Scale-Space Image Analysis Based on Hermite Polynomials Theory

摘要

The Hermite transform allows to locally approximate an image by a linear combination of polynomials. For a given scale σ and position ξ, the polynomial coefficients are closely related to the differential jet (set of partial derivatives of the blurred image) for the same scale and position. By making use of a classical formula due to Mehler (late 19th century), we establish a linear relationship linking the differential jets at two different scales σ and positions ξ involving Hermite polynomials. For multi-dimensional images, anisotropic excursions in scale-space can be handled in this way. Pattern registration and matching applications are suggested.