Let R, denote the Radon transform on R” that integrates a function over hyperplanes in given smooth positive measures p depending on the hyperplane. We characterize the measures ,u for which R, is rotation invariant. We prove rotation invariant transforms are all one-to-one and hence invertible on the domain of square integrable functions of compact support, Li(R”). We prove the hole theorem: i...

A key challenge in the seismic imaging of reflectors using surface reflection data is the subsurface illumination produced by a given data set and for a given complexity of the background model (of wavespeeds). The imaging is described here by the generalized Radon transform. To address the illumination challenge and enable (accurate) local parameter estimation, we develop a method for partial ...

The radon transform arise in natural way, if X-rays traverses a body, like in a computer tomograph. Thus, to nd out the internal structur of a body in computer tomography corresponds to reconstructions a function from their radon transform. This report deals with a parallized numerical reconstruction algorithm, in particular the ltered backprojection. The ltered backprojection uses high dimensi...

In this study a time-frequency method based on Wigner-Ville Distribution (WVD) is used for detection and parameter estimation of Frequency Modulated Continuous Wave (FM-CW) Radar Signal. The proposed method uses the Pseudo-Wigner-Ville Distribution (PWVD) as a time-frequency detection technique and Radon Transform to identify the parameter of the modulation. The Wigner-Ville Radon Transform (WV...

Alignment of images of printed text is needed as a preprocessing for the purpose of OCR. The test for an image alignment is easily developed by summation of pixels horizontally. However, the angel of orientation of the text is not easily estimated. In this paper, a method for estimation of this angle is presented. The Radon transform is used. The spaces between lines are considered as thick lin...

We present a novel approach to parameterised curve detection. The method is based on the generalised Radon transform, which is traditionally applied to a 2D edge/line map. The novelty of our method is the mapping of the original 2D image to a 3D orientation space, which then forms the input for the Radon transform. The orientation space representation can represent multiple intersecting structu...

In this paper a novel filtered back-projection algorithm for inversion of a discretized Radon transform is presented. It makes use of invariance properties possessed by both the Radon transform its dual. By switching to log-polar coordinates, both operators can be expressed in a displacement invariant manner. Explicit expressions for the corresponding transfer functions are calculated. Furtherm...

We present a novel approach for the estimation of 3D-motion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a similarity function on feature pairs with a Dirac function embedding the epipolar constraint. Th...