How the stereo analysis works

Abstract

Every stereoview listed in the Macrafly catalogue carries a verdict: genuine stereo pair, monoview (identical duplicate), camera moved, or inconclusive. That verdict comes from software that compares the two prints on the card, followed by a human review. This paper documents the complete method: image normalization, global alignment by normalized cross-correlation, block-wise disparity estimation, the three published measurements, and the exact decision rules and confidence formulas that produce each verdict. All thresholds and formulas are stated literally, so any reader can see exactly why a card received the call it received.

Keywords: stereoview, stereograph, disparity, normalized cross-correlation, block matching, cataloguing

1. Introduction

The companion piece, Stereoviews, explains what these card types are and how to check one by eye. This paper is about the machine side of it. Nothing here is a secret, and nothing is a black box. If you collect stereoviews, you should be able to see exactly why a card got the call it got.

2. Method

2.1 Working size

Both eye images are converted to greyscale and shrunk to a fixed working size: each half 420 pixels wide, so the whole scan measures 840 pixels across. Every number that follows is measured at that size. That is why the figures on a listing are relative to the working scan, not inches on the original card. Two different cards can still be compared to each other, because both were measured the same way.

2.2 Global alignment

Before anything can be measured, the two prints have to be lined up. The software takes a large patch from the inner part of the left eye's view — 36% of the full scan's width, 70% of its height — and slides it across the right eye's view looking for the best fit. The search runs coarse first, at quarter scale, then refines at full scale.

Every candidate position is scored with normalized cross-correlation: essentially, "how identical is this patch." The best-scoring offset wins. On Sweeps, the best global correlation was 0.99 — the two halves align as one scene almost perfectly.

2.3 Block-by-block disparity

The aligned region is then divided into 28×28-pixel blocks. Blocks that are basically flat — sky, blank mount, featureless background, anything with variance under 60 — are skipped, because a featureless patch can "match" anywhere and tells you nothing.

Each textured block is allowed to slide up to ±10 pixels horizontally and ±4 pixels vertically from the global offset, and the best-matching position wins again. That produces, per block, a horizontal displacement — how far that patch sits compared to its twin, which is the depth signal — and a vertical displacement, which should be near zero on a true stereo shot.

3. Measurements

• Match. Matched textured blocks divided by all textured blocks. High means the two prints really are the same scene. Sweeps: 99%.
• Depth spread. The 90th percentile of horizontal block displacements minus the 10th percentile. A real stereo shot has near objects shifted a lot and far objects barely shifted, so the spread is wide. Identical duplicates have everything at zero. Sweeps: 4px.
• Vertical. The same percentile spread of vertical displacement. A genuine stereo shot taken on a bar moves nothing up and down. Large vertical spread means the camera was shifted between exposures, or the card is skewed. Sweeps: 1px.

4. Verdict rules

The verdict is a set of literal if-statements, evaluated in this order:

1. Fewer than 15 usable textured blocks → inconclusive, confidence 0.30. There simply isn't enough picture to judge.
2. Match below 45%, or vertical spread of 4px or more → camera moved. Confidence = 0.5 + (0.45 − match) + vertical × 0.05, capped at 0.95.
3. Depth spread of 1px or less, with global correlation above 0.9 → monoview (identical duplicate). Confidence = 0.6 + (correlation − 0.9) × 3, capped at 0.97.
4. Depth spread of 2px or more → genuine stereo pair. Confidence = 0.55 + (spread × 0.05) + (match − 0.45) × 0.4, capped at 0.97.
5. Anything in between — spread of 1–2px, weak correlation → inconclusive, confidence 0.40. Set aside for a closer look by eye.

Worked example. Where Sweeps' 97% comes from: spread of 4 gives 0.55 + 0.20 = 0.75; match of 0.99 adds 0.4 × 0.54, which brings the total to about 0.97 — the cap. So it reads 97%.

5. Limitations

The genuine-pair and duplicate calls are the solid ones. Depth either varies between the prints or it doesn't, and that is hard to fake and hard to misread. The moved-camera call is softer, because a crooked scan or a heavy crop can look like camera movement. That is why every card gets a human review on top of the software, and why any verdict can be overridden when the evidence says otherwise.

The confidence score is a formula score based on how far the numbers clear their thresholds, capped so it never reads as certainty. It is not a laboratory probability. Read it as "how clearly did this card pass," not "how sure are we." A card with a 2px spread and 50% match might score around 62% — real, but borderline — and those are exactly the cards the human review exists for.

One rule stands above all of this: depth effects only ever appear on cards the analysis calls genuine pairs. A second view is never faked from a single photograph.

References

The thresholds, block sizes, and confidence formulas above are our own choices, set by testing against real cards in this collection. They are not taken from any published source, and these references don't vouch for them. What the references cover is the general principles the method rests on.

1. Wheatstone, Charles. "Contributions to the Physiology of Vision. Part the First. On Some Remarkable, and Hitherto Unobserved, Phenomena of Binocular Vision." Philosophical Transactions of the Royal Society of London 128 (1838): 371–394. doi:10.1098/rstl.1838.0019. The founding paper on binocular depth: each eye sees a slightly different picture, and that difference is what reads as depth.
2. Lewis, J. P. "Fast Normalized Cross-Correlation." Vision Interface, 1995. Expanded version online. Explains normalized cross-correlation, the comparison used in our alignment and block matching.
3. Scharstein, Daniel, and Richard Szeliski. "A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms." International Journal of Computer Vision 47 (2002): 7–42. doi:10.1023/A:1014573219977. The standard survey of stereo matching, including block matching over a search window, which is the family of methods ours belongs to.
4. Darrah, William C. The World of Stereographs. Gettysburg, PA: Darrah, 1977. The standard history of the stereograph, with guidance on how stereographs were made and how to date them.