grain2d.smoothBoundary

grain2d.smoothBoundary edit page

turn the pixel staircase of a grain boundary into a smooth curve

Description

EBSD data is measured on a regular grid, so a grain boundary comes out of calcGrains as a staircase of pixel edges - every segment runs along one of the grid axes, whatever direction the boundary actually has. This is repaired in three steps

simplifyBoundary drops every vertex whose removal moves the boundary by less than epsilon. A staircase is never further than d/sqrt(2) from the straight line it approximates, d being the pixel spacing, so that is the tolerance which removes the grid and nothing else
refineBoundary resamples what is left at equal arc length delta, which gives the smoothing evenly spaced degrees of freedom that are no longer tied to the grid
the smoothing itself, by default a constrained Laplacian applied iter times

Which algorithm performs the last step is decided by a boundaryFilter

laplaceFilter - the default, repeated local averaging. Shrinks, and its knob is an iteration count rather than a length
taubinFilter - follows every smoothing pass by a slightly larger unshrinking pass, so the area is given back
curvatureFilter - one sparse solve instead of an iteration, stated as a smoothing length and therefore independent both of the iteration count and of the step size of the map
huberFilter - the same, but with an l^1/l^2 penalty that keeps a genuinely faceted boundary faceted

Both tolerances are derived from the median segment length before the first step - afterwards the median is the length of the straightened runs, not the pixel spacing.

Neither of the first two steps is cosmetic. Simplifying alone leaves a curve as a handful of long chords, and smoothing those cuts the corners off the polygon they form - a circle of 15 pixel radius loses 14% of its area over 25 iterations, against 0.4% for the full three steps. Smoothing alone leaves the boundary directions of a straight boundary scattered around the grid axes.

Junctions - triple points, quadruple points, and the vertices where the inner boundary ends on the outer one - stay exactly where they are throughout, unless moveTriplePoints is given. When grains were segmented using alphaShapes, all grains next to holes have outer boundary.

Note that the first two steps change the number of boundary segments, and a resampled segment no longer runs between a specific pair of pixels. Where gB.ebsdId is analysed per segment, switch them off with 'noSimplify' and 'noRefine'.

Syntax

grains = smoothBoundary(grains)
grains = smoothBoundary(grains,iter)
grains = smoothBoundary(grains,iter,'noSimplify','noRefine')
grains = smoothBoundary(grains,iter,'simplify',epsilon,'refine',delta)

grains = smoothBoundary(grains,taubinFilter)
grains = smoothBoundary(grains,curvatureFilter('smoothingLength',3))

Input

`grains`	`grain2d`
`iter`	`number of smoothing iterations (default: 1)`
`F`	`boundaryFilter, the smoothing algorithm to use`

Output

`grains`	`grain2d`
`F`	`boundaryFilter that was used`

Options