Rough Path Signature-Guided Geometry Augmentation for Few-Shot Industrial Surface Defect Detection

What the math gives to ML

The paper provides a transferable representation for boundary-dominated visual data: encode an ordered planar contour by its truncated path signature, whose second-order antisymmetric component measures oriented enclosed-area geometry rather than merely local edge strength. This is useful because two contours with similar pointwise gradients can have different turning, orientation, and self-interaction structure, while the signature aggregates these relations over the whole path. The most promising neural-network transfer is a lightweight contour-signature branch that injects area and iterated-displacement channels into a CNN or vision transformer, particularly under few-shot supervision where geometric inductive bias can reduce sample complexity.