Discontinuities

Every correlation criterion since Correlation Criteria, and every worked example through Parallelism with PyTorch, depends on one tacit assumption: the true displacement field is smooth. A kernel window moves as a rigid or gently stretching patch. The search for its match assumes one answer exists.

Real specimens may not always have a continuous displacement field. A crack, a slip band, or a material interface can produce a genuine jump in displacement instead of a continuous displacement. Image Transformation already built exactly that jump:

Crack Dislocation	Image
Original
offset=4 pixels

A vertical crack splits the image at its vertical midline. The left half shifts down 4 pixels. The right half shifts up 4 pixels. Standard DIC can't represent that jump.

This chapter seeks to identify characteristics of the correlation map in the presence of a discontinuous displacement field. Specifically, what does a correlation surface look like when a kernel window straddles a real discontinuity instead of sitting cleanly on one side of it?

Synthetic Dislocation answers that with a known, exact ground truth: the same 4-pixel offset above, now carrying a speckle pattern a correlation can actually track. Experimental Dislocation then repeats the same straddling window on a real experimental crack image pair. There the ground truth isn't known in advance, so it checks whether the same signature shows up outside a synthetic setup.

Neither section proposes a discontinuity-aware correlation algorithm on its own. Discontinuity Localization addresses that challenge.