Lecture 4: The spectrum, color theory and absorption and photogrammetry Friday, 14 January 1 Reading: Ch 2.3 – photography basics

What was covered in the previous lecture 2 LECTURES Jan 051. Intro Jan 072. Images Jan 123. Photointerpretationprevious Jan 144. Color theorytoday Jan 195. Radiative transfer Jan 216. Atmospheric scattering Jan 267. Lambert’s Law Jan Volume interactions Feb 029. Spectroscopy Feb Satellites & Review Feb Midterm Feb Image processing Feb Spectral mixture analysis Feb Classification Feb Radar & Lidar Feb Thermal infrared Mar Mars spectroscopy (Matt Smith) Mar Forest remote sensing (Van Kane) Mar Thermal modeling (Iryna Danilina) Mar Review Mar Final Exam Tuesday’s lecture? Color, shape and texture Lighting and shadows Image examples Photogrammetry Orbits Image geometry Parallax and stereo Today: Color and the spectrum Color perception Additive & subtractive color mixing Ternary diagrams and color transformations Selective absorption of light

Color Color is a sensation that can be predicted and controlled Color has 3 dimensions and can be simulated by radiances at three different ’s In natural color those are red, green and blue but In remote sensing any 3 may be combined as a “false-color” image Therefore we need to understand color Color is created by selective absorption, so we need to understand that first 3

For SI units frequently used in Remote Sensing, see back cover of text The electromagnetic spectrum Light is energy - Q =h in ergs  or joules (J)  where h = Planck’s constant, 6.63· J s = frequency (s -1 ) = c/ (c = speed of light, 3.00x10 8 ms -1, = wavelength (µm,nm,mm,cm,m) In remote sensing we commonly measure the flux of photons from a unit surface for a certain amount of time and by a camera or scanner a certain distance away with a lens of a particular diameter This flux is called the radiance L and the units are W m -2 sr -1. Watts W (power) are energy per unit time (J s -1 ) Sr stands for steradian and is the solid angle subtended by the pixel 4

On a plane, we can measure the angle q between 2 vectors sharing endpoint P, the center of a circle of radius r. A radian is defined as the angle that subtends an arc on a circle equal to the radius. It is about 57 degrees (360/2  ). A circle is divided into 360 degrees, or 2  radians. In a volume, we can measure solid angles as shown to the right, where P is the center of a sphere of radius r and q is the solid angle of a cone that intersects the sphere in a small circle of circumference  *C. A sphere (area = 4  r 2 ) contains 4  steradians, where a steradian (sr) is the unit of solid angle. The cone defined to the right subtends a solid angle of 1 sr. Review On Solid Angles, class website (Ancillary folder: Steradian.ppt) 5

Let’s start with how humans sense color: Cone-shaped cells within the eye absorb light in 3 wavelength ranges – RGB They send signals to the brain proportional to how much light is absorbed The brain turns these signals into the sensation of color Color has three attributes – hue, saturation, and intensity or lightness color (perception) is related to radiance (physical flux) 6 Section of the eye

DAY Bright light NIGHT Dim light Rods are more sensitive than cones In bright light, the three sets of cones send strong signals to the brain that drown out the signal from the rods. The signals are interpreted as the sensation of color In dim light, the signal from the single set of rods is dominant. It is interpreted as the sensation of black/white (gray) 1 nanometer (nm) = m =  m 7

Additive Color 8

Blue Green Red The spectrum and color Blue Green Red Blue Green Red Spectral yellow 9 brightness Wavelength, (  m) Gray Cartoon spectrum – A useful tool

Additive Color Blue Green Red Blue Green Red + Blue Green Red = Blue Green Red 10

b r g Additive mixtures – another framework 11 0, 100, 0% 0, 0, 100% 100, 0, 0% 33, 33, 33% 50, 50, 0%

ADDITIVEMIXINGADDITIVEMIXING 12

To work with color, we use three different data “spaces”: *Perceptual data space – how we sense color intuitively (Hue, saturation, intensity) *Radiance data space – how the color stimulus is described by the measured image data *Transformed DN space – a mathematical description of color that is related to radiance 13

HUE SATURATION INTENSITY (LIGHTNESS) A simple perceptual color space (HSI) 14

2) RGB radiance space 0 R B G r g b r=R/(R+G+B) g=G/(R+G+B) b=B/(R+G+B) 15

The CIE system: characterizes colors by a brightness parameter Y plus two color coordinates x and y. The response of the eye is best described in terms of three tristimulus coordinates rgb. Colors that can be matched by combining a set of three primary colors (ie, Red, Green, Blue) are represented on the chromaticity diagram by a triangle joining the coordinates for the three colors. Any H,S pair can be expressed in terms of the CIE color coordinates x and y, but intensity is not represented. 3) Transformed data space x y b r g r=R/(R+G+B) g=G/(R+G+B) b=B/(R+G+B) 16

b r g Additive mixtures 17

Transformation from a Cartesian XYZ radiance space to a spherical color space Longitude = hue (H) Co-latitude = saturation (S) Radius = intensity (I) XYZ may be any three tristimulus fluxes but are treated as RGB 0 X Z Y 18

Natural color Intensity Transformed Viking Lander RGB images of Mars HUE SAT INT 19

Color is created by selective Absorption If L is the radiance from a source at strength L o after passage through an absorbing medium such as the atmosphere, then: L = e -kz L o W m -2 sr -1 (Beer-Lambert-Bouguer Law) Light must either be reflected, absorbed, or transmitted This is the “rat” law of conservation: L= L r + L a + L t e -kz describes the % of light transmitted through the medium (assuming L r =0) k is a value characteristic of the absorptivity of the medium z is the length of passage through the medium (which we take to be homogeneous) Bouguer 20

Fraction of light transmitted Thickness, mm If it goes through z mm of medium, the total light remaining is e -kz %, where 1/k is the scale depth – that is, for every 1/k passage through the medium, 1/e = 1/2.718 % = 36.8% of the light remains. Absorption by a homogeneous medium is a constant-rate process – for every mm of material the light passes through, a certain fraction is absorbed. Graph of absorption as a function of medium thickness 21

Absorption and color k is commonly different from wavelength to wavelength (k ) –eg, more light might be absorbed in green than in red or blue When we see light having passed through such a filter, it appears magenta to us ( ie, no green ). We need to consider remote-sensing fluxes to be functions of wavelength Thus, radiance L (W m -1 sr -1 ) becomes spectral radiance L (W m -1 sr -1 µm -1 ) 22

A word about filters… Filters Filter functions,  m Transmittance 23

“Subtractive” Color 24

“Subtractive” Color Blue Green Red Blue Green Red Blue Green Red * = 1% 100% Red-transmitting filter Input spectrum Filtered spectrum Scene Filter 25

Remember: “subtractive” mixing is physically done by multiplication white light green filter yellow filter green light dark green light R: 1.0 * 0.0 = 0.0; * 0.8 = 0.0 G: 1.0 * 0.9 = 0.9; * 0.8 = 0.7 B : 1.0 * 0.0 = 0.0; * 0.0 =

What was covered in today’s lecture? Color, shape and texture Lighting and shadows Image examples Photogrammetry Orbits Image geometry Parallax and stereo 27

Radiative transfer theory - where light comes from and how it gets there - we will trace radiation from its source to camera - the atmosphere and its effect on light - the basic radiative transfer equation: DN = a·I g ·r + b 28 What will be covered in next Tueday’s lecture?