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--- isp:brightness [2023/09/06 09:08] – [In RGB color space] Igor Yefmov
+++ isp:brightness [2023/09/10 21:49] (current) – [Calculation reference] Igor Yefmov
@@ Line 6: / Line 6: @@
 ===== In RGB color space =====
-In RGB color space the operation is a matrix multiplication of the RGB's vector by a given "brightness" matrix. However we should make sure that the relative proportion of color channels is preserved so that the colors are not washed out.
+The mathematically correct way to do the brightness is to first convert into HSL color space, adjust the L (luma) component, and then convert back into RGB. That gives the correct result but costs way too many transistors and cycles. So we've got to improvise!
-Considering that the luminance is calculated as (see [[isp:luminance]])
+==== Algorithm ====
+Here's the algorithm to follow, assuming \(R, G, B \in [0..4095]\) and \(br \in [-1024..+1023]\):
+  - calculate luminosity
+  - adjust the brightness additively and clamp the value to range \([0..4095]\)
+  - figure out the slope for each components based on whether luma is below or above 50% and set chroma components to values that correspond to that 50% luma
+  - figure out if the new luma is going to cross the 50% boundary and if so - "flip the slopes"
+  - recalculate RGB components
-\[lum = 0.2126 * R + 0.7152 * G + 0.0722 * B\]
+==== Calculation reference ====
-Further consider that the brightness is simply a "boost" to RGB components, or in other words: gains. And as such all that is needed is to add the brightness \(br\) proportionally to each channel:
+To calculate luminosity we just find the max and min of the triplet and get a simple average:
+\[L = \frac{min(R, G, B)+max(R, G, B)}{2}\]
+Brightness adjustment is a trivial addition, clamping the value to its proper limits:
 \[
-\begin{bmatrix}
+L` = L + br \\
-R \\
+L` \in [0..4095]
-G \\
-B
-\end{bmatrix}
-+
-\begin{bmatrix}
-.2126 * br \\
-.7152 * br \\
-.0722 * br
-\end{bmatrix}
 \]
-Of course when implemented on FPGA the preference is to use integer arithmetic, which can be easily achieved by multiplying the "inconvenient" floating point numbers by \(1024\):
+The slope \(k_R\) for the red component calculation depends on whether \(L\) is above or below the middle:
+\[
+k_{R} =
+\begin{cases}
+R / L & \text{if} \; L \leq 2047 \\
+\frac{R - 4095}{L - 4095} & \text{if} \; L > 2047
+\end{cases}
+\]
+Finding the "middle point" value also depends on whether the \(L\) is above or below the middle:
 \[
-\frac{
+R =
-\begin{bmatrix}
+\begin{cases}
-R \\
+k_R * 2047 & \text{if} \; L \leq 2047 \\
-G \\
+- k_R * 2047 & \text{if} \; L > 2047
-B
+\end{cases}
-\end{bmatrix} \times 1024
-+
-\begin{bmatrix}
-* br \\
- * br \\
-* br
-\end{bmatrix}}{1024}
 \]
-N.B. In the above calculations the range for \(R, G, B\) values is \([0..1.0]\), so keep that in mind when using a different scale.
+If we are crossing the middle luma boundary as the result of this adjustment - flip the slope:
+\[
+k_R = 2 - k_R
+\]
+Applying the new \(L`\) to R component and clamping the result is trivial:
+\[
+R` = k_R * (L` - 2047) + R \\
+R` \in [0..4095]
+\]
+\(G\) and \(B\) calculations are similar to \(R\).
 ===== In HSL color space =====
 When using the HSL color space the adjustment is as simple as elementary school's arithmetic operation. Namely - just a simple addition.

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