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--- isp:brightness [2023/09/10 18:30] – [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 =====
-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 improvise!
+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!
-Here's the algorithm to follow, assuming \(R, G, B \in [0..4095] and br \in [-1024..+1023]\):
+==== Algorithm ====
+Here's the algorithm to follow, assuming \(R, G, B \in [0..4095]\) and \(br \in [-1024..+1023]\):
   - calculate luminosity
-  - figure out the slope for each components based on whether luma is below or above 50%
   - 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:
@@ Line 22: / Line 33: @@
 \begin{cases}
 R / L & \text{if} \; L \leq 2047 \\
-\frac{R - 2047}{L - 2047} & \text{if} \; L > 2047
+\frac{R - 4095}{L - 4095} & \text{if} \; L > 2047
 \end{cases}
 \]
-Similarly find the \(k_G\) and \(k_B\) for green and blue components respectively.
+Finding the "middle point" value also depends on whether the \(L\) is above or below the middle:
-Brightness adjustment is a trivial addition, clamping the value to its proper limits:
 \[
-L` = L + br \\
+R =
-L` \in [0..4095]
+\begin{cases}
+k_R * 2047 & \text{if} \; L \leq 2047 \\
+- k_R * 2047 & \text{if} \; L > 2047
+\end{cases}
 \]
-Apply the new \(L`\) to R component and clamp the result:
+If we are crossing the middle luma boundary as the result of this adjustment - flip the slope:
 \[
-R` = k_R \times (L` - 2047) + R \\
+k_R = 2 - k_R
-R` \in [0..4095]
 \]
-Similarly perform calculations for green and blue components.
+Applying the new \(L`\) to R component and clamping the result is trivial:
-==== Integer arithmetic ====
-Of course when implemented on FPGA the preference is to use integer arithmetic, so for 12-bit RGB components and a 12-bit signed \(br\), the math looks like this:
 \[
-\begin{bmatrix}
+R` = k_R * (L` - 2047) + R \\
-R \\
+R` \in [0..4095]
-G \\
-B
-\end{bmatrix}
-+
-\begin{bmatrix}
- \\
-\\
-\end{bmatrix} \times br \times \frac{1}{1024} \\
 \]
+\(G\) and \(B\) calculations are similar to \(R\).
 ===== In HSL color space =====

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