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<h1>Method</h1>
<pre class="card">frame − reference → dI, signed RGB difference
dI → surface gradient ← the only step that needs a choice
∇ integrate → depth
depth → 5 features → newtons ← fitted on presses of known load</pre>
<h3>Lookup table</h3>
<p>A (90,90,90,2) array from difference colour to gradient, filled by pressing
a sphere of unknown radius: <code>a² = d(2R−d)</code> recovers the radius and
the depth datum from the data. ~700 frames per sensor.</p>
<h3>Calibration-free</h3>
<p>Three LEDs at known azimuths, so each channel reads the gradient projected
on one direction and <code>(gx, gy)</code> is a 3×2 least-squares solve.
No table, no sphere presses. This is the GelSight Wedge driver's approach. It
recovers shape but not scale.</p>
<h3>Fitting the newtons, and why the weights can lie</h3>
<p>Five collinear contact features, then a monotone isotonic calibration.
Isotonic clips outside its fitted range, so transfer ρ is scored on the linear
projection: on the isotonic output a fully extrapolated target returns a
constant, and a constant has no ranks. Least squares can also cancel large
opposite-sign terms, a balance holding only at the ratios it was fitted on —
that sends one row of the <a href="results.html">transfer matrix</a>
negative.</p>
<h2>Stage 1 scored on its own — no force labels</h2>
<p>Force estimation is image→depth then depth→newtons, and a ρ only ever scores
the pair: a geometrically wrong depth that is monotone in contact size still
ranks force well. Depth has no ground truth, so stage 1 is judged by eye on the
panels below and by physical checks that need no labels.</p>
<div class='tablewrap'><table><thead><tr><th>dataset</th><th>n</th><th>flat-gel leak, LUT</th><th>leak, calib-free</th><th>peak [mm]</th><th>over the gel</th><th>truncated</th><th>LUT vs calib-free shape</th></tr></thead><tbody>
<tr><td>cnc_mini_26</td><td>120</td><td>0.016</td><td>0.013</td><td>2.71</td><td>14%</td><td>90%</td><td>+0.796</td></tr>
<tr><td>cnc</td><td>120</td><td>0.014</td><td>0.013</td><td>1.66</td><td>1%</td><td>76%</td><td>+0.838</td></tr>
<tr><td>feats</td><td>120</td><td>0.064</td><td>0.041</td><td>1.12</td><td>0%</td><td>100%</td><td>+0.703</td></tr>
<tr><td>sparsh</td><td>89</td><td>0.016</td><td>0.011</td><td>0.93</td><td>0%</td><td>64%</td><td>+0.895</td></tr>
<tr><td>faf</td><td>117</td><td>0.045</td><td>0.041</td><td>1.69</td><td>8%</td><td>89%</td><td>+0.845</td></tr></tbody></table></div>
<p class="dim">Leak is mean |depth| off-contact over peak — zero for a coherent
surface. “Over the gel” counts peaks past the 4.25 mm elastomer, possible
only where the contact runs off the sensor and the depth is extrapolated.
“Truncated” is a fact about the capture, not the method, and bounds what any
reconstruction can know. The last column is the two reconstructions agreeing
with each other, which is evidence neither invents the shape — not that either
is right.</p>
<p class="dim">One row needed a fix before it could be read at all — see
<a href="sensors.html">sensors</a>.</p>
<figure><img src="assets/panel_cnc_mini_26.png" alt="cnc_mini_26 — GelSight Mini, CNC presses, 0–20 N"><figcaption>cnc_mini_26 — GelSight Mini, CNC presses, 0–20 N · markerless · 8 samples. Columns 5 and 6 are the same surface from each reconstruction; the calibration-free one is drawn with relative height because its scale is not recovered.</figcaption></figure><figure><img src="assets/panel_fota_cnc.png" alt="FoTa cnc_Mini — GelSight Mini, CNC probes"><figcaption>FoTa cnc_Mini — GelSight Mini, CNC probes · markerless · 8 samples. Columns 5 and 6 are the same surface from each reconstruction; the calibration-free one is drawn with relative height because its scale is not recovered.</figcaption></figure><figure><img src="assets/panel_feats.png" alt="FEATS — marker gel, FEA force labels"><figcaption>FEATS — marker gel, FEA force labels · MARKER · 8 samples. Columns 5 and 6 are the same surface from each reconstruction; the calibration-free one is drawn with relative height because its scale is not recovered.</figcaption></figure><figure><img src="assets/panel_sparsh.png" alt="Sparsh / Meta — 10 gel pads"><figcaption>Sparsh / Meta — 10 gel pads · markerless · 8 samples. Columns 5 and 6 are the same surface from each reconstruction; the calibration-free one is drawn with relative height because its scale is not recovered.</figcaption></figure><figure><img src="assets/panel_faf.png" alt="FeelAnyForce — 42 captures"><figcaption>FeelAnyForce — 42 captures · markerless · 8 samples. Columns 5 and 6 are the same surface from each reconstruction; the calibration-free one is drawn with relative height because its scale is not recovered.</figcaption></figure>
<details><summary>Three claims made here and withdrawn (with their
numbers)</summary>
<p class="dim">“React's poor reconstruction is cross-sensor transfer” — the
sensors were the other way round; the table's own capture is a GelSight Mini.
“A DC-biased gradient integrates into a dome” — removing the DC moved the leak
0.0715 → 0.0713. “Calibration-free is 2–3× better” — three frames of noise; on
24 it is a tie. And the LED map was first chosen by a criterion that rewards a
small reconstruction, which split a connector into two blobs while scoring
best; it is now set by sphere presses reconstructing as circles (axis ratio
1.266 vs 1.798).</p></details>
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