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On Numerical Reconstruction of a Function from Incomplete Data on Arc Means in Seismic Tomography

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Denisiuk A.

tom Vol. 20, No. 4

413-437

Consider the problem of reconstruction of a small perturbation of the acoustic wave speed field from traveltime data with linear background slowness. Mathematically, the problem is equivalent to reconstruction of a function from the data of integrals along the circle arcs. The data is limited, in the sense that the base points belong to a compact set. We propose and numerically test a new approach, based on reduction of the problem to the inverse problem for the Radon transform. The data completion procedure is considered as well.

Irregular pattern recognition using the Hough transform

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Żorski W. , Foxon B. , Blackledge J. , Turner M.

Machine Graphics and Vision

2000

tom Vol. 9, No. 3

609-632

The paper presents an application of the Hough Transform to the tasks of learning and identifying irregular patterns in computer vision systems. The method presented is based on the Hough Transform with a parameter space defined by translation, rotation and scaling operations. An essential element of this method is the generalisation of the Hough Transform for grey-level images. The technique simplifies application of the Hough Transform to pattern recognition tasks as well as accelerates the calculations considerably. The technique could be used, for example, in a robotic system or for image analysis.