A Research On The Theory Analysis And Practical Algorithm Of Beamlet Transform

In the past decade, a number of independent developments in mathematical analysis, in computer vision, in pattern recognition, and in statistical analysis have independently developed tools and theories which can now be seen to be closely related, as parts of an area which should be called Multiscale Geometric Analysis. Multiscale Geometric Analysis has been shown to be a useful mathematical tool for many practical applications and become to a focus of attention recently.The aim of Multiscale Geometric Analysis is to find a kind of optimal representation of high dimension function in the sense of nonlinear approximation. Based on the nonlinear approximation of 2-D function, the mathematical and neurophysiologic backgrounds of Image Multiscale Geometric Analysis are studied on this paper, and its development history, current and future challenges are reviewed in details.There is enormous difficulty while detecting line in the images polluted seriously by the noise in the traditional method. These problems become more serious when the image is polluted seriously by the noise. Beamlet transform is one kind of multiscale geometric analysis (MGA) developed fast in recent years, especially suited to the line detection in the images. Beamlets are a special dynamically organized collection of line segments, exhibiting a range of lengths, positions and orientations. This paper describe a framework for multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis. The study on beamlet theory of this paper still belongs to the first time at home. Implementation of beamlet transform has been studied in this paper and it is applied in line detection in the images polluted seriously by the noise. Experimental results show the power of this approach.The practical algorithm of beamlet transform is studied. Some experiments are done to detect line in images polluted seriously by the noise, such as synthetic aperture radar (SAR) image, to test the quality of the new theory. And some new ideas are brought into the beamlet method. The simulation results show the good performance of the new method.