Measure box dimensions with a depth camera for palletizing

A palletizer can only stack what it can size. Before the first grip closes, the layer planner needs each parcel's length, width and height, and a depth camera over the infeed delivers all three from one capture - no stop-and-gauge fixture, no mechanical measuring station. This page walks the measurement chain: standoff and field of view, pixels on the box top, plane fits on the point cloud, and the accuracy budget behind the ±5 mm per dimension you can quote at 1-2 m standoff. It ends with the sensor decision for static overhead mounts, moving belts and packed pallets.

What the depth camera actually measures

A depth camera returns one range value per pixel. Deprojected with the sensor's factory intrinsics, that depth map becomes a 2.5D height map of the scene; 2.5D height map to 3D point cloud: pixels to XYZ works the conversion step by step. Three numbers then fall out of the cloud for each parcel:

• Length and width - the extent of the top face, measured in the plane fitted through it.
• Height - the gap between the top-face plane and the belt or pallet plane below it.

Segmentation decides which points belong to the box; the plane fits turn them into numbers. If the sensor choice itself is still open, box dimensioning: depth camera or RGB camera, which measures compares the two for exactly this task. Logistics-class volume cameras of the Logistics / volume type in the 3D sensors range integrate the whole chain - speckle structured light, depth map, volume output - in one housing.

Standoff, field of view and pixels on the box top

Two geometric relations size the mount. Coverage: a sensor with horizontal half-angle θ at standoff z sees a window of width

Two thresholds turn that into a design. Keep at least 20 × 20 pixels on the box top, so the plane fit has enough inliers and the edge trim has margin. Keep p at or below 2 mm per pixel: 1-2 pixels of depth edge bleed then cost 4 mm or less, which the accuracy budget below absorbs. For a 400 mm face the 20-pixel floor sits at a loose 20 mm per pixel, so sampling is easy to meet; it is the 2 mm pitch that really sets the window.

FOV is where mounts go wrong. A 90° wide-angle depth map with 640 pixels across spans about 3 m at 1.5 m standoff - 4.7 mm per pixel, and the accuracy envelope is gone before you start. Narrow-field modules, or a cropped ROI inside a wide map, are what buy the fine pitch.

The calculator below runs the pitch relation backwards: enter the window width and the mm per pixel you need, and it returns the pixel count the depth map must carry.

Worked example: a 600 × 400 × 300 mm box at 1.5 m standoff

The inputs, and where each comes from:

• Box 600 × 400 × 300 mm - a typical euro-pallet half-layer carton, the standard case for a palletizing infeed.
• Standoff 1.5 m above the box top, 1.8 m above the belt - the middle of the 1-2 m band.
• Depth map 640 × 480 px covering a 1,000 × 750 mm window at box-top height - a 37° horizontal FOV at this height, or an equally sized ROI inside a wider map.
• Single-pixel depth scatter assumed at 5 mm (1σ) - deliberately conservative for this camera class at this range.
• Edge trim of 8 px per side - the rule of thumb for mixed pixels at a depth wall.

The rules: pitch is window width over pixel count; face pixels are face size over pitch; height is the top-plane mean minus the belt-plane mean; random error falls with the square root of the fitted pixel count.

The arithmetic:

• Pitch: 1,000 mm / 640 px = 1.56 mm/px (750 mm / 480 px confirms square pixels).
• Face: 600 / 1.56 ≈ 385 px by 400 / 1.56 ≈ 256 px.
• After the 8 px trim: 369 × 240 = 88,560 fitted pixels, about 220 times the 20 × 20 minimum.
• Random error: 5 mm / √88,560 = 5 mm / 298 ≈ 0.02 mm. The fit averages single-pixel noise away completely.
• Height uses two such means, top face and belt reference, so it averages the same way.

Result: sampling is nowhere near the limit. Every dimension is set by systematic error, and the realistic envelope at this standoff is about ±5 mm per dimension.

Decision: the mount holds the envelope. Keep the window at about 2 mm/px or finer and every face you measure above 20 × 20 px after trim - even a 200 mm parcel still spans 128 px at this pitch. Break either bound and the fix is mechanical: lower the camera, narrow the FOV, or raise the pixel count.

From fitted planes to length, width and height

Segment first, fit second. Plane fitting on 3D point clouds: least squares vs RANSAC covers the estimator choice: RANSAC over the top-face points to reject stray returns, then least squares on the inliers for the final coefficients, with an inlier band of about ±10 mm around a 300 mm carton - wide enough for wrap bulge, tight enough to exclude background.

Length and width are the inlier extent projected onto the fitted plane, pulled in 1-2 px per side for edge bleed. Height is top plane minus belt plane; where a full fit is more than the job needs, the mean depth over the object mask minus the belt reference gives it - the same operation as segmentation mask average depth: select valid object pixels, with the arithmetic in measuring surface height difference from a 3D point cloud. Fit the belt plane once per shift from an empty-belt capture: if the reference drifts half a millimetre, every height you quote drifts with it.

What sets the ±5 mm envelope

Random noise is gone after the fit; the example above drove it below 0.02 mm. What remains, combined as a root sum of squares:

• Edge bleed: 1-2 px of mixed pixels per wall, 2-4 mm at the worked pitch.
• Systematic depth error of the sensor class: 2-3 mm at 1.5 m.
• Temperature drift across a shift: millimetre-scale, and largely common to every axis.

√(4² + 3²) = 5 mm - the envelope, and the reason the 2 mm per pixel ceiling exists. Standoff moves it fastest: triangulation sensors (stereo, structured light) lose single-pixel accuracy roughly with the square of distance, so 3 m multiplies that term by four over 1.5 m, while ToF degrades closer to linearly. Surface moves it next: black or glossy film drops projector returns and opens holes in the top face, and metallised film bends ToF multipath. When standoff creeps up, the edges fail first - why depth image edges of a cardboard box vanish at long standoff shows the mechanism.

AI segmentation or classical model fitting

On a clean belt with one parcel at a time, the classical pipeline wins: height and colour preselection, ground-plane removal, RANSAC box fit. It is deterministic, runs in milliseconds on an edge processor and needs no dataset. It fails exactly where real infeeds get hard: parcels flush against one another on a packed pallet, a jumble of mixed cartons in a bin, shrink wrap that matches the belt. There, a trained segmentation model that labels each visible top face restores per-box footprints, and every failure case you record improves the next training run.

The production answer is hybrid. The network does separation only; the dimensions still come from plane fits on the masked points, so the numbers stay deterministic and auditable. What the robot then does with them - layer planning, grip sizing - is the subject of 3D vision for robot palletizing: sizing boxes for pick.

Choosing the sensor

Match the family to the station:

• Static overhead mount, pallet-size window: the Logistics / volume class of speckle structured-light cameras is built for exactly this job - depth map plus volume measurement in one housing - and several units tile a wide infeed. For shorter robot-cell windows, a projected structured-light stereo camera fills the same role over a smaller scene.

• Robot cell, shorter window: projected structured-light stereo such as the MV-DPS200P-02 returns a dense cloud over a shorter throw.

• Continuous flow, moving scenes: a ToF sensing camera such as the MV-DT01WMU reads depth without a projected pattern and keeps pace with continuous conveyor flow.

Values as printed in each product's data sheet; open a part for its drawing and full specifications.

• Full-width, conveyor-speed dimensioning: a line-scan 2.5D system images the whole belt continuously. The MV-HLVS-16K100-L60 pairs a 16K line sensor with a 600 mm emitting area and samples at up to 120 kHz, while a 3D laser profile sensor such as the MV-DP4180-03P resolves single parcels with very fine height detail, one box at a time.

The label still needs photons the depth map does not carry: a colour global-shutter model from the area scan cameras range, such as the MV-CH120-11UC at 12 MP, reads barcode and shipping label on the same trigger while the depth camera sizes the box.

When the usual answer fails

• Glossy or black shrink film. Structured light loses returns and opens holes; matte wrap or a shallow projector angle closes most of them. Metallised film bends ToF multipath and skews the fits.
• Coverage computed at belt height. Compute the window at the top of the tallest parcel, or tall boxes clip the map.
• Belt speed without triggering. A depth frame smeared by motion reads walls long in the smear direction; expose short and trigger per parcel.
• Flexible or shared mounts. Camera and belt reference must behave as one rigid body; relative motion shows up as ripple in every fit.

Before you order: five checks

1. Window and pitch: window width over depth-map width gives 2 mm/px or less at the mounting height.
2. Smallest face: the worst-case parcel top still spans 20 × 20 px after an 8 px trim.
3. Worst surface: scan the glossiest, darkest parcel you ship; visible holes across its face mean fixing wrap, angle or sensor before anything else.
4. Range and reference: standoff inside the sensor's specified depth range with margin, plus a per-shift empty-belt capture to re-fit the belt plane.
5. Takt: depth capture, segmentation and the fits must close inside the cycle time - budget it before the mechanical design freezes the standoff.

These checks plug straight into the 3D sensors finder, and the 3D vision topic page collects the measurement guides around this one. Sizing the rest of the cell - trigger chain, mount, PLC handshake - is walked through in 3D vision robot palletizing integration checks.