Lecture 23: Imaging, Color CAP 5415

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# Lecture 23: Imaging, Color CAP 5415 - PowerPoint PPT Presentation

Lecture 23: Imaging, Color CAP 5415. Working with Intensity Values. Simple Non-Linearities can have a great effect on image appearance. Working with Intensity Values. Simple Non-Linearities can have a great effect on image appearance. Working with Intensity Values.

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Working with Intensity Values
• Simple Non-Linearities can have a great effect on image appearance
Working with Intensity Values
• Simple Non-Linearities can have a great effect on image appearance
Working with Intensity Values
• Simple Non-Linearities can have a great effect on image appearance
Working with Intensity Values
• This is not just linear scaling
Working with Intensity Values
• Can go the other way
Gamma correction
• Model this non-linearity using this type of curve:
Cameras and Gamma
• Consumer cameras put a similar non-linearity into photos
• Makes images look better
• You (as a vision person) don't want nice-looking images
• You want ACCURATE images
• Need to calibrate camera to remove gamma
Which leads to a second problem
• Most camera only give you 8 bits of precision
• Hard to capture both bright and dim regions
• Solution:
• Use multiple images to create a High Dynamic Range Image
• Can be solved as a least-squares problem if you account for saturation and dimness
Now that we can get accurate intensities, what about color?
• Engineering problem:
• I have sensor that records the amount of light at different pixels
• How do I get a color image instead of a black and white image?
Solutions
• Three sensors
• One sensor with a color mask
• Each pixel records one wavelength
• A common pattern for the mask is the Bayer pattern:
Mosaicing
• So, if I took a picture of this edge
• My sensor would record this image
Demosaicing
• I have 1 color at each pixel
• I need three
• Easy solution: Interpolate

+

Problem! This smooths across the edge
• Because the different pixels are used to red and green, the smoothing may be different

+

Color Fringing

(Results from Brainard et al)

Fast Solution
• The fringing occurs when the correlation between the color channels is incorrectly estimated
• One measure of this correlation is the color difference
• Can fix errors using median filtering
Simple Demosaicing Algorithm (Freeman)
• Use linear interpolation to get first estimate
• Compute difference images between color channels
• Median filter these difference images
• Use filtered difference images to reconstruct
Color matching experiments - I
• Show a split field to subjects; one side shows the light whose color one wants to measure, the other a weighted mixture of primaries (fixed lights).
• Each light is seen in film color mode.

(Slide by Forsyth)

Color matching experiments - II
• Many colors can be represented as a mixture of A, B, C
• write M=a A + b B + c C

where the = sign should be read as “matches”

• Gives a color description system - two people who agree on A, B, C need only supply (a, b, c) to describe a color.

(Slide by Forsyth)

Subtractive matching
• Some colors can’t be matched like this: instead, must write

M+a A = b B+c C

• This is subtractive matching.
• Interpret this as (-a, b, c)
• Problem for building monitors:
• Choose R, G, B such that positive linear combinations match a large set of colors

(Slide by Forsyth)

The principle of trichromacy
• Experimental facts:
• Three primaries will work for most people if we allow subtractive matching
• Exceptional people can match with two or only one primary.
• This could be caused by a variety of deficiencies.
• Most people make the same matches.
• There are some anomalous trichromats, who use three primaries but make different combinations to match.

(Slide by Forsyth)

Grassman’s Laws
• For colour matches made in film colour mode:
• symmetry: U=V <=>V=U
• transitivity: U=V and V=W => U=W
• proportionality: U=V <=> tU=tV
• additivity: if any two (or more) of the statements

U=V,

W=X,

(U+W)=(V+X) are true, then so is the third

• These statements are as true as any biological law. They mean that color matching in film color mode is linear.
RGB: primaries are monochromatic energies are 645.2nm, 526.3nm, 444.4nm.

CIE XYZ: Primaries are imaginary, but have other convenient properties. Color coordinates are (X,Y,Z), where X is the amount of the X primary, etc.

Usually draw x, y, where x=X/(X+Y+Z) y=Y/(X+Y+Z)

Linear color spaces
• A choice of primaries yields a linear color space --- the coordinates of a color are given by the weights of the primaries used to match it.
• Choice of primaries is equivalent to choice of color space.
Perceptually Linear Color Spaces
• When doing thing like segmentation or edge detection, we would like to compare colors in a way that is similar to how humans judge similarity
• A perceptually-linear space tries to match the numerical distances to our perceptual differences.
CIE L*a*b*
• Can be computed from CIE XYZ Space