Chapter2 Image Formation Reading: Szeliski, Chapter 2.
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Transcript of Chapter2 Image Formation Reading: Szeliski, Chapter 2.
Chapter2 Image Formation
Reading: Szeliski, Chapter 2
What are we tuned to?
The visual system is tuned to process structures typically found in the world.
What is a natural image?
The structure of ambient light
What is a natural image?
The visual system seems to be tuned to a set of images:
What is a natural image?
The visual system seems to be tuned to a set of images:
Did you saw this image?
What is a natural image?
The visual system seems to be tuned to a set of images:
Demo inspired from D. Field
6 images
Not all these images are the result of sampling a real-world plenoptic function
http://www.rowland.harvard.edu/images/ModPurp.jpg
http://www.alexfito.com/
• Proposition 1. The primary task of early vision is to deliver a small set of useful measurements about each observable location in the plenoptic function.
• Proposition 2. The elemental operations of early vision involve the measurement of local change along various directions within the plenoptic function.
• Goal: to transform the image into other representations (rather than pixel values) that makes scene information more explicit
Cavanagh, Perception 95
What are “visual features”
Shape, color, texture, etc
2.1 Photometric Image Formation
• Discrete color or intensity values• Where do these value come from?
– Geometry, projection– Camera optics, sensor properties – Lighting, surface properties
Images as Functions
Images as Functions• We can think of an image as a function, f, from R2 to R:
– f( x, y ) gives the intensity at position ( x, y )
– Realistically, we expect the image only to be defined over a rectangle, with a finite range:
• f: [a,b]x[c,d] [0,1]
• A color image is just three functions pasted together. We can write this as a “vector-valued” function:
( , )
( , ) ( , )
( , )
r x y
f x y g x y
b x y
Images as functions
What is a digital image?
• We usually work with digital (discrete) images:– Sample the 2D space on a regular grid– Quantize each sample (round to nearest integer)
• If our samples are apart, we can write this as:• f[i ,j] = Quantize{ f(i , j ) }• The image can now be represented as a matrix of integer
values
Photometric Image Formation
Perspective projection Light scattering
Lens optics Bayer color filter array
Photometric Image Formation
2.2 Lighting• Point light source
– Single location (small light bulb)– Infinity: the sun --directional light
• Area light source – A finite rectangular area emitting light equally in all
directions
• Environment map • Light direction to color mapping
2.2.2 Reflectance and Shading
many models for reflectance and shadingBRDF: Bidirectional Reflectance Distribution Function
BRDF
• BRDF is reciprocal
• For isotropic surface, no preferred directions for light transport
BRDF
• Light existing a surface point:
Foreshortening factor
Diffuse Reflection
• Also called Lambertian or matte reflection– Light is scattered uniformly in all directions, i.e. – BRDF is constant:
Think about the inverse problem
Specular Reflection• Depends on the direction of outgoing light• Mirror surface:
– Specular reflection direction
rv
cos( ) ( )s r iv s
Specular Reflection• Amount of light
– Phone model – Micro-facet model
– Larger , , more specular surface with hightlights ; Smaller, softer gloss
Phone Shading Model
• Diffuse • Specular • Ambient:
– Does not depend on surface orientation– Color and both ambient illumination and
the object
Phone Shading Model
( ; ) ( ) ( )
( ) ( )( )
( ) ( )( ) e
r r a a
d i i ii
ks i r i
i
L v k L
k L v n
k L v s
The recent advent of programmable pixel shaders makes the use of more complex models feasible.
Example
Realistic Rendering
The recent advent of programmable pixel shaders makes the use of more complex models feasible.
Ioannis Gkioulekas, et al, Siggraph’13
Optics
• Lens, sensor• Ideal pinhole camera • More complex: focus, exposure, vignetting,
aberation,…,
Thin lens model Thin lens: low, equal curvature on both sides
Optical axis
Thin lens model
object
Focus plane
Thin lens model
object
Circle of confusion
Pinhole camera
Pinhole Camera Model
object
Pinhole Camera Model
object
Pinhole Camera Model
object
2.3 3D to 2D Projection
• 3D perspective: the most commonly used projection in computer vision and computer graphics
3D view of world perspective
book: pp32-60
Pinhole Camera Model
object
xfu
zyf
vz
Pinhole Camera Model
object
Pinhole Camera Model
• Using homogeneous (projective) coordinate –
0 0 0/
0 0 0/
0 0 1 01 1
0 0 0 1 1
f xu fx z
f yw v z fy z
z
wx = Kp
xfu
zyf
vz
Camera Intrinsics• Imperfect camera• image sensor
• s: possible skew between sensor axes• a: aspect ratio • : optical center• F : focal length
0
0 0 1
x
y
f s c
af c
K
. ., ( , ) ( / 2, / 2)x ye g c c W H
( , )x yc cFive intrinsic parameters
Camera Intrinsics
• Focal length• Actual focal length, e.g. 18~55mm, • Conventional sensor width: 35 mm• Digital Image: integer values, [0,W) x [0,H)
Focal length Sensor width
Field of view
Extrinsic Parameters
• World Coordinate system to Camera Coordinate system
[c wp R | t]pExtrinsic parameters
j
i
kj
i
k
O
C
1wC R t
Extrinsic Parameters
wx = Kpwith
[ ww x K R | t]p
[M K R | t]Camera Matrix
2.3 Digital Camera
• Process chart
2.3 Digital Camera
• Process chart
2.3.2 Color
• Light from different parts of the spectrum is somehow integrated into discrete RGB color values
[ ww x K R | t]p
2.3.2 Color
• Primary and Secondary Colors• Additive colors (projector, monitor)• Subtractive colors (printing, printing)
CIE color matching
• Commission Internationale d’Eclairage (CIE)• Color matching experiments
pure colors to the R=700.0nm, G=546.1nm, and B=435.8nm
XYZ Color Space
Y=1 for pure R (1,0,0)
XYZ Color Space
• Y=1 for (1,1,1)
XYZ Color Space
• Chromaticity coordinates
• Yxy (luminance plus the two most distinctive chrominance components)
Chromaticity Diagram
L*a*b* Color Space
• Human visual system is roughly logarithmic• Differences in luminance or chrominance are
more perceptually uniform• Non-linear mapping from XYZ to L*a*b* space
L*a*b* Color Space
Color Cameras
• Spectral response function
• Make sure to generate the standard color values
HDTV, new monitors, new standard ITU-R BT.709
Color Filter Arrays
• Separate sensors for three primary colors
Bayer RGB pattern: (a) color filter array layout; (b) interpolated pixel values
Bayer Pattern, 1976
• Green filters are twice as many as red and blue filters
• Human visual system is much more sensitive to high frequency detail in luminance than chrominance
• Luminance is mostly determined by green value
Color Balance
• Move the white point of a given image closer to pure white (R=G=B)– Multiply RGB values by a different factor – Color twist, general 3x3 transform matrix– Exercise 2.9 (optional)
Gamma
• CRT Monitor: non-linear relationship between the voltage and the resulting brightness is determined by gamma
• Pre-map the sensed luminance Y through an inverse gamma
2.2
10.45
Gamma Compensation
Noise added during transmission or quantization will be reduced in the darker regions of the signal where it was more visible
Other Color Spaces
• XYZ, RGB for spectral content of color signals• Others for image coding and computer
graphics– YUV, YCrCb, HSV
YUV Color Space
• YUV for video transmission– Luma
– Two lower frequency chroma channels
YCrCb Color Space
• Closely related to YUV• Different scale factor to fit within the 8-bit
range for digital signals
• Useful for careful image de-blocking, et al.
HSV Color Space
• Hue: direction around a color wheel
• Saturation: scaled distance from the diagonal
• Value: mean or maximum color value
More suitable for color picking
Color Ratios
• Suitable for algorithms that only affect the value/luminance and not saturation or hue
• After processing, scale rgb back by the color ratio Ynew/Yold
Color FAQ, http://www.poynton.com/ColorFAQ.html
2.3.3 Compression
• Converting signal into YCbCr (or related variant)
• Compress the luminance signal with higher fidelity than the chrominance signal