Am 7.02.2014 fand der Workshop an der Fakultät für Informatik und Mathematik der Universität Passau statt.
Am 19.07.2013 fand der Workshop an der Fakultät für Informatik und Mathematik der Universität Passau statt.
Am 08.02.2013 fand der Workshop an der Fakultät für Informatik und Mathematik der Universität Passau statt.
Zum Thema "New Trends in Harmonic Analysis, Fractional Operator Theory and Image Analysis" fand vom 17. bis 21. September 2012 in Inzell eine Sommerschule statt.
Robust and precise image feature extraction based on sampling theory for signals with finite rate of innovation
Vortrag von Professor Akira Hirabayashi (Yamaguchi University, Ube, Japan)
22. Mai 2012 um 14.30 Uhr
This talk will present a new image feature extraction method based on sampling theory for signals with finite rate of innovation. We focus on a straight line edge, which is one of the most important image features exploited in, such as, registration, object recognition, and vehicle navigation. The standard method to extract straight lines is the Hough transform, which suffers from theoretical limitations. This difficulty was reduced by using more precise acquisition model. This approach was first taken by Baboulaz et al., who used B-spline functions for the acquisition model and proposed a method which can exactly retrieve line-edge parameters including orientation, offset, and amplitude. However, this methods suffers from noise sensitiveness. To overcome the two above mentioned problems, we introduced two key factors. One is that we use a trigonometric E-spline function, instead of B-spline, to model the acquisition process. The other is that we formulate the line-edge extraction process as an optimization problem, instead of that of obtaining analytic solutions for simultaneous equations. By computer simulations, we show that our method achieved small variances, which are much closer to the Cramer-Rao lower bound than the analytic solution approaches. Further, we show that our method can retrieve line-edge precisely from real images obtained by a commercial digital SLR camera.
Splines of Complex Order - A New Tool in Harmonic Analysis
Splines of complex order z are an extension of the classical polynomial Schoenberg splines B_n, n in N. Whereas the order n for Schoenberg splines is only an indicator of the integral smoothness of B_n, the complex order z provides a pair of indices with the real part representing the continuous smoothness class and the imaginery part the phase information. Thus, splines of complex order not only fill in the gaps between the integral smoothness classes but also provide a means of employing the phase information contained in Im z to resolve singularities such as edges and corners in images.
In this talk, we motivate the definition and present some of the basic theoretical background of splines of complex order, and indicate their relationship to fractional derivatives and integrals, and Dirichlet averages. In addition, we discuss potential applications of these splines to signal and image processing.