Research On Smoothlet Transform Algorithm

An effective representation is one of the main issues in image processing tasks.Smoothlet is an adaptive multi-scale and geometric representation method,which can adaptively expresses different positions,scales,directions,curvature and smooth edges of image.Smoothlet transform uses extruded surface to define a blurred edge,which can be obtained by translating the edge curve in the horizontal or vertical direction.Although the Smoothlet transform can represent various blurred edge,the edge of the grayscale image in the real image may be complex.And the extruded surface that is only defined in the horizontal or vertical direction is not enough to express the real image edge.So it’s necessary to improve the Smoothlet.In this paper,new transform is used to improve the Smoothlet transform.The main contents are as follows:1.An improved framework for Smoothlet transform-Extended Smoothlet(ExSmoothlet)is proposed.The framework defines the direction of the curve as a reasonable direction.And two implementations of the framework are proposed.The Elliptical ExSmoothlet(EES)algorithm is proposed in which the translation direction of all points in the transition zone is unified by the normal direction of the straight line parameters.Based on the fast Wedgelet,the Fast Elliptical ExSmoothlet Transform(FEEST)is implemented based on the Fast Wedgelet.FEEST is compared with the Fast Smoothlet Transform(FST)algorithm.Experimental results show that FEEST is better than FST for image approximation and denoising in PSNR sense.2.Homocentric Elliptical ExSmoothlet(HEES)is presented.When EES and Smoothlet use the elliptical model for the edge curve,only a part of the semi-ellipse(part or lower part of the ellipse)can be used in order to make the two edge curves do not intersect.When the real image edge continues beyond the semi-ellipse,the EES and Smoothlet can’t be accurately expressed.HEES use an elliptic fitting method to fit any part of an ellipse and define trasition direction in the adaptive way.In the application of HEES,the experimental results show that HEES is better than EES for image approximation,edge detection and image denoising with lower noise.