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--- isp:brightness [2019/05/09 00:30] – Igor Yefmov
+++ isp:brightness [2023/09/10 21:49] (current) – [Calculation reference] Igor Yefmov
@@ Line 4: / Line 4: @@
 Again, in the simplest terms, increasing or reducing pixel's brightness can be interpreted as adding or subtracting a fixed "gain" value (others may argue that a more natural approach would be to use a multiplier, while others still may bring the "vibrancy" approach into picture).
+===== In RGB color space =====
+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!
+==== 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
+==== Calculation reference ====
+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:
+\[
+L` = L + br \\
+L` \in [0..4095]
+\]
+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:
+\[
+R =
+\begin{cases}
+k_R * 2047 & \text{if} \; L \leq 2047 \\
+- k_R * 2047 & \text{if} \; L > 2047
+\end{cases}
+\]
+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.
 With that the implementation of the Brightness adjustment can be as simple as the following (where the "luma", or brightness component \(\in[0..100]%%\)):

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