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Fix the implementation of the HLG EOTF function #23

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Jul 31, 2024
Merged

Fix the implementation of the HLG EOTF function #23

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8762be6
Fix the implementation of the HLG EOTF function
Jul 29, 2024
4580d18
Fix the tests for HLG
Jul 31, 2024
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13 changes: 9 additions & 4 deletions siti_tools/siti.py
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Original file line number Diff line number Diff line change
Expand Up @@ -482,19 +482,24 @@ def eotf_hlg(
Returns:
frame_data: pixel values in the physical luminance up to 10,000 cd/m^2
"""
frame_data = np.maximum(frame_data, 0.0)
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According to the ITU-R Recommendation BT.2100, the values below 0 and above 1 are also possible and acceptable (see NOTE 5g).

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Yes, fine, note 5h per latest version.

frame_data = np.minimum(frame_data, 1.0)

a = 0.17883277
b = 0.02372241
c = 1.00429347
gamma = 1.2
if l_max <= 1000.0:
gamma = 1.2
else:
gamma = 1.2 + 0.42 * np.log10(l_max/1000.0)
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See NOTE 5e in the Recommendation BT.2100

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LGTM, it appears to be NOTE 5f though in the latest verson (https://www.itu.int/dms_pubrec/itu-r/rec/bt/R-REC-BT.2100-2-201807-I!!PDF-E.pdf).


frame_data = (frame_data <= 0.5) * (np.power(frame_data, 2.0) / 3.0) + (
frame_data > 0.5
) * (np.exp((frame_data - c) / a) - b)

frame_data = (l_max - l_min) * np.power(frame_data, gamma - 1.0) + l_min
# NOTE: The following is only valid when the function is applied to the Y channel.
# If frame_data was a color channel (R, G, or B), the correct implementation would be:
# (l_max - l_min) * np.power(Y, gamma - 1.0) * frame_data + l_min,
# where Y would be obtained from linearized R, G, B channels.
frame_data = (l_max - l_min) * np.power(frame_data, gamma) + l_min
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If frame_data = Y the equation in the NOTE can be written as:

(l_max - l_min) * np.power(frame_data, gamma - 1.0 + 1.0) + l_min

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This part I don't see in BT.2100, but to be honest I have only looked very briefly.

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@slhck You are right, it is not in the recommendation as it only defines the functions for the individual components. The "most correct" way would therefore be to convert the YUV input to RGB, apply the EOTF on individual components, and convert back to YUV. But I believe that is not really needed for our use case and this solution seems like a reasonable approximation. Would you agree?

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I see, yes, that makes sense. I was more confused about the subtraction gamma - 1.0 in the original code and where that came from.


return frame_data

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18 changes: 9 additions & 9 deletions test/ground_truth/fall-hlg.json
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Original file line number Diff line number Diff line change
@@ -1,16 +1,16 @@
{
"si": [
11.60486742434359,
11.348906881585735,
11.550420779275415,
11.302442575496784,
11.53252417160579
56.859746855102614,
55.967538925996365,
56.31768629091642,
55.72770870085969,
56.65520632442709
],
"ti": [
1.8983682229673808,
2.222959198823672,
2.006899224083598,
1.8976135425959544
9.282396642166805,
10.913202661020888,
9.818995292103207,
9.34710188339459
],
"settings": {
"calculation_domain": "pq",
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18 changes: 9 additions & 9 deletions test/ground_truth/lights-hlg.json
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Original file line number Diff line number Diff line change
@@ -1,16 +1,16 @@
{
"si": [
8.498430920800487,
8.321574730146757,
8.408620911280588,
8.276614669711085,
8.502094759638036
38.29655050751715,
37.94350168275566,
38.24326954168339,
37.92370519326262,
38.491130718383644
],
"ti": [
0.885369996432793,
0.8380038034866518,
0.840396082605608,
0.8602735745148169
3.6567758609168197,
3.5211110820450493,
3.5537786270630987,
3.599255913659733
],
"settings": {
"calculation_domain": "pq",
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18 changes: 9 additions & 9 deletions test/ground_truth/sunset-hlg.json
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Original file line number Diff line number Diff line change
@@ -1,16 +1,16 @@
{
"si": [
0.7738618954474061,
0.7693658477258258,
0.8061181693471522,
0.8313873320178494,
0.8783931251175974
3.9986325451625366,
3.945613616354972,
4.138035019599985,
4.246972345956456,
4.48982814719558
],
"ti": [
1.0383126165513015,
1.0963192748625727,
1.1724608964066017,
1.2326597542789979
5.477032037410652,
5.759358031721984,
6.133345611005933,
6.424600294368263
],
"settings": {
"calculation_domain": "pq",
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