Fractal Cross Product: Theory, Differentiable Implementation and Application to Medical Image Analysis
The magnitude of the generalized Euclidean cross product is a Gram volume whose degree under common scaling is fixed by the integer dimension of the spanning frame. We formulate a generalized Fractal Cross Product (FCP) as a nonlinear radial deformation with a prescribed positive degree $D$, which may be non-integer. The scalar construction applies in any ambient dimension $m\geq k$, while its canonically oriented vector form requires codimension one. It recovers the classical generalized cross product exactly at $D=k$ and retains orthogonality, alternation, rotation equivariance, and $D$-homogeneity, but is generally not multilinear. For exact self-similar frame systems, the construction...
| Authors | Noaman Khan, Nihad Hadj Sahraoui, Samir Brahim Belhaouari |
|---|---|
| Primary category | cs.CV |
| Published | 26 September 2026 |
| Last updated at source | 26 September 2026 |
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