【正文】 基于圖論的閾值化圖像分割方法研究摘要圖像分割是圖像處理與計(jì)算機(jī)視覺(jué)領(lǐng)域低中最基礎(chǔ)和重要的領(lǐng)域之一，是圖像進(jìn)行視覺(jué)分析和模式識(shí)別的基本前提?；趫D論的圖像分割方法是圖像分割領(lǐng)域中的一個(gè)研究熱點(diǎn)，該類方法將圖像映射為帶權(quán)無(wú)向圖，把像素視作節(jié)點(diǎn) , 利用最小割集準(zhǔn)則得到圖像的最佳分割，會(huì)有一些問(wèn)題不可避免的出現(xiàn)。但是，如果單純的使用這類方法對(duì)圖像進(jìn)行分割的話，無(wú)法得到好的分割效果。因此需要結(jié)合其他的理論和知識(shí)對(duì)其進(jìn)行改進(jìn)，以便使得這類圖像分割方法具有更好的實(shí)效性。本文針對(duì)基于圖論的圖像分割方法中存在的問(wèn)題，把基于Normalized Cut準(zhǔn)則和MinMax Cut準(zhǔn)則圖像分割方法分別與閾值化圖像分割方法相結(jié)合，并對(duì)衡量像素點(diǎn)間相似性的計(jì)算公式進(jìn)行改進(jìn)，取得了一定的實(shí)效性。本文主要的研究工作如下：（ 1） 研究和分析了基于圖論的圖像分割方法和閾值化分割方法的理論及進(jìn)展，對(duì)兩者的結(jié)合的可行性進(jìn)行了探索。（ 2） 針對(duì)基于圖論的圖像分割方法在處理含有噪聲圖像時(shí)的不足，提出一種新的具有抑制噪聲能力的圖像閾值化分割方法。該方法采用NormalizedCut準(zhǔn)則劃分測(cè)度作為劃分目標(biāo)和背景的閾值分割準(zhǔn)則，并在圖權(quán)計(jì)算公式中，增加了像素點(diǎn)與其鄰域的空間相關(guān)信息，以提高算法的抗噪性。實(shí)驗(yàn)結(jié)果表明，該方法具有很強(qiáng)的抑制噪聲能力。（ 3） 針 對(duì) 基 于 圖 論 的 圖 像 分 割 方 法 中 通 用 性 的 不 足 ， 提 出 了 一 種 新 的 基 于MinMax Cut的閾值化圖像分割方法。該方法采用MinMax Cut劃分測(cè)度作為區(qū)分目標(biāo)和背景的閾值化分割準(zhǔn)則。在描述圖像各像素間的相似性關(guān)系權(quán)值矩時(shí)，把基于圖像像素的權(quán)值矩陣換成基于灰度級(jí)的權(quán)值矩陣，大大節(jié)約了算法實(shí)現(xiàn)的復(fù)雜度和算法所需要的存儲(chǔ)空間度。并用類似于基因勢(shì)函數(shù)的計(jì)算公式作為圖權(quán)公式，該公式以統(tǒng)計(jì)學(xué)的形式更為全面的反映了兩像素點(diǎn)間的相似性，同時(shí)又避免了通過(guò)手動(dòng)的形式來(lái)設(shè)置控制像素點(diǎn)間相似性因素的差異敏感程度參數(shù)的不足，提高了算法的通用性。通過(guò)實(shí)驗(yàn)結(jié)果，驗(yàn)證了本章算法的實(shí)用性。關(guān)鍵詞：圖劃分；圖像分割；Normalized Cut；MinMax CutResearch of Threshold Image Segmentation Based on GraphTheoryABSTRACTAs one of the most important and typical problems in image processing andputer vision fields, image segmentation is the basic premise in image visionanalysis and pattern segmentation based on graph theory is aresearch focus in image segmentation fields,this approaches are the formation of aweighted graph,where each vertex corresponds to an image pixel,the bestsegmentation of the image can be obtained by minimal cut sets,and achieve goodresults of image some problems and deficiencies may be found inthe process of implementation, if we just simply use this approaches. other theoriesare bined with this approaches to get better effectiveness.Aiming at the problem exists in the image segmentations based on graphtheory, the thesis bines the Normalized Cut standard and MinMax Cut standardwith threshold image segmentation, and improves the putational formula whichused to measure the similarity between the pixels to reach a well effectiveness. Themain works can be organized as follows:Part one: To make sure the feasibility of the bination of the two methods, thetheories and progress of image segmentation based on graph theory and thresholdsegmentation were researched.Part two: Aiming at the problem in the process of the image segmentationsbased on graph theory, a new algorithm is presented to resist noise in the process ofimage segmentation. Normalized Cut standard is adopted as the standard of thedivision between the objective and background, and the relevant space informationbetween pixels and its neighborhood are used to improve the noise immunity. Theexperimental results show that the method has well noise immunity.Part three: Aiming at the inadequate of monality in the image segmentationsbased on graph theory, a new method based on MinMax Cut threshold imagesegmentation is proposed. This method adopts Min Max dividing measure as thethreshold segmentation rule to distinguish the target and background. In describingthe weight matrix of similarity between the pixel values of each image,we useweight matrix based on grey level to replace that based on image pixels so that thealgorithm plexity and the storage space degrees are greatly saved. By using theputational formula of the potential function as the graph weight matrices, theformula can reflect the similarity between pixels better in statistics. Meanwhile, itavoids the defect by the manual forms to set the control of some similaritiesbetween the degree of sensitivity parameters, and improves the monality of thealgorithm. The experimental results show that the algorithm has been betterpractical.Key words: Graph Cut； image segmentation； Normalized Cut； MinMax Cut插圖清單圖 圖像分割的作用 ................................................................................................. 1圖 圖 圖 無(wú)向圖 ............................................................................................................. 10有向圖 ............................................................................................................. 10加權(quán)圖 ............................................................................................................. 11圖 圖像分割與圖的分割間的關(guān)系 ....................................................................... 12圖 cameraman 圖片及其分割結(jié)果...................................................................... 23圖 image 圖片及其分割結(jié)果 ................................................................................. 23圖 加了 saltamp。pepper 噪聲 cameraman 圖片及其分割結(jié)果 .................................. 24圖 加了 saltamp。pepper 噪聲 image 圖片及其分割結(jié)果 .......................................... 25圖 對(duì)稱矩陣 M 的示意圖..................................................................................... 31圖 本章算法流程圖 ............................................................................................... 34圖 原 man 圖片 ....................................................................................................... 35圖 本章分割結(jié)果 .................................................................................................... 35圖 方法的分割結(jié)果 ....................................................................................... 35圖 方法的分割結(jié)果..................................................................................... 35圖 方法的分割結(jié)果 ..................................................................................... 35圖 Yanowitz 方法的分割結(jié)果 ................................................................................ 35圖 方法的分割結(jié)果 ................................................................................... 36圖 Pal 方法的分割結(jié)果 ....................................................................................... 36圖 原 lina 圖片圖 ..................................................................................................