Color2Gray: PCA Image Analysis and projection

Color2Gray PCA Image Analysis and Projection

We explored linear dimensionality reduction techiniques via principal component analysis (PCA). Below is a brief explanation of the algorithm and the results of PCA in both RGB and CIELAB color spaces. Algorithm:

Resize image
- Down Sample images to have a width of 20 (and proportional height); save computation time
Use PCA
- Use Principal Component Analysis to find the primary and secondary axis in a tristimulus color space (in this case RGB and CIELAB).
- PCA also finds the mean value of the image
Plot
- Plot downsampled image pixels with respect to RGB/CIELAB
- Plot primary (black dashed line) and secondary axis (red dotted line)
- Axis are centered at mean value of image
Project
- Project the full-resolution original image pixels onto the primary axis using closest point
- Scale this new luminance image to use full range
  - For the RGB iamge, I map the image to the max and min of the original RGB image and then map that to [0,1]
  - For LAB, I map the Luminance of the original L channel to the new values and then convert the image to an RGB grayscale image (this is the "normal range" image)
  - The other LAB grayscale image is the result of mapping the projected values to 0,1 and doesn't convert back to RGB
Problems:
- Dynamic range mapping; what is white, what is black?
- Sometimes the image is inverted; This is a problem for abWB, EquiLumDots, and GreyWheel; so they are shown with the corrected "inverted" images
- PCA is quite sensitive to the color space in which computation takes place. If the mage is largely isoluminant, then the weighting of the luminances will not matter and the result will just reflect how the color space stretches the chromatic differences.

abWB
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

abWB
LAB_2_Gray

Projected Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)

colorBlind12
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

colorBlind12
LAB_2_Gray

Project Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)

colorBlind35
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

colorBlind35
LAB_2_Gray

Project Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)

colorBlind45
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

colorBlind45
LAB_2_Gray

Project Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)

colorBlind6
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

colorBlind6
LAB_2_Gray

Project Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)

colorwheel
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

colorwheel
LAB_2_Gray

Project Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)

EqLumDots
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

EqLumDots
LAB_2_Gray

Projected Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)

greywheel
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

greywheel
LAB_2_Gray

Projected Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)

rg15x10
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

rg15x10
LAB_2_Gray

Project Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)

Sunrise
RGB_2_Gray

Gray (Maps to [min, max] of original image, then [0,1])

Plot perpendicular to primary & secondary axis

Plot RB axis

Plot RG axis

Plot GB axis

Sunrise
LAB_2_Gray

Project Gray [0,1]

Plot perpendicular to primary & secondary axis

Plot LB axis

Plot LA axis

Plot AB axis

Gray in Normal range ([min,max] of L, then conv to RGB Grayscale)