A Multi-scale Geometric Analysis Method Based On Beamlet Transform

With the development of modern science technology, more and more new theories appeared in the field of Digital Image Processing. Fourier Transform is called as the exploiter of Digital Image Processing, and the analysis of wavelet takes the Digital Image Processing to a fire-new domain, while Multi-scale Geometric Analysis which generated only few years ago also brings the new development to Digital Image Processing.Six new theories in Multi-scale Geometric Analysis are introduced in this paper from theory and application, which are Beamlet transform, Wedgelet transform, Ridgelet transform, Curvelet transform, Contourlet transform and Bandelet transform. Compared with the multi-scale wavelet transform, the new theories of MSGA aren't restricted by time and space. And images can be coded and transformed with geometrical properties of image itself by MSGA. The beamlet transform is so far the best method in processing the image with strong noise, and Wedgelet transform is generated from beamlet transform. Ridgelet transform have the highest rate of capability-value and it is also one of the most popular transform in research and the application. Because of the high redundancy rate of Ridgelet transform, Curvelet transform and Contourlet transform are put forward. These above five transforms belong to no-self-adaptive methods while Bandelet transform is one kind of the self-adaptive methods.This paper focuses on beamlet transform. The theory of beamlet can be divided into following five parts, the beamlet dictionary, the beamlet transform, the beamlet pyramid, the beamlet graph and Beamlet Algorithms. Lines of various length and direction are stored in the beamlet dictionary, which is the base of beamlet transform and directly influence the accuracy of configured image. Beamlet algorithms not only include some common algorithms in wavelet transform such as the dyadic tree structure, also include local or global optimal chaining of line segments. Thus the compression ratio is increased, the redundancy rate is reduced and the algorithms are optimized. When an image being processed, in the first step it should be transformed by beamlet transform, then secondly the transformed image is divided by the beamlet pyramid and the beamlet graph in order to pick-up the segments, and we should match...