Ruble Harbor

PORTFOLIO/06/FIRST PLACE · 2012

Low Cost
3D Mapping

This is where the computer vision work on this site starts. Detection, extraction and vision in production all run on the geometry learned here.

A final-year project in the Department of Electrical, Electronic and Computer Engineering at the University of Pretoria: a 3D scanner made from a projector, a webcam, and a turntable I specified, built and wrote the firmware for. Gray-coded patterns go onto the object, line-plane intersection turns every decoded pixel into a depth, and eighteen scans taken 20° apart merge into one textured model.

Three months, and it runs the whole stack: stepper selection and PIC32 firmware at one end, ICP registration, Marching Cubes and Taubin smoothing at the other. It also has a measured failure in the middle that was never fixed, and that is on this page too.

CAPTURE TO MODEL/FIVE STAGES

  1. The soft toy used as the scan subject, photographed before scanning.

    The object

    Fig 35 · p.49

    A soft toy on the turntable platform. Rigid enough to hold its shape, matte enough to take a projected pattern.

  2. Footage of the scanner running: Gray-coded stripe patterns projected onto the object on the turntable in a darkened room, stepping from coarse bands to fine lines.

    Capture

    ORIGINAL FOOTAGE

    The rig running. Gray-coded patterns step from coarse to fine across the object and the webcam reads each one back; line-plane intersection then gives every decoded pixel a depth.

  3. A dense point cloud of the object rendered in the WPF virtual environment.

    Point cloud

    Fig 33 · p.43

    One view, thresholded against a background scan and rendered in the WPF viewer. Over a hundred thousand points from a single exposure.

  4. Three registered point clouds with a good initial alignment, showing visible spread between them.The same three point clouds with an improved initial alignment, visibly tighter.

    Pairwise registration

    Fig 39 · p.52

    Three clouds, colour-coded, merged by ICP. Left: a good initial alignment. Right: the same scans seeded from the rotation axis instead. Same data, converging much tighter.

  5. The reconstructed surface straight out of Marching Cubes, visibly faceted.The same surface after Taubin smoothing, visibly cleaner without having shrunk.

    Surface & texture

    Fig 43 · p.57

    Marching Cubes over the merged cloud, then Taubin smoothing. Left: the raw isosurface at MC 10. Right: smoothed at MC 16, with per-face colour averaged from the points it was cut from.

0.7mm

About the thickness of a credit card

Three cardboard markers set 2.00 cm apart, measured back off the point cloud. Across all five trials it averages 1.0 mm, and the worst single reading in the set is 3 mm.

That is the figure the whole rig stands on. Every scan after it inherits it, so a single view being accurate is what makes a merged model worth measuring at all.

18 × 20°SCANS PER ROTATION
0.056°TURNTABLE ERROR PER STEP
1.25 cmPIN SETS ABSOLUTE SCALE
> 100kPOINTS PER SINGLE SCAN
MEAN DEVIATION · BEST SCAN
Point clouds of the three cardboard markers with the centre-of-rotation pin between them.
Fig 34 · p.46. The three measured markers, with the 1.25 cm centre pin standing between them.

MEASURED/TABLE 2 · P.47

Scan (cm)1 → 2 (cm)2 → 3 (cm)2 behind 1 (cm)3 behind 2 (cm)Mean dev. (mm)Rel. (%)
1†1.921.941.921.940.73.5
21.871.881.911.951.04.9
31.961.981.841.930.73.6
41.941.961.701.801.57.5
51.961.841.791.931.26.0
Allfive trials, twenty gaps1.05.1

Four gaps per scan, each 2.00 cm by tape measure, read back off the point cloud. Deviation and relative error are computed from those measurements against the 2.00 cm truth. † Scanned inside the calibrated focus area; the remaining four were positioned randomly around it, which is what the spread in the last two columns is measuring.

THE INSIGHT/§2.2.3.3

ICP needs a decent starting pose or it settles into a local minimum, and every cloud merged after it is then wrong. Rather than have an operator align each scan by hand, a 1.25 cm square pin stands at the centre of the platform and is scanned once. Its orientation gives the rotation axis; that corrects the camera tilt out of every cloud and lets each new scan be seeded with the rotation the turntable has just made, a known 20°.

0.40 cm0.16 cm60% better

Four diagrams: a good initial alignment converging to an ideal result, and a 180-degree rotated initial alignment converging to a misalignment.
Fig 21 · p.29. The same two curves, same algorithm. Only the starting pose differs.

Average misalignment across seventeen pairwise registrations, first full scan against second. §3.4.2.2

THE FAILURE/§3.5.2

Merging eighteen clouds in sequence accumulates error, so the first and the last no longer meet: a 1.33 cm seam, and a sea-shell fold where they overlap. Global relaxation was meant to redistribute that error across every cloud and close it. Over five iterations it did not converge:

1.330.962.031.092.41cm

A line chart of alignment distance in centimetres against five global relaxation iterations, wandering rather than converging.
Fig 40 · p.54. Alignment distance against iteration. It was supposed to fall.

Diagnosed in the report itself: the error was spread evenly across the merged clouds instead of weighted. The fix was identified too late in the timeline to re-run the results. §4.2

BUILD/HARDWARE & STACK

CAPTURE

Projector and webcam, both at least 800×600, calibrated with ProCamCalib. Gray coding rather than phase shift: flood-fill phase assignment gives no unique row or column identity, so line-plane intersection has nothing to key against.

TURNTABLE

PMG4250 geared bipolar stepper, 0.15° resolution at ±7%, driven by an A4988 and a PIC32MX320F032H over RS-232 through a MAX3232. 133 steps lands 19.95° against a 20° target at 166.25 Hz; 2.5 kg·cm required at a safety factor of 2, against 10 kg·cm available. Carries 4 kg.

RECONSTRUCTION

C#, OpenCV 2.4 and WPF. ICP over Canny critical points, nearest neighbours through a KD-tree, non-overlapping points trimmed to remove alignment bias. Marching Cubes then Taubin smoothing: vertex-to-cloud distance falls 0.122 → 0.065 cm as the sampling cube goes 43 → 13 mm, and smoothing improves it at every size without shrinking the model.

WHERE IT BREAKS

Transparent and reflective surfaces, ambient light, an over-exposed camera, a mis-calibration, or a centre pin out of focus. Marching Cubes ambiguity leaves occasional holes in the mesh. Anything past 30 × 30 × 30 cm runs out of memory: WPF degrades near a million points and eighteen scans clear a hundred thousand each.

Trapezoidal operating pulse speed profile for the stepper motor, peaking at 166.25 Hz over a one second positioning period.
Fig 4 · p.13. The motor’s operating profile. One 20° index in one second: 0.25 s ramping up, 0.25 s down, 166.25 Hz across the plateau.

Every figure and measurement on this page is reproduced from Low Cost 3D Mapping using Structured Light, M. Vosloo, Department of Electrical, Electronic and Computer Engineering, University of Pretoria, project EPR400, November 2012. The capture footage in stage 02 is from the original build rather than the report. Scope, stated plainly: the Gray-code decode is a port of Lanman & Taubin’s cvStructuredLight from C++/OpenCV 1.1 to C#/OpenCV 2.4, disclosed in the report’s own engineering change proposal. Everything else was built from first principles: the initial-alignment method, ICP, global relaxation, Marching Cubes, Taubin smoothing, texturing, artefact removal, and the whole turntable from motor selection through firmware and housing. The project took first place for Computer Engineering in the final-year project competition and exhibition, and was invited for poster presentation at PRASA, the Pattern Recognition Association of South Africa.