Research On Application Of Fractional Differential To Digital Image Processing And Support Vector Machine To Face Recognition

Interest in digital image processing methods stems from two principal application areas: improvement of pictorial imformation for human interpretation; and processing of image data for storage, transimission, and representation for autonomous machine perception. The application of fractional differential to image processing is a new field with little research until now. Compared with traditional integral-based differential image enhancement approaches, the application of fractional differential to image processing has remarkable advantages. Face recognition is an important research field of pattern recognition.The application of support vector machine to face recognition is a hot research issue in recent years. The dissertation mainly concerns the application of fractional differential to image processing and support vector machine to face recognition. The main work and research results are as follows:First, this dissertation systematically analyzes and summarizes the fundamental theories of image processing areas, incuding the concept of image processing, research situation and meaning of traditional image processing technology, and reseach situation of fractional differential-based image processing technology, and so on. While studies and discusses the fractional calculus theory, including its development course, three classical definitions and special functions, and so on. At the same time, this dissertation also systematically analyzes and summarizes the fundamental theories of face recognition, inculding various face recognition technonlogies, research situations of face recognition technology and the appliction of surport vector machine to face recognition, and so on. While studies and discusses the surpport vector machine theory, inculding its development course, background theory and basic theory, and so on.Second, an adaptive mathematical function is propoesed. This function, which is based on window size, Grunwald-Letnikov (G-L) formula, image gradient and visual property theory, could automatically generate fractional differntial order. At the same time, the fractional differential operator masks are designed and realized by employing this order. The proposed method could make fractional differetil automatically applied in digital image processing without the manually assigned optimal fractional differential order, which saves significant time seeking manually optimal fractional differential order. So it, to some extent, could meet the requirements to process a large number of real-time dynamic image sequences.The evaluation parameters of image texture are, such as information entropy and average gradient, used to do quantitative analysis and experimental verification. The results show that, for any gray-scale image, this method can obtain a successive enhancing result that is better to satisfy human visual sense, and it approximates the results of optimal fractional differential order. So, it's an effective approach to enhance image texture.Third, previous edge-based image interpolation algorithm hardly can improve the medium and low-frequency texture details of interpolated image effectively. In order to preserve the texture-rich information, an image interpolation approach, which is based on edge detection of fractional differential, is studied and proposed. The fractional differential operator mask, which can extract medium and low-frequency texture detail effectively, is designed and realized by employing fractional differential theory. Then linear interpolation, quadratic interpolation and bilinear interpolation are used for these pixel points to be interpolated along edge directions, perpendicular to edge directions and in smooth areas, respectively. The evaluation parameters of image quality are, such as peak signal to noise ratio (PSNR) and information entropy (IE), used to do quantitative analysis and experimental verification. The results show that this method could obtain image texture-rich information, and raise the peak signal to noise ratio. This result is better to satisfy human visual sense.Fourth, in order to improve recognition rate, face recoginition algorithm based on principle component analysis (PCA) and support vector machine (SVM) is proposed. PCA+NN, SVM and PCA+SVM methods are taken to do experiments on the Cambridge ORL Face database, respectively. This experimental results show that recognition rate of this proposed method, under small samples circumstance, is better than the other two methods. It shows that, for face recognition, sending PCA features to SVM classifiers is feasible and correct.Fifth, a face recognition method based on fractional differential-based binary edge map and surport vector machine is studied and proposed with a great deal of insensitivity to large variation in illumination and facial expression. The recognintion performance of binary edge map-based image and gray-based image is cmpared and analyzed on the ORL and Yale face database, respectively. This experimental results show that this proposed recognition method based on binary edge map extracted by fractional differetial is robust to variation in illumination and facial expression. It is more suitable for classifiction and recognition.