The Jet Metric

In order to define a metric on jet space, linear scale space is considered from a statistical standpoint. Given a scale σ, the scale space solution can be interpreted as maximizing a certain Gaussian posterior probability, related to a particular Tikhonov regularization. The Gaussian prior, which governs this solution, in fact induces a Mahalanobis distance on the space of functions. This metric on the function space gives, in a rather precise way, rise to a metric on n-jets. The latter, in turn, can be employed to define a norm on jet space, as the metric is translation invariant and homogeneous. Recently, [1] derived a metric on jet space and our results reinforce his findings, while providing a totally different approach to defining a scale space jet metric.