Applications Of Fractional Differentiation In Edge Detection And Image Matching

Edge detection and image matching are two core issues in the field of computer vision. Image edge holds important visual information, which is the foundation of image understanding and scene perception. For the image with complex texture, the traditional edge detectors are difficult to extract the desirable edge, especially the needed texture details. Image matching has extensive applications and prospect in the fields of image retrieval, object recognition, robot navigation, medical image analysis,medical diagnosis, sensor network and character recognition, etc. SIFT algorithm is an available image matching method based on the local feature. However, in blurred or weak texture image, the extracted effective feature will reduce, which will result in the low matching accuracy. This paper tries to investigate the applications of fractional differentiation in edge detection and image matching. The main work are as follows:1. Discuss the theory of fractional calculus in detail. Fractional calculus is an extension of integral order calculus, it can solve the operation of arbitrary order calculus,the applications of fractional calculus are more and more extensive. With the continuous development of the theory of fractional calculus, its advantage in signal processing is becoming more and more significant. In digital image processing, while fractional differential enhances the high frequency components of image, it can enhance the intermediate frequency and retain the low frequency components non-linearly, this property takes advantage to process the image which holds fractal structure or weak texture.2. An improved Canny edge detector based on fractional differentiation has been proposed. The method calculates the image gradient using the classical GrünwaldLetnikov(G-L) fractional differential definition instead of the derivative of the Gaussian function, the detection accuracy and robustness are both improved. A new edge detection mask based on fractional differentiation is suggested, the quantitative relation curves between the edge-detecting capability and the tuning parameters are presented,which can guide one to choose more appropriate parameters. Finally, we compare the proposed algorithm with the typical edge detecting algorithm and the method based on the Riemann-Liouville(R-L) fractional differential definition. The experiment results demonstrate that the proposed algorithm is more robust and accurate.3. An improved SIFT algorithm based on fractional differentiation has been proposed. In order to improve the accuracy of SIFT algorithm, we introduce the fractional differentiation to SIFT algorithm. The method calculates the image pyramid combining the Riemann-Liouville(R-L) fractional differentiation and the derivative of the Gaussian function. Thus image feature has been enhanced, and more feature points can be extracted. As a result the matching accuracy is improved. Additionally, a new feature detection mask based on fractional differential is constructed. The proposed method is a significant extension of SIFT algorithm. The experiments carried out with images in database and real images indicate that the proposed method can obtain good matching results.