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

【摘要】：圖像矩是用來(lái)抽取圖像特征的一種算法。自上世紀(jì)60年代圖像矩被提出以來(lái),立刻引起各國(guó)學(xué)者的關(guān)注與研究,并被廣泛應(yīng)用于目標(biāo)識(shí)別、模式識(shí)別和圖像處理等領(lǐng)域中。與其它圖像特征相比,圖像矩特征在上述領(lǐng)域的應(yīng)用中具有無(wú)與倫比的優(yōu)勢(shì),可以說(shuō),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(jì)算精度的問(wèn)題。在利用矩函數(shù)提取和處理圖像時(shí)會(huì)伴隨有計(jì)算誤差,這些計(jì)算誤差在運(yùn)算過(guò)程中會(huì)逐漸放大,導(dǎo)致圖像矩算法不收斂,最終損害圖像矩運(yùn)算的精度,造成模式識(shí)別困難與圖像重構(gòu)失真。目前只有少量的研究者對(duì)該問(wèn)題進(jìn)行過(guò)研究,尚無(wú)研究者系統(tǒng)地、定性地研究過(guò)圖像矩誤差的問(wèn)題。筆者在查閱了國(guó)內(nèi)外的相關(guān)資料后發(fā)現(xiàn):沒(méi)有任何判斷圖像矩收斂性的準(zhǔn)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(chǎn)生與傳遞機(jī)理,嘗試找出一些評(píng)判圖像矩收斂性的準(zhǔn)則與判據(jù),并在此基礎(chǔ)上對(duì)傳統(tǒng)的圖像矩算法作出一些優(yōu)化與改進(jìn),以抑制其計(jì)算過(guò)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(duì)象,介紹了圖像矩誤差的產(chǎn)生根源與種類(lèi),研究了圖像矩運(yùn)算中誤差的傳遞過(guò)程,闡釋了誤差對(duì)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(chǔ)。(2)將迭代法圖像矩中的誤差傳遞式轉(zhuǎn)換為二階離散誤差系統(tǒng)來(lái)研究,通過(guò)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(shí),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(gè)判斷常規(guī)圖像矩算法收斂性的判據(jù)。最后通對(duì)幾種圖像矩進(jìn)行誤差分析與圖像重構(gòu)實(shí)驗(yàn),驗(yàn)證了上述判據(jù)與準(zhǔn)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(guò)修正不穩(wěn)定圖像矩迭代式的參數(shù)將不收斂的算法轉(zhuǎn)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(guò)的方法對(duì)圖像進(jìn)行了重構(gòu)和誤差分析實(shí)驗(yàn),結(jié)果驗(yàn)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(xué)位授予單位】：湖北工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TP391.41

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