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Old 17th June 2018, 15:12   #1  |  Link
shekh
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underwater correction

Share practice and ideas, continuation of https://forum.doom9.org/showthread.php?t=175479

Some testing samples

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Old 17th June 2018, 15:14   #2  |  Link
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Quote:
Originally Posted by WorBry
Hi Shekh,
Re: the trigger fish results. The difficulty in both cases was finding a neutral reference to go by for the channel mixing. With GOPR0304 I opted for the (assumed) white stripe on the head of the small yellow fish swimming around the Trigger Fish. After zooming in on the stripe I then used the Vectoscope as a reference for setting the channel mix i.e. manipulating the data plot as close as possible to the cross hairs. The sampled RGB values tallied also and the resulting Trigger Fish coloration seemed to match with images of the 'Titan' species, so I thought I'd got it about right. But if you think the coral (in particular) is coming through too pink, I'll have another look at it.

Same goes for GOPR1596. There I used the 'white' stripes on the fish coming into frame (top left) at around 2 sec. I was careful to exclude what was clearly some yellow coloration on dorsal side but thought it was probably close to white (turned grey) on underside of the fish, and so used that. Actually on the first attempt the color balance came out even warmer than and I 'cooled' it back a tad, but if you think it's too yellowish, I can tweak it some more. I'd also increased the saturation a smidge because I thought it looked a little washed out - possibly that could have skewed the balance a tad also...doesn't take much.
GOPR0304 looks tough. Did several attempts and it always looks too green and too pink at the same time. Maybe It's just unavoidable contrast (left side is deeper and farther away)
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Old 18th June 2018, 03:08   #3  |  Link
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Quote:
.I'd also increased the saturation a smidge because I thought it looked a little washed out - possibly that could have skewed the balance a tad also...doesn't take much...
Correction on that - it was the other one with the pinkish coral (GOPR0304) where I added some saturation - and it was just a smidge added through a qualifier targeting the pink colors with very low saturation. It hardly made a difference.

Quote:
Originally Posted by shekh View Post
GOPR0304 looks tough. Did several attempts and it always looks too green and too pink at the same time. Maybe It's just unavoidable contrast (left side is deeper and farther away)
I don't think there's anyway of avoiding the pink without screwing up the balance and fish coloration. Just one of those cases where the resulting color contrast is less pleasing.

As for GOPR1596, here's a slightly cooler version - takes a bit of that yellow off:



All done with with fine tweaks to the channel mix.
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Old 19th June 2018, 05:19   #4  |  Link
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I am looking at the remaining three clips btw but I have to say they are quite challenging, especially using only the Channel Mixer to make the color corrections.

In the 'Cave' clip (cave-GOPR0238) the B&W striped Sergeant Major fish make an appearance again, but if I use them for neutral reference I'm fighting marked yellow discoloration of the 'skylight' opening and color variegation in the aura around it.

Best strategy looks to be:

1. Apply a 'soft clip' to pull-down that super-white data with a smooth roll-off gradient - easy to do in Resolve, maybe could be done in VDub2 with (gradation) curves, I'll have to see. Incidentally, your clips are all recorded with full range luma (0-255) and all of the grading in Resolve is being done at full 'data levels', so there's no forced hard clipping (limiting) going on. Obviously in VDub2 the full range flagging on decode ensures that 'PC.709' conversion coefficients are applied by default.

2. Use the 'skylight' opening as neutral (daylight balanced) reference for the channel mix in the first instance.

3. Adjust the mix to achieve best compromise with the 'white' stripes on the Sergeant Major fish.

I'm making headway but hitting that fine balance is finicky to say the least. I'll post once I've arrived at something presentable. I'm determined not to resort to qualifiers and the like, as I want to replicate the process in VDub2.

BTW, did you use a dive light in that clip? Looks like the Sergeant Major fish closest to the camera are receiving some artificial illumination. If so, might explain why I'm finding it so hard to hit a good compromise.

As for the other two clips. Difficulty in both is finding an identifiable neutral reference to go by. GOPR0201 at least has some skylight so I could try to apply the above strategy. There's also that shoal of really tiny fish that are possibly black and white - maybe can sample off those at really high magnification.

But GOPR0233, nothing, not even sure what color the fish there are supposed to be - bluish grey maybe ? Only inroad I can see there is to start 'rebuilding' the Red channel with an initial RG/RB sub-channel shift, align the Red and Green channel profiles as closely as possible (referencing Histogram), see what colors that looks to be pulling-up and plumb for a color mix that is in someway believable.
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Old 19th June 2018, 09:46   #5  |  Link
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There is no torch. In "cave" there is a wide opening behind the camera, this is how I get there. Also since light falls off with distance it looks like the camera emits some light.
I have an idea to try: when clipping is applied to colored highlight, the highlight remains colored (6-axis), or saturates slowly per rgb channel (levels). It might be more convenient if clipping/overflow resulted in desaturation of highlight.

GOPR0233
Hard to say, some bright spots could be dead coral, I consider these white. Also coral rock to the right.

Ideally we want white references at multiple distances. The fishes on top maybe gray or very close to.
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Old 19th June 2018, 14:58   #6  |  Link
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Quote:
Originally Posted by shekh View Post
There is no torch. In "cave" there is a wide opening behind the camera, this is how I get there.
'Cave', I should have figured.

Quote:
Originally Posted by shekh View Post
Also since light falls off with distance it looks like the camera emits some light.
Right, and that's something that needs to be taken into account. It's acting like a near range 'key light'.

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I have an idea to try: when clipping is applied to colored highlight, the highlight remains colored (6-axis), or saturates slowly per rgb channel (levels). It might be more convenient if clipping/overflow resulted in desaturation of highlight.
If I were doing this purely as a Resolve 'showcase' I'd be tackling that skylight with a qualifier and 'power window' (garbage matte), likely applying desaturation along with blur over a gradient. There's also Saturation vs Luminance and Hue vs Saturation curves.

Many years back I concocted an AVS function (SelSah) that could be helpful there - applies Tweak parameters (including Saturation) over a defined luma range.

http://blog.niiyan.net/post/666717637/selsahv3

This is the type of situation I had in mind when I queried the prospect of a '3-way' version of the '6-axis color correction' filter in the other thread.

Anything else in VDub that could be brought to bear? Create a luminance mask with gradation curves maybe?

Still, the 'soft clipping' approach works quite well in Resolve. One of the nice things about Resolve is that it does all processing in the background at full 'data' levels with 32-bit float. So no data is lost. Even when working at constrained 'Video' (Limited/broadcast safe) levels on the timeline (which I'm not in this case), outlying values can be pulled into range.

If I can arrive at a decent result (using only Channel Mixer) in Resolve, I'll look at the options more closely in VDub2.

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Originally Posted by shekh View Post
GOPR0233
...some bright spots could be dead coral, I consider these white. Also coral rock to the right.

…...The fishes on top maybe gray or very close to.
OK thanks. That's helpful.
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Old 20th June 2018, 00:41   #7  |  Link
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OK, here's one of the better attempts at correcting the 'Cave' clip in Resolve using just the RGB Channel Mixer for the color balancing.



The 'soft clip' strategy for dealing with the 'skylight' worked out quite well. It did increase the gain some to compensate for the 'soft-clip'. Could be a bit brighter I guess but I tend to prefer a moodier look.

I think it achieved what I set out to do i.e.

Quote:
Originally Posted by WorBry View Post

...2. Use the 'skylight' opening as neutral (daylight balanced) reference for the channel mix in the first instance.

3. Adjust the mix to achieve best compromise with the 'white' stripes on the Sergeant Major fish.
And by that I'm referring to the fish in the foreground that does appear to be receiving some additional light from above-behind the camera. The fall-out from that however is that the fish just back from it have retained more of a blue/magenta tint. Whatever way I adjusted the mix to try and offset that I was always fighting (and losing) a yellowish or yellowish/green cast to the light flooding in, which didn't look right at all. I sneaked a bit of red in there to bring out some color on the rocks - they looked pretty bland otherwise. In hindsight - bit too magenta maybe, but that could be easily rectified, and all that would do is turn the residual tint on the fish more blueish.

Anyhow, this was the best compromise I could find and evidently there are limitations to what can be done with the Channel Mixer alone in a scenario like this. It clearly begs for further fine tweaking with the 3-way Color Wheels.

With that, I'll give it a go in VDub2. Depending on how it comes out of the Channel Mixer, I see what can be done to tweak it with the '6-axis corrector' or maybe RGB curves.

Edit: Just realized when I brought the rendered file (Cineform) from that Resolve grade into VDub2 to take the above frame shot I forgot to specify full range luma in the decode interpretation options. Here it is again:



That looks better. Some very pale yellow discoloration in the 'skylight' opening is showing through there, but it's barely noticeable. That said, having gone on to replicate the color correction process in VDub2 I am having issues with that. Need to look at it more closely.
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Old 20th June 2018, 11:01   #8  |  Link
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Interesting, your result looks nice. This is where I get to with vdub:

Would be good to go if I somehow fixed the skylight.
Some ideas I'm thinking about:
adding another gauge to desaturate overflows (turns something very bright into white)
adding 3-way thing with adjustable split points (it seems a fixed split is not enough)
producing alpha mask at some point and applying it to secondary filter (too much complexity begins)

What is the soft-clip you are talking about, is it a tweak in Channel Mixer? What it does?

Re: cineform does Resolve always export full range? I saw no obvious flag in SDK to realize full/limited range. Can you export this same frame as cineform?
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Old 20th June 2018, 19:35   #9  |  Link
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Would be good to go if I somehow fixed the skylight.
It's a pain to workaround that's for sure.

Quote:
Originally Posted by shekh View Post
Some ideas I'm thinking about:
adding another gauge to desaturate overflows (turns something very bright into white)
adding 3-way thing with adjustable split points (it seems a fixed split is not enough)
producing alpha mask at some point and applying it to secondary filter (too much complexity begins)
Adding 3-way control to the '6-axis' filter with definable ranges for Shadows, Mid-tones and Highlights, would be a great option to have.

Resolve has two sets of ('4-way') color wheels - the 'Primary Wheels' that operate through Lift, Gamma, Gain and (master) Offset, and the 'Log Wheels' that operate on definable Shadow, Mid-Tone, Highlight domains (plus master 'Offset'); there's no Mid-Tone range setting per se - that is automatically adjusted when the Shadow and Highlight domain ranges are defined. They are called 'Log Wheels' because the flexibility in control makes them particularly well suited for grading log gamma footage - they are just as useful for 'linear' video.

This article by Alex Van Hurkman gives a nice overview of differences in the control modalities applied to color tools with similar names in different software and clarifies the sometimes confusing terminologies associated with them:


https://www.provideocoalition.com/whats-in-a-name/

Quote:
... adding another gauge to desaturate overflows (turns something very bright into white)
….could be useful in this context, but I think you'd want control over the degree of desaturation - might not always be desirable to turn to pure white.

Quote:
Originally Posted by shekh View Post
What is the soft-clip you are talking about, is it a tweak in Channel Mixer? What it does?
In Resolve it's part of the curves tool set. Allows you to create a custom smooth roll-off to a set clip point, instead of 'hard' clipping. This is the 'soft-clip' I applied in that 'Cave' clip grade.



The scopes are scaled for 10-bit.

There are separate 'soft-clip' controls for Highlights and Shadows, but options to apply the 'soft-clip' to the RGB channels individually or ganged together. Very useful tool.

Resolve also has a dedicated Soft-Clip LUT generator, allowing the soft-clip to be applied via a LUT in the node workflow. Typical use might be when you are grading full range footage at full 'Data' levels but want to render out at 'Video' (Limited, 'broadcast-safe') levels - it offers an alternative to hard-clipping (limiting) or compression.

I used it in this context because the channel mix was increasing the net gain and crushing more of the highlights in the aura around that 'skylight', so producing a more diffuse light beam. Bringing those values down with a hard clip caused marked color variegation - the values in the centre of the opening were of course already blown (clipped) in the original footage. Applying the 'soft-clip' helped to create a smoother transition gradient and at the same time brought near-blown highlights down to a level that I legitimately could use as neutral reference. It meant though that there was a limit to which I could 'tighten' the spread of the light beam (closer tp the original) - anymore than I did and the yellowish discoloration would be much more stronger. Selective desaturation of the offending color would mitigate that, but I decided not to apply it in Resolve because there's no equivalent tool in VDub2.....yet

Attempting the same technique in VDub2 using RGB (gradation) curves to create the 'soft-clip' is proving tricky. Need to get the curve gradient just right, and avoid adding contrast, which only makes it worse. Best results so far are when the soft-clip is applied before the Channel Mixer in the filter sequence, which makes sense - once crushed (clipped) up at 255 that 'super-white' data can't be recovered - in Resolve it can, so it doesn't matter if the 'soft-clip' is applied after the channel mix.

Quote:
Originally Posted by shekh View Post
Re: cineform does Resolve always export full range? I saw no obvious flag in SDK to realize full/limited range. Can you export this same frame as cineform?
Resolve gives the option to export at Full (Data) or Limited (Video) range, but has some querks when it comes to full range flagging and import interpretation of some formats. With Cineform (now using the native SDK implementation) it does not appear to apply any flags, whether exporting as AVI or MOV. If you render out at Full (Data) levels and import the file back into Resolve it 'auto' interprets it as 'Video' levels and you have to manually set-it to 'Full'. Other formats like DNxHR are flagged and interpreted 'correctly'.

Not surprising then that VDub2 doesn't register any full range flag with these Resolve Cineform exports either. Not a big deal. Just something to be aware of....and remember.
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Old 21st June 2018, 03:00   #10  |  Link
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OK, here are my best attempts at correcting the 'Cave' clip in VDub2 using only Channel Mixer for the color balance and applying the 'soft-clip' strategy for dealing as best with the 'skylight'.



Input was the source clip pre-denoised with SMDegrain (same as used in the Resolve grade) - I've yet to get reacquainted with hqdn3d

The applied filters were, in order:

* 'Soft-clip' applied with RGB Gradation Curves
* Channel Mixer
* 6-axis Color Correction - saturation only
* Levels - adjusted only the black point (Input level 44) (I know, why didn't I use '6-axis' - old habits I guess)
* Unsharp Mask
* Color Tools - for scope monitoring, and Resize, Crop when I needed them for isolating the neutral references.

No added contrast was applied - it only hindered the sensitive 'skylight' workaround. Hardly needs contrast anyway.

The first two results (Mix 1A and B) were obtained using the skylight itself as the neutral reference for the channel mix. Mix 1B is a tad warmer. As seen in the Resolve grade, there is more of a residual blue tint on the Sergeant Major fish. The other two results (Mix 3 and 4) attempted to lessen that and reach a better compromise, but at the expense of an arguably less appealing greenish tinge on the margins of the skylight glow.

In all 4 cases I tweaked the 'soft clip' as best to limit spread of the skylight 'glow' whilst avoiding discoloration of the (now obscured) opening. The 'soft clip' curve is not as smooth as I would like - there's a bit of posterization coming through at the outer margins of the skylight glow as it spills over the rocks, but it's difficult to get right by hand. 'Poetic license' might see that as the contours in the rock, which is fine by me. In the original clip there were some flashes of what looked like reddish lens flare on the left side of frame, so attribute it to that

Personally, I think Mix 4 is a bit too green, and it's between the other three. For the fish I'd say Mix 3. For the 'skylight', Mix 1A.

What does Toupe Turtle think ?

http://birdsasart.com/248/Pacifc-Gre...-Galapagos.jpg

Errrrrrrrrrrrrrrrrr......none of them
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Old 24th June 2018, 11:04   #11  |  Link
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Can you post your settings 1A?
I'm away on vacation, will resume experiments when I come back.
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Old 24th June 2018, 18:31   #12  |  Link
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Can you post your settings 1A?
Sure. That was using the pre-denoised (SMDegrain) clip:

Filters, in order:

*Gradation Curves - RGB (adjusted)

Soft clip curve co-ordinates:
In/Out Values
0, 0
64, 64
128, 128
192, 192
224, 221
237, 230
255, 239

*Channel Mixer (Emiliano Ferrari's)

RR 67.68
RG 73.73
RB 16.50

GR 48.63
GG 100
GB 0

BR 20.51
BG 29.59
BB 74.71

Note: the channel value sliders don't actually allow fine control to 2 decimal points - they nudge in increments, just not whole numbers.

*6-Axis Corrector: Saturation 1.522

*Levels: Input 44,255, Output 0,255

*Unsharp Mask:

Radius: 1.6
Strength: 1.11
Threshold: 0

Edit: I also looked at applying the 'soft-clip' curve at increasing strengths, to pull the skylight glow in tighter. Absolute maxiumum you can go before the 'clipped value' discoloration starts to come through is around:

In/Out
0,0
64,64
128,128
192,176,
209,184,
234,190
255,192

But then banding in the transition gradient becomes more noticeable and the curve starts to impact linearity in the upper-mids requiring more tweaks to the channel mix and Levels/Gamma adjustment. It's a balancing act.
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Old 26th June 2018, 05:30   #13  |  Link
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Here's another version that (I think) achieves better balance on the 'cave' clip.



This used the same preliminary channel mix as Mix 1A (with the skylight for neutral balance) but I then used RGB curves to apply a progressive shift in the Blue/Red balance over the tonal curve to produce a warmer mix in the darker tones. In essence, it substitutes for what, in Resolve, could be (better) applied with the Primary Wheels or Bars (i.e. Lift, Gamma, Gain). I could probably manipulate the curves further to target that feint blue tint that is still coming through on the Sergeant Major fish, but it's very finicky. The curves tool in Resolve has a nice feature where samples taken off the image are marked by the component values on the RGB curves, making it easier to target and manipulate specific colors. Still the VDub2 result is better than it was and it holds up pretty well throughout the clip.

Untested as yet, but I'm sure the same can be done in AVISynth with RGBAdapt.

The settings are the same as those I posted for Mix 1A above, but with the addition of RGB gradation curves, placed between 'Levels' and 'Unsharp Mask 'in the filter sequence. The R and B curve coordinates were:

Mode: RGB Adjusted + R/G/B

Red Channel:
In/Out
0,6
255,255

Blue Channel:
In/Out
23,0
255,255

Simple as that, just linear shifts in the R and B curve gradients.

Moving on to the remaining two test clips, similar considerations apply to GOPR0201 where we again have patches of skylight flooding in from above. Like the 'cave' clip, it makes sense to use the skylight as a reference for the channel mix (especially as there is a paucity of other neutral subject matter) but with the inevitable consequence that colored objects at lower depths are blighted with blue/magenta casts and under-representation of reds/yellows, resulting in washed-out, off colors - that yellow (ochre) coral bed in GOPR0201 being a prime example. Tweaking the channel mix at best achieves a mediocre and unsatisfying compromise.

So far I've managed to come up with some quite nice grades in Resolve using the Channel Mixer and Primary Color wheels, coupled with 'soft-clips' applied to the individual RGB channels for fine tuning of the highlights and shadows - and without recourse to 'qualifiers'. The tricky part is now translating those manipulations into RGB curve representations that can be applied in VDub2 and in a way that produces a smooth transition of hues in the sea background.

This type of scenario is where a 3-way version of the '6-axis color corrector' would come in very handy (hint, hint).

I'll post some results when I'm done, but will be going on vacation myself next week.
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Old 26th June 2018, 21:24   #14  |  Link
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Moving on to the remaining two test clips, similar considerations apply to GOPR0201 where we again have patches of skylight flooding in from above...

....So far I've managed to come up with some quite nice grades in Resolve using the Channel Mixer and Primary Color wheels, coupled with 'soft-clips' applied to the individual RGB channels for fine tuning of the highlights and shadows - and without recourse to 'qualifiers'
Examples:

Original GOPR0201 clip:



Pre-denoised (SMDegrain) and graded in Resolve using just the RGB Channel Mixer for setting the color balance - 'skylight' used as the neutral reference. And then the usual levels/contrast adjustment, mid-tone detail' (local contrast) and sharpening:




Same initial channel mix followed by some secondary manipulations with the color wheels to shift the bias to warmer tones at the lower depths:



A 'soft clip' applied to the Red channel helped to preserve the cooler neutral balance of the skylight. Also applied some lift in the shadows (without raising the black point) to bring out more detail - Resolve has a tool specifically for that. Plus the usual contrast, mid-tone detail, sharpening.

A lot better I think. Brings the coral to life.

Replicating the grade in Vdub2 with Channel Mixer + RGB curves is proving more tricky. Very difficult to achieve smooth transition of hues in the sea background, especially when saturation (which it needs) and a little contrast are added. Here's a preliminary result using only linear shifts in the R,G and B curve gradients (no soft clipping) and no added saturation or contrast. Very much work in progress:



The color balance per se holds up reasonably well over the entire clip, but I think it would need dynamic adjustment of levels (and saturation) at key points - just the job for 'Master Blend'.

If you want to play with it, the settings were, in sequence:

Source: Original clip pre-denoised (SMDegrain)

*Channel Mixer:

RR 71.68%
RG 101.76%
RB -58.69%

GR 10.55%
GG 90.72%
GB 0%

BR -11.52%
BG 7.52%
BB 101.76%

*RGB Gradation Curves:

Mode: RGB Weighted + R/G/B

Red:
In/Out
0,7
255,235

Green:
In/Out
10,0
255,255

Blue:
In/Out
28,0
247,255 (Keeps a slight cool bias on the 'skylight' )

*Levels:
In: 32,255
Out:0,255

*UnSharp Mask:

Radius: 1.6
Strength: 1.09
Threshold: 0

Edit: I guess it's not too bad 'as-is' with added saturation. Here Saturation +1.4 with the '6-axis corrector' placed between the RGB Curves and Levels in the sequence.



As you can see though, it brings out more green hues around the margins of the 'skylight'. Needs some fine re-tweaking of the color balance.

Edit: Alternatively, could be done using 'RGB Levels' filter in place of RGB Curves:



So, there:

*Channel Mixer: As above

*Levels:

In: 0, 1.080, 255
Out: 12, 234

*RGB Levels:

Red: 0.14, 0.985
Green: 0.213, 0.923
Blue: 0.246, 0.95


*Unsharp Mask - as above

It would benefit from a 'soft clip' instead of 'hard clip' on the Red channel highlights, but it's OK.


Edit: And the last remaining test clip GOPR0233.

Original:



Corrected with VDub2 using the same process - Channel Mixer > Levels > RGB levels, plus (in this case) some added contrast and saturation, and the usual sharpening:



I think that combination works rather well. Process settings in that case were:

Source: Original clip pre-denoised (SMDegrain)

*Channel Mixer:

RR 53.61%
RG 164.94%
RB -73.73%

GR 10.55%
GG 98.73%
GB 0

BR -28.61%
BG 18.55%
BB 83.69%

*Levels:
Input: 20, 1.080, 255
Output: 0,255

*RGB Levels:
Kept a slight blue bias on the 'skylight'

Red: 0.13, 0.95
Green: 0.194, 0.921
Blue: 0.241, 0.926

*RGB Gradation Curves (for centre-relative contrast):

Mode: RGB Adjusted
Coordinates:

In/Out
0,0
64,57
128,128,
192,196
255,255

*'6-Axis Corrector' (for Saturation only) + 1.461

*Unsharp Mask:

Radius: 1.6
Strength: 1.09
Threshold: 0
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Old 28th June 2018, 15:37   #15  |  Link
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Shekh, in your video demo of Master Blend you used a hover-over 'RGB picker' tool:

https://youtu.be/3PHcVBgqoHY

Where can that be found?

Also, re: your 'RGB Levels' filter. I see that the Gamma parameter is not implemented as yet. Do you plan to do so ? With that addition it would better serve as a '3-way' (Lift, Gamma, Gain) substitute for the Primary Color Wheels/Bars in Resolve.
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Nostalgia's not what it used to be

Last edited by WorBry; 28th June 2018 at 16:02.
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Old 2nd July 2018, 12:22   #16  |  Link
shekh
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Thanks for great correction examples, I think I will review my procedures and update/replace some filters.

> your 'RGB Levels' filter. I see that the Gamma parameter is not implemented as yet. Do you plan to do so ? With that addition it would better serve as a '3-way' (Lift, Gamma, Gain) substitute for the Primary Color Wheels/Bars in Resolve.

I abandoned this filter since It wasn't useful for me (per-channel correction did not feel intuitive and I liked the idea of single filter for all changes). Will see what I could do with the new suggestions.

> hover-over 'RGB picker' tool

This is activated by holding "Shift" key. It also was present in old VD but with many issues.
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Old 2nd July 2018, 13:48   #17  |  Link
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OK thanks. On vacation myself just now so won’t be doing any video processing for a couple of weeks
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Nostalgia's not what it used to be

Last edited by WorBry; 2nd July 2018 at 22:58.
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Old 19th July 2018, 14:14   #18  |  Link
WorBry
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Quote:
Originally Posted by shekh View Post

> hover-over 'RGB picker' tool

This is activated by holding "Shift" key. It also was present in old VD but with many issues.
Thanks. Works great in VDub2. Wish I'd been aware of that when I was doing the corrections
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