Detection of elongated structures by using invertible angular representations of scalar images

A unitary approach for locally apertured orientation analysis of 2D and 3D scalar images is proposed. The size of the local aperture (the scale) needed for the orientation representation induces in general a loss of spatial acuity, or blur. Our construction permits a compensation of the blur by a reconstruction procedure. For this purpose, a special scale-dependent orientation bundle (map of the visual space into a function of both position and orientation) is built from the local Gaussian-derivatives jet of a scalar image. In this construction there is an invertible relation between the orientation bundle and the original image in the space domain. This invertible transformation is used to regain the original acuity in the spatial domain after analyzing orientation features at any given scale. This type of orientation “encoding” might contribute to understand both the role of orientation columns and the hyper-acuity phenomenon in biological visual systems. The approach turns out to be highly effective for the detection of elongated structures and for removal of elongated artifacts in 2D images. The results from the detection task can be enhanced by applying an anisotropic diffusion of the orientation field and thus closing missing contour segments