The Colour of the Dark

Four new colour studies and four new slide labs went up together, and they share a colourist. Joker, Joker: Folie à Deux and The Bride! were photographed by Lawrence Sher and graded by Jill Bogdanowicz at Company 3; The Grand Budapest Hotel was photographed by Robert Yeoman and graded by her at Modern VideoFilm. Laid side by side, what these frames share first is their shadows. They are not grey. They carry a colour, and the colour looks oddly saturated for something so dark. That is the impression this report set out to test, and it began as ours.

This report takes that impression and makes it testable. It re-measures the dark end of every analysis-eligible shot of every film in this repository, 66,986 frames from 51 films, and asks three questions of the four: whether more of their picture is dark and coloured, which way their dark turns against the rest of the picture, and where the saturation comes from. The corpus is not background. It is the control: "coloured shadows" means nothing until it is said what the other films' shadows do.

The short answer runs against the impression and then explains it. These films do not put more chroma into the dark than cinema does. What they do is take a channel out. In the three Sher films the red channel reaches black before green and blue do, so the dark turns cyan-green and each dark pixel sits close to a single hue: high saturation at ordinary chroma. The Grand Budapest Hotel takes green out instead, and its dark goes magenta-red. Cinema's usual dark takes blue out first, and is warm.

Corpus. 51 films · 66,986 analysis-eligible shots, every one re-measured

Subject. Joker, Joker: Folie à Deux, The Bride!, The Grand Budapest Hotel · 5,970 shots

Pixels. full resolution on a two-pixel stride · no resampling

Toe / mids. L* 2–10 against L* 25–55

Floor. ΔE00 0.13 and 0.45° between adjacent 8-bit toe colours; differences called only above ΔE00 2 and 7°

Intervals. bootstrap over films, 2,000 draws

Masters. Joker and Folie à Deux also read from 10-bit PQ masters, the same frame of every eligible shot

1. census — More of Folie à Deux's picture is dark and still coloured than of most films (26%, 6th of 51), but the other three are near the middle and none puts more chroma into its toe than the corpus does.
2. census — Cinema's dark usually turns warm against its midtones (median −4.8°, 23 films against 13). The three Sher films turn the other way — Folie à Deux by +42°, the largest turn among the gamma-2.4 films — and The Grand Budapest Hotel turns warm.
3. census — The saturation is subtraction. In the median film blue is the lowest channel in 68% of toe pixels; in Folie à Deux red is, in 83%, and 26% of its toe pixels sit at HSV saturation 0.9 or above against under 1% in the median film.
4. census — The Grand Budapest Hotel drops a different channel: green is lowest in 16% of its toe, second in the corpus, and its dark goes magenta-red.
5. census — It is not noise and not a few scenes. Folie à Deux is red-first in every tenth of its running time; Joker switches by scene; The Bride! does so for a third of its length.
6. census + documented — The first full digital intermediate, on which she started as an assistant, sits at the other end: O Brother's toe gives up blue in every pixel.
7. census — Read from 10-bit masters, the two Joker films show the look more strongly, not less: Folie à Deux is red-first in 85.5% of its master's toe and 32% of it fully saturated.
8. census + documented — A saturated toe is the most film-owned property measured here (intraclass correlation 0.41) — and the films nearest to Folie à Deux in this space are not hers.

Eight new studies of four films, and one colourist behind all four.

The four grade reconstructions take eight frames each and reconstruct how they could be built in DaVinci Resolve. The four slide labs lay out thirty to forty-four frames of the same films against six scopes. Three of the grade reconstructions and all four labs are of films Jill Bogdanowicz graded; the fourth reconstruction, The Aviator, is here because it arrived in the same batch.

Read one at a time they are four films. Read together they raise the question this report answers, because the same observation recurs in all of them: the shadows are coloured, and oddly saturated for how dark they are.

• Grade reconstruction · Skin at One Pole, Sky at the Other · The Aviator, its two-colour first 53 minutes
• Grade reconstruction · Small Pools in a Black Room · The Bride!, its dark scenes
• Grade reconstruction · The Colour Was Built Before the Camera · The Grand Budapest Hotel
• Grade reconstruction · Sodium, Fluorescent and Greasepaint · Joker
• Slide lab · Orange Satin, Ballroom Cyan and Marquee Bulbs · The Bride!, 36 frames
• Slide lab · Sodium Amber, Stairwell Teal and Clown Red · Joker, 43 frames
• Slide lab · Arkham Teal, Stage Orange and a Blue Moon · Joker: Folie à Deux, 31 frames
• Slide lab · Mendl's Pink, Elevator Red and Lobby-Boy Purple · The Grand Budapest Hotel, 44 frames

"Coloured, oddly saturated shadows" can be measured three ways, and each needs the corpus to mean anything.

Taken literally, the impression makes three claims. The first is quantity: more of the picture is dark and still carries a hue. The second is direction: the dark has a hue of its own, turned away from the colour of the rest of the frame. The third is mechanism: something about how the dark is built makes it look saturated. The three can come apart, and in these films they do.

Every one of 66,986 shots was re-measured from its delivered midpoint frame. For each, the toe is the pixels between L* 2 and 10 and the mids are those between L* 25 and 55; the report records their colour, the turn between them, and, pixel by pixel in the toe, which encoded channel is lowest.

Eight bits leave little room at the bottom of the range. Enumerating every 8-bit colour whose L* falls in the toe, adjacent codes sit a median ΔE00 0.13 apart and turn hue by a median 0.45°, with a 95th percentile of 2.3°. This report calls two toes different only above ΔE00 2 and calls a hue turn real only above 7°, three of those 95th-percentile steps. That is the licence for everything below: a difference this report names is one the delivered file can express.

The pictures in this report are curated slide-lab frames, used as illustrations only. Measured against their own films, a lab's selection sits a median 6 percentile points from the film's middle on these statistics: close, and still not a sample, so no film-level number here comes from them.

Only Folie à Deux keeps unusually much of its picture dark and coloured, and none of the four puts more chroma into its toe than the corpus.

In the median film, 16% of the frame is both darker than L* 20 and still carries chroma of 6 or more. Folie à Deux reaches 26%, 6th of 51. Joker is 12th, The Grand Budapest Hotel 16th, and The Bride! 24th at 16% — exactly the corpus median, in the darkest of the four.

The toe's own chroma is more telling. Folie à Deux measures 5.9, Joker 5.7 and The Bride! 5.2 — ordinary values in this corpus; only The Grand Budapest Hotel, at 7.5, is above the crowd. Whatever makes these shadows look saturated, it is not that they are more chromatic. If the amount of colour is ordinary, what is left to be unusual is where the colour points.

Most films' shadows turn warmer than their midtones. The three Sher films' turn cooler, towards cyan; Folie à Deux turns furthest of any gamma-2.4 film.

So the next cut is direction. Hue is measured per shot as the chroma-weighted mean angle of the toe and of the mids, and the turn is the signed difference between them. Across the corpus the median film turns −4.8°: its dark is slightly redder, warmer, than its middle. 23 films turn warm by more than the 7° threshold and 13 turn cool.

Folie à Deux turns +42°, from a midtone hue of 110° to a toe at 170°, olive to green-cyan, and 82% of its shots turn cool. That is 3rd of 51 and first among the films read at gamma 2.4. The Bride! turns +19° (6th) and Joker +16°, from 98° to 121° (7th). The Grand Budapest Hotel turns −18°, 43rd: warm, like most of cinema.

Drawn as a path, the difference is a direction. Every film's colour has to arrive at black eventually; what differs is the side it comes in from. The median film comes down on the warm side and meets black at a* +0.6, b* +0.5. Folie à Deux starts high on the yellow-green side, at a* −13 in its lightest band, and enters black at a* −1.4, b* −0.7: from green-cyan, slightly blue. The Grand Budapest Hotel comes in along red at a* +1.3, b* −0.3, the magenta edge of warm. A direction is a result, not yet a mechanism: something has to build a dark that points at cyan without being more colourful.

What does a Sher-film toe actually contain?

The frame as delivered, then the same frame with everything below L* 20 lifted and its chroma multiplied by four: the colour that is already there, made legible. Nothing is added; a neutral dark pixel stays neutral however far it is lifted.

Measured on: curated.

The look is one channel leaving first. In Folie à Deux the red code reaches black before green and blue, so dark pixels sit near a single hue: saturated, at ordinary chroma.

The mechanism turns out to be subtraction. A pixel's HSV saturation is how far its lowest channel sits below its highest. A dark pixel can be fully saturated while carrying almost no CIELAB chroma: if one channel is at zero and the others at a low code, the colour is pure and dim. That is what "weird saturation" in a shadow measures.

In the median film blue is the lowest channel in 68% of toe pixels and red in 16%; 35 films are blue-first, and 10 red-first. That is why cinema's dark is usually warm. Folie à Deux is red-first in 83% of its toe pixels, 3rd of 51 and first among the gamma-2.4 films, and 26% of its toe pixels sit at saturation 0.9 or above, 5th, against under 1% in the median film. Joker is red-first in 52% (10th) with 5% fully saturated; The Bride! in 31% (17th). The ordinary chroma of section 03, the cyan turn of section 04 and this saturation are not three findings. They are one toe, described three times. If subtraction is what builds it, it should grow as the picture darkens.

Is the red-first toe a property of whole frames or of a few pixels?

Each dark pixel painted by its lowest channel — cyan where red is lowest, amber where blue is, magenta where green is — at a strength set by its saturation. Brighter pixels are dimmed to grey.

Measured on: curated.

The deeper the pixel, the more often red is gone: in Folie à Deux red-first rises from about a third of pixels in the mids to nine in ten at the floor.

It does. Pooling every measured pixel of a film by lightness band shows where the subtraction happens. In Folie à Deux red is the lowest channel in 35% of pixels between L* 40 and 55 and in 92% below L* 2, and the share of fully saturated pixels rises from 13% to 62% over the same fall. The corpus's median film goes from 21% red-first in the mids to 35% at the floor: black drifts cool everywhere a little, and in this film a great deal.

A channel that runs out before the others as the picture darkens is something a print-film emulation can do when its dye curves do not meet at black, and the documented show LUT for Joker was engineered to look like Kodak EXR 200T 5293. The measurement cannot see the LUT. It sees a toe that loses red first, and loses it more the darker it gets. The three Sher films share that LUT line; the colourist's fourth film is the test of whether the toe travels with her.

The Grand Budapest Hotel does not lose red at all. Where it loses anything unusual, it loses green, and its dark goes magenta-red.

It does not. The Grand Budapest Hotel is red-first in 1.5% of its toe pixels, 40th of 51. Its toe sits at a hue of 29° against mids at 50°: red against orange, the ordinary warm turn. But green is the lowest channel in 16% of its toe, second in the corpus, where the median film is close to zero. Those pixels are in the pink, red and purple rooms: the uniforms, the elevator, the lobby.

So the same colourist, in a film with a different cinematographer, director and palette, does not bring a cyan dark with her: two thirds of The Grand Budapest Hotel's toe gives up blue first, as most of cinema's does. What recurs is narrower. Where these films' darks are unusual, they are unusual by losing a channel rather than by gaining chroma. Before asking whose decision that is, two duller explanations have to be ruled out.

Where does The Grand Budapest Hotel's green-first dark live?

Magenta marks dark pixels whose green channel is lowest, amber those whose blue is. The purple uniforms and the lobby boy's jacket are magenta almost throughout.

Measured on: curated.

The toe's hue is as coherent as any film's, and in Folie à Deux the red-first dark holds through every tenth of the running time; Joker and The Bride! switch with the scene.

The first is the encoder: compression noise in the dark adds chroma of random hue. But noise has no direction, and these toes do. The chroma-weighted concentration of hue in Folie à Deux's toe is 0.90 against a corpus median of 0.89, as coherent as any film's, and every difference quoted above is many times the 7° threshold.

The second is that a few memorable scenes stand for the film. Cut into tenths of the running time, Folie à Deux is red-first in all ten, never below 65%. Joker is red-first in five of ten, from 30% to 77%: it switches, and the frames show why. Sodium streets and lamp-lit rooms keep a warm dark; fluorescent interiors and night exteriors a cyan one. The Bride! is red-first in three tenths, from 3% to 85%; The Grand Budapest Hotel in none. Neither rival survives for Folie à Deux, and lighting survives in part for the other two, which is why the next question is what a film keeps.

What does a Sher film's dark look like when it is not cyan?

Frames from the same three films whose dark gives up blue first, as most of cinema's does. They are lamp-lit or stage-lit: warm sources, warm dark.

Measured on: curated.

A saturated toe belongs to the film more than anything else measured here. It does not belong to one person: the films nearest Folie à Deux are not hers, and her fourth film does something else.

What a film keeps can be measured directly, by splitting each measure's variation into what differs between films and what differs between shots of one film: the share of fully saturated toe pixels has an intraclass correlation of 0.41 (0.23 to 0.55 over films), the toe's a* 0.32, red-first 0.27, the turn 0.13 and coloured dark 0.14. A saturated, one-channel-down toe is a decision a film keeps; how much of the frame is dark and coloured is mostly the scene's.

So the question the impression began with becomes askable: whether that decision is hers. The films nearest to Folie à Deux in this space (toe colour, red-first, turn, saturation) are Drive My Car, The Toxic Avenger and Oppenheimer; Joker's nearest is First Cow; The Grand Budapest Hotel's is Django Unchained. None of them was graded by her. And across her four films the signature follows the LUT line of section 06 rather than the colourist: strongest in its middle, Folie à Deux, and absent from The Grand Budapest Hotel. One part of the record bears on her and not on the films: where she started.

The film on which Jill Bogdanowicz began, the first full digital intermediate, has the warmest kind of dark there is: blue is its lowest toe channel in every pixel.

Company 3's biography records three things that bear on the question. She majored in art and minored in physics at SUNY Geneseo. Her father spent his career as a scientist at Eastman Kodak; he is the colour scientist Mitch Bogdanowicz, with whom she engineered Joker's show LUT to look like a Kodak negative. And she started as an assistant colourist at Cinesite on O Brother, Where Art Thou?, the first feature finished entirely as a digital intermediate.

O Brother is in this corpus. Its toe gives up blue first in 100% of its pixels, 44th of 51 for red-first, and turns −22° against its mids: dust and sepia all the way to black, and in Figure 2 it comes down the warm side and meets black at a* +1.8, b* +1.2. It was graded by someone else; she assisted. It is here only as the other end of a line that runs from a digital sepia to a digital cyan.

A physics minor does not grade a film, and a biography is not evidence of intent. What the record does show is a colourist who builds her looks as models (a negative stock emulated from its dyes, extended for a second film, used as the foundation of a third) and a measurement that finds, in exactly those three films, a toe in which one dye's worth of signal runs out before the others. That is the most this study can connect. It is stated as a coincidence of documented method and measured result, not as a cause, and it is where the evidence stops.

Two of the four films were read again from 10-bit masters, frame for frame. The finding survives and sharpens: Folie à Deux's master is red-first in 85.5% of its toe and 32% fully saturated, against the 83% and 26% this report measured in its web copy.

Of the three things the closing names as able to change this reading, one can now be done for two of the films. Joker and Joker: Folie à Deux were read again from 10-bit PQ masters, a UHD disc remux and a 4K WEB-DL: the same frame of every shot, 1,302 and 1,320 of them, found at the cuts both copies share. Read through this report's own code, the 8-bit copies return exactly the numbers above, so whatever differs is the copy's and not the instrument's. That is the licence for this section.

Every measure of the look is stronger in the master. Folie à Deux is red-first in 85.5% of its toe against 83%, 32% of that toe sits at full saturation against 26%, and its dark turns +51° against its mids against +42°. Joker is red-first in 55% against 52%, and turns +21°. The web copies this report measured undersold the look it is about; they did not invent it.

Where the difference comes from was taken apart one loss at a time: the master shown at 1080p, then at 8 bits, then with its colour halved (4:2:0), then encoded with each web copy's own x264 settings at its own bitrate. None of those moves red-first by more than about a point. The one that does is the arithmetic of 8 bits itself: the web copy's toe spans sixteen code values, not the thirteen this report first said (the masters span 61 and 65), and where two channels tie for lowest the census counts red, which adds 1.3 points to Joker and 0.8 to Folie à Deux. The rest belongs to the web copy's own SDR version, which is not the master made smaller: it places Folie à Deux's toe as a 128-nit white would, not the 102 at which Joker's copy simply shows its master, and in doing so it yellows that dark (b* +1.7), takes about ten degrees off its turn and three points off its red-first. What the Copy Forgets follows the rest of what a web copy loses; for this report the result is narrower. Its two strongest films are, in their masters, more of what it says they are.

In these films the dark is coloured by taking a channel away, not by adding chroma — cyan where red goes, magenta where green goes — and the clearest case is the middle of one documented LUT line.

The impression was right about the look and wrong about its cause. These shadows are not more colourful than cinema's; they are purer. One channel reaches black before the others, most often red in the three Sher films, and so the dark sits close to a single hue at an ordinary chroma — which the eye reads as saturation because there is no grey left in it to dilute the colour. Where a 10-bit master exists, the look is stronger in it than in the copies measured here.

The statistics are the form the cause takes here. They are consistent with a print-emulation toe whose red record runs out first, which is what the documented show LUT for Joker set out to be, and with the grade keeping that toe for whole films, not scene by scene. They are equally consistent with lighting and production design that feed that toe: fluorescent and night exteriors go cyan, lamps and stages do not. What cannot be separated here, and is not claimed, is how much of it belongs to Jill Bogdanowicz rather than to Lawrence Sher, to the LUT they built together, or to the rooms they lit.

Every figure the prose quotes is declared with the path it came from in the measurements and re-verified at build time; a number that drifts fails the build. The figures read the same measurements, so none can disagree with the sentence beside it without the build noticing.

Three things would change the reading. Another film graded by Jill Bogdanowicz for a different cinematographer — or one Lawrence Sher shot with another colourist — would separate the two. The masters: for Joker and Folie à Deux this has been done (section 11), and it strengthened the reading; The Bride! and The Grand Budapest Hotel are still read from 8-bit copies whose toe spans sixteen code values. And an observer study: this report measures what makes a shadow read as saturated; it has not asked anyone whether it does.

• Jill Bogdanowicz & Lawrence Sher Collaborate on The Bride! and Apex — Company 3
• Face the Music and Dance: Jill Bogdanowicz Colors Joker: Folie à Deux — Company 3
• Clubhouse Conversation: Lawrence Sher, ASC on Joker — American Society of Cinematographers
• Jill Bogdanowicz — Company 3 artist biography
• Enhancing color at The Grand Budapest Hotel — postPerspective
• Census measurements: bogdanowicz_report/data/shots.parquet and bands.parquet, from the repository's midpoint stills.
• Master comparison: hdr_study/, the same frames decoded from the 10-bit HEVC masters and read through the same code.