Pattern Recognition Based On PDE

Pattern recognition came into being in the 1920s. With the appearance of the computers and the starting of the artificial intelligence, pattern recognition as a field of study developed significantly in the 1960s. In the past decades, the research of pattern recognition obtained rapid development. It was very much an interdisciplinary subject, covering developments in the areas of optical character recognition (OCR), DNA sequence analysis, chemistry smell recognition, medicine member recognition, image understanding, expression recognition, hand signal recognition, speech recognition, information retrieval, data mining, and signal processing, among others. However, compared with the biological cognition system, the existing artificial pattern recognition system cannot be satisfying with its adaption and the recognition capability.As an important research technique, the partial differential equation (PDE) methods have been gradually applied in the image division, restores and other image processing problems. As far as we know, there is no worker deal with the pattern recognition problems by using the partial differential equation methods. In this monograph, we firstly introduce the PDE method to deal with the pattern recognition problem. The introduction of this method will certainly rich the theories in pattern recognition.We know that the final goal of pattern recognition is to seek a curve or a surface by the real known samples. If we take the curve or the surface as the classifier, this curve or the surface can separate the samples as we need exactly, and then achieve the recognition. By analyzing the distribution of the samples, we know that this curve (surface) is the image of some function which satisfy some certain conditions. And by minimizing some special functional, we can obtain the implicit iteration of the function. These expressions had reflected exactly the feature of the curve (surface) we need to seek. Therefore using the expression to establish the classifier and complete the pattern classification is the main work of this monograph.The main results in this monograph are divided into three chapters.In chapter 2, we use the active contours without edges modelF2(cuc2,C) = \uo(x,y)-cl\2dxdy + \uo(x,y) - c22dxdy + u\C\JQi=u) Jn2=fi\ujto discuss a class of pattern classification problem. We firstly deduce the model by using some mathematical methods. Then by analyzing the properties of the model, we find that it can detect the edges of the discrete point set. Finally, we use it as a classifier to deal with a class of problems on recognizing online handwritten signature.In chapter 3, we consider a extended active contours without edges model-Munford-Shah modelinf Ef f[u, t] = / \u - uq\2dx +/j, \Vu\2dx + u\r\.Ja Jn\rWe know that under most circumstances, samples are not regarded as equally. For those sparse and dense areas, we tend to separate consideration. In order to discuss this class of problems, we usually weighted samples at different locations. After the adoption of these weighted samples, sample space becomes similar sample points set and the set is piecewise smooth. Just because the true weighted samples setcan be considered as a piecewise smooth set, we can use Munford-Shah models to determine the edge of the set. Applying the Munford-Shah models, we can find the edge of the set which includes the uneven distributed samples, and then we can make classification. Finally, we utilize the classifier to deal with a human face detection problem.In chapter 4, we study a class of multi-classification problem, which is not easy to deal with. We know that in many cases, we need to detect two or more different types of things in a same test samples set. If these two (or more) things have little difference and all these samples are inseparable, then the traditional methods are no longer effectual. In such cases which the samples are inseparable, we introduced the multiphase Munford-Shah model, c) = / (u -Ems(uwhere u is piecewise smooth, andu(z,y) =, y),vT~ (x, y),\Vu\2dxdy + v\c n\c(x,y) > 0, 2(x,y) > 0,{x,y)>Q, 0,(x, y) < 0, (j>2 {x, y) < 0.By minimizing the model, we can get a classifier which can detect two or more different types of things in a same test samples set. Finally, we apply it to the detection of red blood cell and white blood cell in the urine slime.