Where depth changes its mind

Observations from two months of pointing AI depth readers at prints, paintings and photographs: what they see, where they waver, what that turned out to be, and what it does to generated images. Russell Parrish, with Claude · November 2026 · observational, not a paper

A monocular depth model looks at one flat picture and guesses how far away each part is. These models were built for photographs. Pointed at a Piranesi etching or a Hogarth engraving, they still answer: they read the plate as a room, a street, a vault. This note is about what happens in that answer: where the model is steady, where it wavers, and what the wavering is and is not.

1. A depth model reads every picture as space

Figure 1
1. Pictures and their whole-image depth readings (Depth-Anything-V2-Small; light = near). Prints, paintings and photographs alike come back as a layered space: a foreground, a middle, a far wall. The model has no notion that an etching is ink on paper.
It reads conventions of drawing (cast shadow, overlap, diminishing hatching) as distance, much as a viewer does. That is what makes it worth watching: it is a fast, tireless, literal-minded viewer.

2. It changes its mind when it sees less

Show the model only a window of the picture, and it reads that window as if it were the whole picture. The pixels have not changed; the context has. A steady reader gives the same layout both times. A wavering one does not.

Figure 2
2. One window on Piranesi's Arch with a Shell Ornament. Top: the window (gold) and the same window shifted (blue). Each row below is one reader: the strip they share, read inside the first window (middle) and inside the second (right). MiDaS pushes back in one what it brought forward in the other. The rank-tone row is a depth-free control: it barely changes.
Figure 3
3. The same construction on Piranesi's Palazzo Barberini, a view of a real building. The facade reads the same whichever window it is seen through.
The amount of wavering separates kinds of picture. Photographs barely waver. Piranesi's views of Rome waver a little. His imaginary prisons, the Carceri, waver a great deal: on held-out plates every Carceri plate wavered more than every view (effect size δ = +1.00, the maximum). The companion toy, Where depth changes its mind (open it), lets you drag the window yourself on twenty pictures (prints, paintings and six of Russell's photographs) or your own (figure 4).
Figure 4
4. The toy on Russell's kitchen-mirror photograph, with the window on the reflection. Right: the patch as read in the whole picture, as read alone, and where they disagree; the verdict is that the reader now reads near and far the other way round. Below it, the crop curve. The toy can also scan a whole picture, place it on a steadiness gauge with advice, and save a full-size depth map and a trust map.
Figure 5
5. Steadiness of the depth reading for the toy's twenty pictures (Depth-Anything-V2-Small in the browser; average share of the layout re-read, over every window of a scan). Windows with little depth structure (flat sky, bare wall) are given less weight, since they add noise.
The order is not prints versus paintings versus photographs. The steadiest are open, legible spaces: Russell's empty warehouse and puddle at sunset (under 2%), his New York rooftops and Canaletto's Piazza San Marco (3–4%), Piranesi's view of the Palazzo Barberini (6%). Hogarth's crowded engravings come next (10–14%). Degas's rehearsal rooms, Vermeer's Maid Asleep and Kalf's still life waver more than Hogarth (18–24%), perhaps because soft edges and interiors lit from one side give the reader less to hold on to (a guess, not tested). Russell's kitchen-mirror photograph reads at 30%, between Degas and the Carceri: the mirror puts a second room inside the picture, and the reader cannot settle which space it is looking at. The Carceri are far above everything (40–43%). This is one reader and a simpler measure than the study's (a window against the whole picture, not two windows against each other), so read it as an observation.

A mirror

Figure 6
6. One window on the reflection in Russell's kitchen-mirror photograph. Seen within the whole picture (third panel), the window is part of the mirror's surface: a smooth plane, darker to the left. Read alone (right), it is the reflected room: the man near, the fridge behind him. The two readings are unrelated (r = −0.16); the reader has turned a surface into a space.
Figure 7
7. Crop curves: keep the centre, shrink the window. The warehouse holds its reading until it is cropped very hard. The mirror holds until the crop loses the room around the mirror (between 80% and 70%), then turns at once. The toy draws the same curve for any spot of any picture.
A mirror is the everyday version of what the Carceri do. Within the whole picture the reader knows the mirror is a flat thing on a wall; given only the mirror, it believes the room inside it. Cropping changes not how much depth it sees but which world it thinks it is in. The turn is abrupt, not gradual.

3. Where it wavers is repeatable, but it is not where the eye finds the contradiction

Figure 8
8. The Well, three impressions from two museums (Met, NGA first and second issue). Right column: where the reader's mind changes most. The hot zone falls on the beam that has been described as spatially impossible, in all three impressions (99.4th–99.5th percentile of placements).

That was the hoped-for result: a machine that finds Piranesi's impossibilities. It did not generalise. On The Gothic Arch, the one other plate with a published, located impossibility, the hot zone landed elsewhere. Against 63 contradictions Russell marked by eye on 15 plates, the maps did no better than chance.

Reading it today. Where a plate makes the reader waver repeats from impression to impression, so the maps describe something real about the plate. They do not track where a trained eye finds the space contradicting itself. They are a map of the reader's trouble, not of Piranesi's impossibilities.

4. Is it Piranesi, or is it the etching?

Figure 9
9. Held-out Carceri (red) and Vedute (blue) under four readers. Both depth readers put the Carceri on top (Depth-Anything δ = +1.00, MiDaS δ = +0.94). Two readers with no notion of depth, which only renormalise tone or line density inside each window, put the Vedute on top (δ = -0.90 and -0.94).

So the effect is not tone and not line density as such. But there was a catch: in these plates, density and kind are the same split. Every Carceri plate is more densely hatched than every Vedute plate. The test that separates them needs dense pictures that are not Carceri and sparse Carceri. Both turned out to be on disk already: Hogarth's crowded engravings, and later, darker-printed Carceri impressions whose plate tone flattens the hatching.

Figure 10
10. Dense prints outside the Carceri, each over its MiDaS reading, with both readers' scores. Depth-Anything keeps these low. MiDaS puts six of seven inside the Carceri range.
The two readers part ways. With density matched, Depth-Anything still separates sparse Carceri from dense non-Carceri prints (δ = +1.00, though that comparison was set up after looking). MiDaS, in the pre-registered test, does not (δ = +0.32, p = 0.17). The honest wording is "Carceri or dense hatching, depending on the reader." MiDaS, ControlNet's own depth annotator, treats dense hatching in general as unstable space; Depth-Anything singles out the Carceri.

5. The structure it proposes

The readings can also be used the other way round: not to score a picture but to show its structure. The most useful view takes out the overall recession (the ramp from near floor to far wall) and shows what stands off it. It is a looking device in the family of squinting or flipping the canvas: suppress one channel so another becomes visible.

Figure 11
11. The Well: the picture, its depth reading, and the relief left after the ramp is removed, with the masses cut from it. The beam, the well-head and the arches stand out of a space that otherwise barely recedes.
Figure 12
12. The same view on a Cézanne still life. The fruit and the cloth's folds become the whole content of the relief.
One signature recurs: in the Carceri, depth barely recedes as the eye moves up the picture. The vaults come down over the viewer instead of opening away. That reading is descriptive and untested, and it is the most art-historically interesting thing the instrument produced.

6. What it does to generated images

The practical question: MiDaS maps of prints waver, and image generators (ControlNet) are steered by such maps, often tile by tile. Do the wavering maps make tiled generations disagree where tiles meet? Two pre-registered tests on a rented GPU: the first was uninformative (see the accidents below), the second said no.

Figure 13
13. Each tile regenerated from its own piece of the picture (img2img, strength 0.5) and steered by a depth map read either from the whole picture or from the tile alone. Per-tile depth made seams no worse, under either reader, even on the Carceri.
When the generator is anchored to the picture, the picture's own structure holds the tiles together and the depth map only nudges. Any depth control made neighbouring tiles agree more than none (median disagreement 0.39 without control, 0.28–0.34 with), and the best "depth" anchor of all was the picture's own ranked tone. The wavering is real in the maps and does not reach the pictures.

The accidents

The first version of that test was flawed: each tile was generated from a prompt and its depth map alone, without the picture. The tiles invented unrelated worlds on the same depth skeleton, and the results are the most striking images of the whole project.

Figure 14
14. Source tile (never shown to the generator), the map handed to ControlNet as depth, and what it made. The rank-tone rows are the strangest: the picture's own texture handed over as if it were depth, so every line and grain is rebuilt as architecture.
Texture misread as space is a picture-making device in its own right: gravel becomes stacked rooftops, a crowd becomes leaves, a vault becomes a face.

7. Practical notes

8. What this is not

Not a detector of impossible space: it found one documented impossibility and missed the others. Not a ranking of individual pictures: a plate's single score barely repeats between two impressions of it; only the maps and large group differences do. Not general: two readers, a few dozen prints, one human annotator for the observer check. Every claimed test above was frozen before it was run, and the ones that failed are reported as failures.

References

Sources. This note draws on two lab books kept in the project archive (depth-holonomy and its second-reader study), with their frozen protocols and result files. The instrument is described on the Depth Holonomy page. Images: Metropolitan Museum of Art and National Gallery of Art open access; photographs © Russell Parrish.

© 2026 Russell Parrish / A.rtist I.nfluencer / Parallax Metrology. All rights reserved. The photographs are by Russell Parrish. No part of this system, visual material, or accompanying documents may be reproduced, distributed, or transmitted in any form or by any means, including AI training datasets, without explicit written permission from the creator. More info: www.artistinfluencer.com and www.parallaxmetrology.com