Straight Line Detection Based On Radon Transform

Linear feature is a stable and invariant to translation,rotation and scale of good characteristics in digital image.It is great significance in improving the image target recognition rate and robustness for extraction of effective linear features of images correctly.Straight line detection has been widely applied to the target object recognition,shape detection,and road/line detection etc.Over the past two decades,there has been a rapid development for the straight line detection,but the accuracy and speed of the detection should be further improved.The method of straight line detection is mainly based on the Hough transform(HT)and its improvement methods recently,but the Hough transform has some drawbacks,such as edge extraction is required prior to line extraction,but such a requirement brings inaccuracy propagation and loss of gradient orientation;The HT is computational expensive and needs large memory.So some researchers have turned their interesting to the Radon transform(RT)which is equivalence with HT on the mathematical definition.Because the Central slice theorem ensures that the Radon transform could be implemented by FFT,it make the computation time of the Radon transform is less than the HT.The conversion from Descartes to polar coordinates in the process of implementing RT by FFT is indispensable.The performance of the Radon transform is affected seriously by the interpolation error in the process of transformation.The zero-padding and cropping technique can alleviate the aliasing,but in turn,bring higher computational cost.The Generalized Interpolated Fourier Transform(GIFT)could reach the precision of the zero-padding and cropping technique and reduce the time complexity at the same time for it can be computed parallel for each layer.In this paper,we describe the GIFT detailly first,and then a method of the GIFT parameters optimized is proposed.Our proposed method made the interpolation error as small as possible.We define the interpolation error of different interpolation methods,and different parameter selection method is given.The precision of the straight line detection based on Radon transform by the GIFT is improved using our proposed method.In the process of the conversion from Cartesian coordinates to polar coordinates,the traditional method is done by calculation(x(28)?cos ?,y(28)?sin ?),and a large amount of calculation is required for every transformation.In order to accelerate the speed of the GIFT,the corresponding mapping location coordinates are related only with corresponding coordinates,and has nothing to do with the information stored in each coordinate.So for the size of the fixed image,we set up a file which have stored the mapping information of the conversion from Cartesian coordinates to polar coordinates,then we implement the conversion through look-up the file which we have established instead of the calculation method.For the images of different size,we only need to calculate the conversion for the first time,and then the mapping information was stored in the file.Afterwards,we just need to look-up the mapping file when we do the conversion from Cartesian coordinates to polar coordinates for the same size image.Compared with the calculation method,our proposed method has saved more time.Finally,we have done the simulation for the improved the Radon transform algorithm based on GIFT.The simulation results indicate that our proposed method is better than the original algorithm.We have tested different image which obtain different width line and were polluted by noise respectively,it verify the robustness of our algorithm.