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====== HSL->RGB ====== | ====== HSL->RGB ====== | ||
- | The text below is based on an Excel workbook attached to this page: {{ :isp:hsl-rgb.xlsm |}}. That Excel file provides a sort of playground where you can try various input data and see the final results, both " | + | The text below is based on a {{ https://docs.google.com/ |
===== Preface ===== | ===== Preface ===== | ||
- | Much is written and is available on the color space conversion from HSL to RGB (for example this [[https:// | + | Much is written and is available on the color space conversion from HSL to RGB (for example this [[https:// |
The below article details the way to perform this conversion without the use of division operations with high enough precision as to satisfy the imaging pipeline quality requirements for the SUB2r camera based on Artix-7 100T FPGA. | The below article details the way to perform this conversion without the use of division operations with high enough precision as to satisfy the imaging pipeline quality requirements for the SUB2r camera based on Artix-7 100T FPGA. | ||
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\[\frac{1}{x} = \frac{1*N}{x*N}\] | \[\frac{1}{x} = \frac{1*N}{x*N}\] | ||
and choosing \(N\) such that \(x*N\) is a whole power of \(2\) we have an optimization where a division is replaced by a pair of a multiplication followed by a (super cheap!) bit-shift operation by \(Z\) bits: | and choosing \(N\) such that \(x*N\) is a whole power of \(2\) we have an optimization where a division is replaced by a pair of a multiplication followed by a (super cheap!) bit-shift operation by \(Z\) bits: | ||
- | \[\frac{C}{x} = C*\frac{1}{x} = C*\frac{1*N}{x*N} = C*\frac{N}{2^Z} = [(C*N)>>Z]\] | + | \[\frac{C}{x} = C*\frac{1}{x} = C*\frac{1*N}{x*N}\Bigg|_{\{x*N=2^Z\}} = C*\frac{N}{2^Z} = [(C*N) |
The value \(Z\) depends on the needed precision and, of course, the higher the \(Z\) the less precision loss there will be in the end. | The value \(Z\) depends on the needed precision and, of course, the higher the \(Z\) the less precision loss there will be in the end. | ||
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\[(R, | \[(R, | ||
- | ===== Step-by-step algorithm ===== | + | ===== Step-by-step algorithm |
Armed with the above information we can now compile the necessary sequence of calculations and format it into an easy-to-use table: | Armed with the above information we can now compile the necessary sequence of calculations and format it into an easy-to-use table: | ||
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| 14 | \[m\] | \[L - C/2\] | '' | | 14 | \[m\] | \[L - C/2\] | '' | ||
| 15 | \[(R,G,B)\] | \[(R_1+m, | | 15 | \[(R,G,B)\] | \[(R_1+m, | ||
+ | |||
+ | |||
+ | ===== Step-by-step algorithm (10x3 bit channel, 30-bit RGB) ===== | ||
+ | Armed with the above information we can now compile the necessary sequence of calculations and format it into an easy-to-use table: | ||
+ | |||
+ | ^ # ^ name ^ math excerpt from Wikipedia | ||
+ | | 1 | \[H\] | \[hue(pixel)\] | '' | ||
+ | | 2 | \[S\] | \[sat(pixel)\] | '' | ||
+ | | 3 | \[L\] | \[luma(pixel)\] | '' | ||
+ | | 4 | \[h\] | \[(H+360^\circ) \bmod 360^\circ\] | '' | ||
+ | | 5 | \[L^\prime\] | \[1-|2L-1|\] | '' | ||
+ | | 6 | \[C\] | \[L^\prime \times S\] | '' | ||
+ | | 7 | \[H^\prime\] | \[\frac{H}{60^\circ}\] | '' | ||
+ | | 8 | \[H^\prime_2\] | \[H^\prime \bmod 2\] | '' | ||
+ | | 9 | \[H^\prime_{2-1}\] | \[H^\prime \bmod 2 - 1\] | '' | ||
+ | | 11 | \[H^\prime_{final}\] | \[1-|H^\prime \bmod 2 - 1|\] | '' | ||
+ | | 12 | \[X\] | \[C \times H^\prime_{final}\] | '' | ||
+ | | 13 | \[(R_1, | ||
+ | /*(C,X,0)*/ | ||
+ | }else if(Hp < 745472*2){ | ||
+ | /*(X,C,0)*/ | ||
+ | }// | ||
+ | | 14 | \[m\] | \[L - C/2\] | '' | ||
+ | | 15 | \[(R,G,B)\] | \[(R_1+m, | ||