Parallax Metrology

How to read a reading

One painting, all four layers

A structural report is forty-odd numbers. On their own they are inert. This page takes one work — Matisse's La Leçon de piano (1916) — down the four layers in order, and names each measurement where it lands on the canvas. Read this once and the thirteen studies become legible.

All values are schema v0.7, read at a 2600 px working copy (long side) of the public-domain reproduction — the same pipeline the comparator uses, so the numbers here and there agree.

Before any number

The discipline starts with the eye. Look at the painting and say what you see, in words, before the first command. The numbers then test that reading instead of seeding one. What follows is the reading after the looking, not a substitute for it.

1

Layer one

The evidence fields

Everything begins with nine per-pixel fields computed over the whole surface. Four are primary — the ones regions are read against — and the rest are substrates for specific measures. None of them knows what a piano is. They know where the surface changes, how sharply, in what channel, and whether the change survives blurring.

Edge gradient field
edge — Sobel gradient magnitude. Where the surface turns sharply.
OKLab chroma field
color — OKLab chroma, perceptually uniform. Where colour is doing work.
Structural mass field
mass — 0.42·edge + 0.32·tone + 0.26·chroma. The structural-weight field.
Soft structure field
canny_gap — soft structure: gradient present, edge uncommitted. Haze, slow transitions.

The mass field is the one to watch. It is a weighted blend of the other three, lightly smoothed, and it is what the region pass carves up. Read against the reproduction, it already tells you the painting concentrates its weight in a single left-of-centre body and leaves most of the surface quiet.

2

Layer two

The spine — one report

A single call, read_image(), runs one region pass — a watershed over the density field — so that the kernel coordinates, the relation system, the colour and tonal measures, and the state classifier all describe the same regions. Here is what it said about this painting, grouped by what each answer is about.

Where the mass sits — the kernel

Δx, Δy−0.066, +0.095centroid offset from frame centre: left and down
μ cohesion0.833the largest body holds 83% of mass
ρ_r packing0.136the mass is loosely packed, not a tight knot
x_p peripheral0.108little pull toward the edges
SDI dispersion0.226moderate spatial spread
void fraction0.7272% of the surface carries no structural weight
Matisse mass map with centroid
The mass map. The kernel offset is the vector from frame centre to the weighted centroid of that field.

Do the constructions agree — mask coherence

Five construction families (edge, tone, colour, perturbation, mass) are each asked where the weight is. Ω measures whether they point to the same place.

Ω0.090low disagreement: the constructions concur
coherence0.640a single readable structure, not a contested one

The relation system — islands

Up to twenty watershed islands, each with a role (anchor or satellite), the corridors between them, and how stable the whole arrangement is under a crop. Counts are capped, so entropy — not the count — is the comparable quantity (finding I-17).

island entropy0.820weight spread across several bodies, not one
bridge cost0.724islands are costly to connect: separated, not woven
crop stabilitystablethe reading survives trimming the frame
edge artifact risklowno frame contamination in this reproduction

Colour, tone, and the frame

β colour-in-void0.137colour largely stays with structure, not the void
coupling index0.146colour and structure only loosely co-occur
τ tonal hierarchy0.680strong value ordering across zones
midtone mass0.900the painting lives almost entirely in the midtones
RC_f radial0.854mass organises well around the frame centre
default gravity33.7"authored against gravity" — among the lowest basin depths in the corpus
What the spine concluded

State: counterweighted — "a region reads as a load-bearing balance term more than a construction outlier." The painting is held in tension between an off-centre main body and a smaller counterweight, across a surface that is mostly quiet. That is a structural fact, not a judgement: the classifier never grades.

3

Layer three

Lenses — pointing outside the spine

The spine reads the load-bearing structure. Some things it is built to pass over — small marks with leverage out of proportion to their mass. The accent lens is a separate instrument for exactly those: it works at 900 px, returns the top marks by leverage, and reports each one's kind and its role in the delay-grammar of the eye.

Matisse gap readout: reproduction, structural accents, chromatic accents
The gap readout. The structural mass system (layer two) does not fire on these marks; the lens does. This is the correction the Degas study forced — the earlier "zero accents" was a scale mismatch, not an absence (findings I-5, I-7).

Other lenses answer other questions, each pinned to its own working scale so its calibrated constants hold:

LensQuestionInvoke
StanceDoes the centre of gravity keep changing heading as detail dissolves across scales (torque), or hold one heading (stand)?isr stance
Layered deltaWhat kind of "same" are two images — same pixels, same tone, or same spatial skeleton built from different pixels?isr delta
CompareAcross 2–20 images in one coordinate space, where does this set genuinely differ?isr compare
PositionAbsolute displacement from a fixed geometric origin on 18 axes — cross-domain coordinates with no reference corpus.isr position
4

Layer four

The pattern shelf & register

When a study needs a move the spine does not have — an emergence index, a substrate audit, a null control — it is written once, generalised so it takes any image, and shelved. The next study greps the shelf before inventing anything. The shelf answers with less authority than the spine, so it is checked, not deferred to.

Above the shelf sits the candidate register: the machinery that decides what is ever allowed to become a permanent spine metric. A measure must clear a promotion bar across the whole corpus, including a null-control check, before it graduates. Most do not — and the register records the declines as carefully as the promotions. That is the subject of the method page.