本文選題：圖像矩　切入點：迭代法　出處：《湖北工業(yè)大學》2017年碩士論文

【摘要】：圖像矩是用來抽取圖像特征的一種算法。自上世紀60年代圖像矩被提出以來,立刻引起各國學者的關注與研究,并被廣泛應用于目標識別、模式識別和圖像處理等領域中。與其它圖像特征相比,圖像矩特征在上述領域的應用中具有無與倫比的優(yōu)勢,可以說,目前找不到任何一種圖像特征能在效率和穩(wěn)定性上與其相比。然而,與其他特征提取算法一樣,圖像矩算法一樣存在著計算精度的問題。在利用矩函數(shù)提取和處理圖像時會伴隨有計算誤差,這些計算誤差在運算過程中會逐漸放大,導致圖像矩算法不收斂,最終損害圖像矩運算的精度,造成模式識別困難與圖像重構失真。目前只有少量的研究者對該問題進行過研究,尚無研究者系統(tǒng)地、定性地研究過圖像矩誤差的問題。筆者在查閱了國內外的相關資料后發(fā)現(xiàn):沒有任何判斷圖像矩收斂性的準則被提出。在這種情況下,筆者打算系統(tǒng)地研究一下圖像矩算法的誤差產生與傳遞機理,嘗試找出一些評判圖像矩收斂性的準則與判據(jù),并在此基礎上對傳統(tǒng)的圖像矩算法作出一些優(yōu)化與改進,以抑制其計算過程中的誤差。本文所做的主要研究工作有以下:(1)以迭代法的圖像矩為對象,介紹了圖像矩誤差的產生根源與種類,研究了圖像矩運算中誤差的傳遞過程,闡釋了誤差對算法精度和算法收斂性所造成的影響,為后兩步的研究打下了基礎。(2)將迭代法圖像矩中的誤差傳遞式轉換為二階離散誤差系統(tǒng)來研究,通過判斷該誤差系統(tǒng)的穩(wěn)定性從而判斷算法的收斂性。在判斷誤差系統(tǒng)的穩(wěn)定性時,筆者采用了李亞普洛夫方法,范數(shù)度量方法和奇異值分解法三種方法,并根據(jù)這三種方法提出了幾個判斷常規(guī)圖像矩算法收斂性的判據(jù)。最后通對幾種圖像矩進行誤差分析與圖像重構實驗,驗證了上述判據(jù)與準則的可行性。(3)提出了兩種優(yōu)化算法抑制傳遞誤差的方法,著重介紹了第二種方法-參數(shù)優(yōu)化方法,該方法通過修正不穩(wěn)定圖像矩迭代式的參數(shù)將不收斂的算法轉化為收斂的算法,從而有效地抑制了傳遞誤差。最后利用此優(yōu)化過的方法對圖像進行了重構和誤差分析實驗,結果驗證了該優(yōu)化方法的可行性。
[Abstract]:Image moment is an algorithm used to extract image features. Since the image moment was proposed in 1960s, it has attracted the attention and research of scholars all over the world, and has been widely used in target recognition. In the fields of pattern recognition and image processing, compared with other image features, image moment features have unparalleled advantages in the application of these fields. At present, no image features can be compared with them in terms of efficiency and stability. However, as with other feature extraction algorithms, Image moment algorithm has the same problem of calculation accuracy. When using moment function to extract and process images, there will be calculation errors, which will be magnified gradually in the course of operation, resulting in the image moment algorithm does not converge. Finally, the accuracy of image moment operation is damaged, which results in the difficulty of pattern recognition and distortion of image reconstruction. At present, only a small number of researchers have studied this problem, and no researchers have systematically studied this problem. The problem of image moment error has been studied qualitatively. After consulting the relevant data at home and abroad, the author finds that there is no criterion to judge the convergence of image moment. In this case, The author intends to systematically study the error generation and transfer mechanism of the image moment algorithm, try to find out some criteria and criteria to judge the convergence of image moment, and on this basis, make some optimization and improvement to the traditional image moment algorithm. In order to restrain the error in the calculation process, the main research work in this paper is as follows: (1) taking the image moment of the iterative method as the object, the origin and type of the error of the image moment are introduced, and the transmission process of the error in the calculation of the image moment is studied. The effect of error on the accuracy and convergence of the algorithm is explained, which lays a foundation for the study of the latter two steps. The error transfer formula in the iterative image moments is converted into a second order discrete error system. By judging the stability of the error system, the convergence of the algorithm is judged. In judging the stability of the error system, the author adopts three methods, namely, the Lyapunov method, the norm metric method and the singular value decomposition method. According to these three methods, several criteria for judging the convergence of conventional image moment algorithm are proposed. Finally, error analysis and image reconstruction experiments are carried out on several image moments. The feasibility of the above criteria and criteria is verified. (3) two optimization algorithms are proposed to suppress the transfer error, and the second method, the parameter optimization method, is introduced emphatically. The method converts the unconvergent algorithm into a convergent algorithm by modifying the parameters of the iterative formula of the unstable image moment, thus effectively suppressing the transfer error. Finally, the image reconstruction and error analysis experiments are carried out by using the optimized method. The results show that the optimization method is feasible.
【學位授予單位】：湖北工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP391.41

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