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Reports (Research Report) Year : 1994

The Intrinsic Structure of the Optic Flow Field

Mads Nielsen


n this paper, a generating equation for optic flow is proposed that generalises Horn and Schunck's Optic Flow Constraint Equation (OFCE). Whereas the OFCE has an interpretation as a pointwise conservation law, requiring grey-values associated with fixed-scale volume elements to be constant when co-moving with the flow, the new one can be regarded as a similar conservation requirement in which the flow elements have variable scale consistent with the field's divergence. Thus the equation gives rise to a definition of optic flow which is compatible with the scale-space paradigm. We emphasise the gauge invariant nature of optic flow due to the inherent ambiguity of its components, i.e. the well-known aperture problem. Since gauge invariance is intrinsic to any definition of optic flow based solely on the data, it is argued that the gauge should be fixed on the basis of extrinsic knowledge of the image formation process and of the physics of the scene. The optic flow field is replaced by an approximating field so as to allow for an order-by-order operational definition preserving gauge invariance, i.e.\ the approximation does not add spurious degrees of freedom to the field. One thus obtains a defining system of linear equations in the optic flow components up to arbitrary order, which remains decoupled from any physical considerations of gauge fixing. Such considerations are needed to derive a complementary system of gauge conditions that allows for a unique, physically sensible solution of the optic flow equations. The theory is illustrated by means of several examples.
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inria-00074327 , version 1 (24-05-2006)


  • HAL Id : inria-00074327 , version 1


Luc Florack, Mads Nielsen. The Intrinsic Structure of the Optic Flow Field. [Research Report] RR-2350, INRIA. 1994. ⟨inria-00074327⟩
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