BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Hermite-Like Representation of Images in Terms of Samples with Local Tangents

C. Conti, L. Romani, M. Unser

SIAM Conference on Imaging Science (IS'18), Bologna, Italian Republic, June 5-8, 2018, session MS47-1.

The aim of this talk is to discuss the construction of minimally supported basis functions for Hermite interpolation on a three directional mesh of the plane. Our model relies on three directional Box-splines and gets advantage from the deep relationship between Hermite and Bézier representation of piecewise bivariate polynomials. Starting by the simpler but analogous univariate case, we will show how the use of Greens' function allows us to unreveil all theoretical properties of the new bivariate Hermite basis functions. The proposed model meets practical requirements such as invariance to affine transformations and good approximation properties.One of its great advantages is its non tensor-product structure which avoids the use of mixed derivatives and makes it suitable to Hermite-like representation of images in terms of samples with local tangents. 

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