyan 180 o reen 120 o Yellow 60 o lue 240 o Magenta 300 o Value ed 0 o White Colorfulness is the difference etween a colour and gray lac Hue Chroma

20 Distances in color space Hardware oriented color spaces such as, HSV, HSI are not perceptually uniform: uniform quan9za9on of these spaces results into perceptually redundant ins and perceptual holes and a distance func9on such as the Euclidean does not provide sa9sfactory results. A difference etween green and greenish- yellow is rela9vely large, whereas the distance dis9nguishing lue and red is quite small. If infinitesimal distances etween two colors as perceived y humans were constant, the color space would e Euclidean and the distance etween two colors would e propor9onal to the lenght of their connec9ng line. Instead in the chroma9city diagram xy, colors corresponding to points that have the same distance from a certain point are not perceived as similar colors y humans. Mac Adams ellipses account for this phenomenon. Ellipses are such that colors inside them are not dis9nguishale from the color in the center.

21 Perceptual color spaces CIE solved this prolem in 1976 with the development of the L*a** perceptual color space. Other perceptual spaces are L*u*v* and L*c*h*. All are ased on transforma9ons that approximate the XYZ iemann space into an Euclidean space. These spaces are less distorted than CIE XYZ space although they are not completely free of distor9on Mac Adam s ellipses ecome nearly circular here. In the L*a** and L*u*v* color spaces distances can e computed as Euclidean distances: Dc1,c2 = [ L* 1 - L* 2 2 a* 1 - a* 2 2 * 1 * 2 2 ] 1/2 Dc1,c2 = [ L* 1 - L* 2 2 u* 1 - u* 2 2 v* 1 v* 2 2 ] 1/2 Mathema9cal approxima9ons introduced cause devia9ons from this property in certain parts of the spaces: In L*u*v* ed is more represented than reen and lue. In L*a** there is a greater sensiility to reen than to ed and lue. lue is however more represented than in L*u*v*. L*a** L*u*v*

22 L*u*v* and L*a** color spaces L* = 903,3 Y/Y n if Y/Y n < 0, Y/Y n 1/3 otherwise u* = 13L* u u n v* = 13L* v v n u = 4X / X15Y3Z v = 9Y / X15Y3Z L* = 903,3 Y/Y n if Y/Y n < 0, Y/Y n 1/3 otherwise a* = 500 [fx/x n fy/y n ] * = 200 [fy/y n fz/z n ] ft = t 1/3 for t T t 16/116 otherwise Y n u n v n are the values of the reference white X n Y n Z n are the XYZ values of the reference white

23 Color space invariance to light- oject interac9on Interac9ons etween light and oject may produce highligh9ng and shadowing. Highligh9ng and shadowing depend on geometry, ody and surface reflectance and illumina9on condi9ons. Highligh9ng and shadowing can highly impair image matching. The appropriate selec9on of color spaces can filter out or account of these effects to provide a transformed and more useful image. Color edges Shadow and geometry edges Highlight eometry edge

24 ,,,, s n em s n em r = = rg color space is photometric shadowing/ highligh9ng invariant C W = E m n, s f C " # c "d" = e m n, s C Considering the ody reflection term: Similarly for the surface reflection term. Hue of HSI color space is photometric shadowing/ highligh9ng invariant,,,, s n em s n em g = =,,,, s n em s n em = =

25 l 1 l 2 l 3 color space l 1 l 2 l 3 color space is otained from manipula9on and is invariant to highligh9ng effects of light interac9on par9cularly for shiny ojects Original image l 1 l 2 l 3 image 3D plot of image 3D plot of l 1 l 2 l 3 image

26 c 1 c 2 c 3 color space c 1 c 2 c 3 color space is otained from manipula9on and is invariant to shadowing effects of light interac9on par9cularly for mae ojects c 1,, = arctan max{ c 2,, = arctan max{ c 3,, = arctan max{, }, }, } 3D plot of image 3D plot of c 1 c 2 c 3 image

27 Classifica9on of oject color edges Local structures of ojects lie edges, corners and junc9ons depend on geometry, surface reflectance and illumina9on condi9ons. Proper9es of color spaces can e used for their classifica9on colour edge maxima y type material shadow or geometry shadows and geometry highlights colour edges

28 Edge classifica9on y color spaces Using oth c 1 c 2 c 3 and l 1 l 2 l 3 color spaces: "#$%"C c1 c 2 c 3 # & c1 c 2 c 3 & "C l1 l 2 l 3 < & l1 l 2 l 3 &'*,--"#.,-'"/'"/'&0/ -"#$%"C l1 l 2 l 3 l 1 l 2 l 3 c 1 c 2 c 3 $ & l1 l 2 l 3 &'*,--"#.,-*1120/-*,--"#.,--',01312/14&2.0/ Color for matte and shiny ojects also highlights for shiny ojects tc1c2c3 c 1 c 2 c 3 highlight l 1 l 2 l 3 Color for shiny ojects; color for matte ojects wea tl1l2l3 shadow or geometry

29 Summary of color space proper9es ed reen lue addi9ve color system ased on tri- chroma9c theory. easy to implement ut non- linear with visual percep9on. device dependent with semi- intui9ve specifica9on of colours. very common, used in virtually every computer system, television, video etc. HSL Hue Satura9on and Lightness, HSI Intensity, intui9ve specifica9on of color. Otained as linear transform from and therefore device dependent and non- linear. Appropriate only for moderate luminance levels. eal world environments are not suitaly represented in this space. HSV HSL HSI Hue component Invariant under the orienta9on of the oject to the illumina9on and camera direc9on. Opponent color axes Advantage of isola9ng the rightness informa9on on the third axis. Invariant to changes in illumina9on intensity and shadows. c 1 c 2 c 3 color space Invariant to shadowing effects for mae ojects I 1 I 2 I 3 color space Invariant to highligh9ng effects

30 CIE L*u*v* ased directly on CIE XYZ, aempts to linearise the percep9ility of unit vector color differences. Non- linear transforma9on ut the conversions are reversile. The non- linear rela9onship for L* u* v* is intended to mimic the logarithmic response of the eye. CIE L*a** ased directly on CIE XYZ, aempts to linearise the percep9ility of unit vector color differences. Non- linear transforma9on ut the conversions are reversile. The non- linear rela9onships for L* a* and * are intended to mimic the logarithmic response of the eye. Suitale for real world scene color representa9on

31 Invariance proper9es of color spaces shadowing highlights ill. intensity color ill. sou rg - - Hue - c 1 c 2 c l 1 l 2 l no invariance invariance