Invertible apertured orientation filters in image analysis

A unitary approach for locally apertured orientation analysis of 2D and 3D scalar images is proposed. The size of the local aperture (the scale) neede d for the orientation representation induces in general a lost of spatial a cuity, or blur. Our construction permits a compensation of the blur by a re construction procedure. For this purpose, a special scale-dependent orienta tion bundle (map of the visual space into function of both position and ori entation) is build from the local Gaussian-derivatives jet of a scalar imag e. In this construction there is an invertible relation between the orienta tion bundle and the original image. This invertible transformation is used to regain the original acuity in the spatial domain after analyzing orienta tion features at any given scale. The approach turns out to be highly effective for the detection of elongate d structures and for removal of elongated artifacts in 2D images.