Granulometry is the measurement of particle (grain) sizes within
a sample. The Particle Size Distribution (PSD)
describes the proportion of particles at each size class,
typically expressed as a cumulative passing curve.
How RGB-D Enables 3D Grain Measurement
An RGB-D camera captures both colour (RGB) and depth (D)
information. The depth map reveals grain topography: each grain
appears as a local peak separated by valleys. GrainSight
exploits these depth features for automatic grain segmentation
using the marker-based watershed algorithm.
Segmentation Pipeline
1. Smooth the depth map (Gaussian filter, sigma adjustable).
2. Compute depth gradient magnitude: |nabla z| = sqrt((dz/dx)^2 + (dz/dy)^2).
3. Detect grain peaks (local maxima of depth).
4. Run watershed transform using peaks as markers.
5. Merge small fragments below the minimum grain size.
Per-Grain Metrics
Equivalent diameter: d_eq = 2*sqrt(A/pi),
the diameter of a circle with the same area as the grain footprint. Aspect ratio: major/minor axis from PCA. Circularity: C = 4*pi*A/P^2 (1 = perfect circle). Volume: integral of depth above the estimated base plane.
Interpretation of D-Values
D10 -- 10% of particles are finer. Used in filtration design. D50 -- median size. Half the material is finer. D80 -- 80% passing. Key metric in comminution circuit design
(Bond work index calculations). D90 -- 90% passing. Controls downstream equipment sizing.
Rosin-Rammler Parameters
The Rosin-Rammler model fits the PSD curve:
F(x) = 1 - exp(-(x/x0)^n) x0 (characteristic size): the size at which 63.2% of material passes. n (uniformity index): higher values indicate a narrower (more uniform) distribution.
Typical values: n=0.8-1.2 for blasted rock, n=2-4 for well-graded crushed aggregate.
Commercial Software Comparison
GrainSight implements algorithms similar to commercial systems like
WipFrag, Split Desktop, and GoldSize,
which are used in mining for muck pile fragmentation analysis. Unlike those 2D-only
systems, GrainSight also uses depth information for improved grain separation and
volume estimation.