Anaglyph HALD Generator algorithm and how to control it

Colors are analyzed and modified in terms of their red-to-cyan or cyan-to red ratio - larger value divided by smaller value.
The key control parameter is MaxBalancedMajorToMaxMinorRatio - the value of sides-ratio that separates balanced and unbalanced ranges. The author assumed the typical value is around 2.0 and up to 3.0, but a formal research would be better.

The change must result in max-minor channel coming in balance with the major side (max-major channel). The value of min-minor channel could be adjusted too; the way of doing it depends on MinMinorScaleOption control parameter.

The drawing below illustrates change to modified color's sides-ratio with the old and new values placed on the red-to-cyan- and cyan-to-red- axis

• The treatments for red-dominated and cyan-dominated colors are symmetrical, while the former deals with red-to-green or red-to-blue ratio, and the later - with green-to-red or blue-to-red ratio
  
• "Min-Balanced" thresholds for both red domination and cyan domination are derived from MaxBalancedMajorToMaxMinorRatio. As of this writing the thresholds are equal
  
• The numeric constants assume 8-bit color - the only option supported (at the time of this writing)
  

 >-{0.5/255}-----(red-cyan-ratio)-----{1.0}-------------------------{255/0.5}->
 <-{255/0.5}-----(cyan-red-ratio)-----{1.0}-------------------------{0.5/255}-<
                                        !
[...<- Cyan-Heavy] [Min-Balanced ...[Neu!tral]... Min-Balanced] [Red-Heavy ->...]
   \/        \/                      \/ !                                    \/
    |         +-----------+           | !                   +----------------+
    +----------------\/   \/         \/ !                  \/  
[...<- Cyan-Heavy] [Min-Balanced ...[Neu!tral]... Min-Balanced] [Red-Heavy ->...]
|                  |                    !                     |                 |
|                  |<---- only-balanced-colors-range (new)--->|                 |
|<--------------------------------- all-colors-range (old)--------------------->|

The main action of Anahald color balancing brings max-minor channel into the balance with max-major channel.

• e.g. if an unbalanced color is green-dominated, red channel must be increased
  

The conceptual formulae for max-minor channel is presented below

colorRangeWidthNew = 1 - 1/{MaxBalancedMajorToMaxMinorRatio}
colorRangeWidthOld = MaxChannelValue - MinChannelValue == 255 - 0 = 255

MinAllowedMaxMinor = OldMaxMajor / {MaxBalancedMajorToMaxMinorRatio}

NewMaxMinor = MinAllowedMaxMinor  +  OldMaxMinor * (colorRangeWidthNew / colorRangeWidthOld)

• control parameters appear in {} - curly braces
  
• on the concept level red-dominated and cyan-dominated colors are treated symmetrically
  
• as the result the original range of RGB color trio-s gets "squeezed" into its subset - the one of the balanced colors.
  

The main color-balancing action - scaling of max-minor channel - brings the color into balance from Anahald point of view. But leaving min-minor channel untouched may produce an unrelated color.

Two approaches provided for balancing min-minor channel, selectable by MinMinorScaleOption control parameter.

If MinMinorScaleOption = 1, min-minor channel undergoes the same treatment as the max-minor, independently of it; in the formulae below lines that completely duplicate prior calculation of max-minor are commented-out with #:

# colorRangeWidthNew = 1 - 1/{MaxBalancedMajorToMaxMinorRatio}
# colorRangeWidthOld = MaxChannelValue - MinChannelValue == 255 - 0 = 255

# MinAllowedMaxMinor = OldMaxMajor / {MaxBalancedMajorToMaxMinorRatio}

NewMinMinor = MinAllowedMaxMinor  +  OldMinMinor * (colorRangeWidthNew / colorRangeWidthOld)

If MinMinorScaleOption = 2, min-minor channel is scaled-up by the same factor as max-minor:

NewMinMinor = OldMinMinor  *  (NewMaxMinor / OldMaxMinor)

If the boundary between balanced and unbalanced is a hard threshold, color gradients crossing this boundary are disrupted with apparent "stair" at appropriate points. Anahald addresses this problem by smoothing the transition - modifying originally balanced colors with sides-ratios (red-to-cyan or cyan-to-red) close to the threshold value:

• such colors are referred to as "marginally balanced"
  
• the more balanced is such a color, the smaller change it undergoes
  
• control parameter MinBndBalancedMajorToMaxMinorRatio specifies the minimum value of color's sides-ratio for the color to be considered marginally balanced; colors with smaller sides-ratios aren't altered at all
  
• control parameter SmoothBndBalancedOption allows to choose one of two approaches for the smoothing action; more on this follows
  
• all the three color channels are affected
  

Two approaches to smoothing balanced-unbalanced boundary
Whatever the approach, the smoothing formulae just takes weighted average between the original and would-be-modified values for each of the three color channels.

channelValueNew = (1 - w) * channelValueOld  +  w * channelValueIfScaled

• channelValueOld is the original color-channel value
  
• channelValIfScaled would be the modified color-channel value as if this (RGB) color was treated as originally unbalanced
  
• channelValueNew is the ultimate color-channel value
  
• w is the weight coefficient; the way of calculating its value depends on control parameter SmoothBndBalancedOption
  
• the goal is to gradually diminish the change in color-channel value (result of balancing) - from its maximum at the balanced-unbalanced boundary, so that this change disappears at colors with sides-ratio equal to MinBndBalancedMajorToMaxMinorRatio
  

The two user-selectable formulas for calculating smoothing weight coefficient (assumuing red-dominated color):

1. "linear weight" - used if SmoothBndBalancedOption = 1
   

   wLinear = 1.0*(red_cyan_ratio - {MinBndBalancedMajorToMaxMinorRatio}) /  ({MaxBalancedMajorToMaxMinorRatio} - {MinBndBalancedMajorToMaxMinorRatio})}]
   

2. "parabolic weight" - used if SmoothBndBalancedOption = 2
   

   a == -1 / ({MinBndBalancedMajorToMaxMinorRatio} - {MaxBalancedMajorToMaxMinorRatio})^2
   wParabolic = a*(red_cyan_ratio - {MaxBalancedMajorToMaxMinorRatio})^2 + 1,
   

Compared to linear-weight, for the parabolic option the weight reduces slower for near-balanced color, and steeper for more unbalanced colors.

Alternative to smoothing balanced-unbalanced boundary
There anyway exists a possibility to keep the boundary as the hard limit (e.g. colors with smaller sides-ratio are unchanged, only colors with larger sides-ratio undergo balancing). But then one has to maintain a collection of LUT-s with different threshold values and choose the LUT on per-image basis. This is perfectly suitable for individual images or finite sequences of images; becomes more complicated for videos. In any case, an automatic tool to select an optimal LUT for an image out of multiple choices would be beneficial and should be a subject for future work - see Anahald_Future_Work.html.