實(shí)驗(yàn)三圖像分割與邊緣檢測

1、實(shí)驗(yàn)三 圖像分割與邊緣檢測上課老師:趙歡喜 實(shí)驗(yàn)指導(dǎo):吳磊 一實(shí)驗(yàn)?zāi)康?. 理解圖像分割的基本概念；2. 理解圖像邊緣提取的基本概念；3. 掌握進(jìn)行邊緣提取的基本方法；4. 掌握用閾值法進(jìn)行圖像分割的基本方法。二實(shí)驗(yàn)基本原理圖象邊緣檢測圖像理解是圖像處理的一個(gè)重要分支，研究為完成某一任務(wù)需要從圖像中提取哪些有用的信息，以及如何利用這些信息解釋圖像。邊緣檢測技術(shù)對于處理數(shù)字圖像非常重要，因?yàn)檫吘壥撬崛∧繕?biāo)和背景的分界線，提取出邊緣才能將目標(biāo)和背景區(qū)分開來。在圖像中，邊界表明一個(gè)特征區(qū)域的終結(jié)和另一個(gè)特征區(qū)域的開始，邊界所分開區(qū)域的內(nèi)部特征或?qū)傩允且恢碌?，而不同的區(qū)域內(nèi)部的特征或?qū)傩允遣煌模?/p>

2、邊緣檢測正是利用物體和背景在某種圖像特性上的差異來實(shí)現(xiàn)的，這些差異包括灰度，顏色或者紋理特征。邊緣檢測實(shí)際上就是檢測圖像特征發(fā)生變化的位置。由于噪聲和模糊的存在，檢測到的邊界可能會變寬或在某些點(diǎn)處發(fā)生間斷，因此，邊界檢測包括兩個(gè)基本內(nèi)容：首先抽取出反映灰度變化的邊緣點(diǎn)，然后剔除某些邊界點(diǎn)或填補(bǔ)邊界間斷點(diǎn)，并將這些邊緣連接成完整的線。邊緣檢測的方法大多數(shù)是基于方向?qū)?shù)掩模求卷積的方法。導(dǎo)數(shù)算子具有突出灰度變化的作用，對圖像運(yùn)用導(dǎo)數(shù)算子，灰度變化較大的點(diǎn)處算得的值比較高，因此可將這些導(dǎo)數(shù)值作為相應(yīng)點(diǎn)的邊界強(qiáng)度，通過設(shè)置門限的方法，提取邊界點(diǎn)集。一階導(dǎo)數(shù)與是最簡單的導(dǎo)數(shù)算子，它們分別求出了灰度在x和

3、y方向上的變化率，而方向上的灰度變化率可以用相應(yīng)公式進(jìn)行計(jì)算;對于數(shù)字圖像，應(yīng)該采用差分運(yùn)算代替求導(dǎo)。一幅數(shù)字圖像的一階導(dǎo)數(shù)是基于各種二維梯度的近似值。圖像f(x,y)在位置(x,y)的梯度定義為下列向量： (3-4)在邊緣檢測中，一般用這個(gè)向量的大小，用表示 (3-5)函數(shù)f在某點(diǎn)的方向?qū)?shù)取得最大值的方向是，方向?qū)?shù)的最大值是稱為梯度模。利用梯度模算子來檢測邊緣是一種很好的方法，它不僅具有位移不變性，還具有各向同性。為了運(yùn)算簡便，實(shí)際中采用梯度模的近似形式。 或者 傳統(tǒng)的邊緣檢測算法通過梯度算子來實(shí)現(xiàn)的，在求邊緣的梯度時(shí)，需要對每個(gè)象素位置計(jì)算。在實(shí)際中常用小區(qū)域模板卷積來近似快速計(jì)算，簡

4、單有效，梯度算子一般采用因此應(yīng)用很廣泛。模板是N*N的權(quán)值方陣，經(jīng)典的梯度算子模板有：Sobel模板、Prewitt模板、Roberts模板、Laplacian模板等。具體模板請見書。拉普拉斯高斯（LoG）算法是一種二階邊緣檢測方法。它通過尋找圖像灰度值中二階微分中的過零點(diǎn)（Zero Crossing）來檢測邊緣點(diǎn)。其原理為，灰度級變形成的邊緣經(jīng)過微風(fēng)算子形成一個(gè)單峰函數(shù)，峰值位置對應(yīng)邊緣點(diǎn)；對單峰函數(shù)進(jìn)行微分，則峰值處的微分值為0，峰值兩側(cè)符號相反，而原先的極值點(diǎn)對應(yīng)二階微分中的過零點(diǎn)，通過檢測過零點(diǎn)即可將圖像的邊緣提取出來。(a)原圖 (b)邊緣檢測后的圖 (c) 閾值處理后的圖圖3-1

5、檢測具有-45度邊緣的圖例1點(diǎn)檢測原理：常數(shù)灰階區(qū)域中的某孤立點(diǎn)對某種模板的響應(yīng)絕對值肯定是最強(qiáng)烈的。最常用的模板有：Matlab 實(shí)現(xiàn)方法：g = abs(imfilter(double(f),w) >= T; where w is a appropriate point detection mask which satisfies the above condition.實(shí)例：the detection of isolated bright point in the dark gray area of the northeast quadrant.(image size: 675*6

6、75)實(shí)例代碼：f=imread('Fig1002(a)(test_pattern_with_single_pixel).tif');w = -1 -1 -1; -1 8 -1; -1 -1 -1;g = abs(imfilter(double(f), w);T = max(g(:);g = g>= T;subplot(121);imshow(f);title('the original image');subplot(122);imshow(g(1:end-400, 400:end);title('the isolated point detec

7、ted (only a part displayed)');=2線 (通常假定一個(gè)象素厚度) 檢測 原理與上同，典型模板有（主要方向性）：實(shí)例：-450 方向線的檢測： 3邊沿檢測方法：使用一階或者二階導(dǎo)數(shù)。對一節(jié)導(dǎo)數(shù)，關(guān)鍵問題是怎樣估計(jì)水平和垂直方向的梯度Gx 和Gy，二階導(dǎo)數(shù)通常使用Laplacian算子計(jì)算，但是Laplacian算子很少單獨(dú)用來檢測邊緣，因?yàn)槠鋵υ肼暦浅Ｃ舾校移浣Y(jié)果會產(chǎn)生雙邊沿，加大了邊緣檢測的困難。然而，如果Laplacian算子能與其他邊緣檢測算法相結(jié)合，如邊緣定位算法，則其是一個(gè)強(qiáng)有力的補(bǔ)充。通常兩個(gè)標(biāo)準(zhǔn)用來測度圖像強(qiáng)度的迅速變化：(1) 找出強(qiáng)度的一

8、階導(dǎo)數(shù)值大于某個(gè)事先閾值標(biāo)準(zhǔn)的位置；(2) 找出圖像二階導(dǎo)數(shù)的跨零點(diǎn)。IPT 工具箱函數(shù)edge 提供了幾種基于上面兩種標(biāo)準(zhǔn)的估計(jì)器：其語法為：g, t = edge(f, method, parameters);這里 method 參數(shù)包括這幾種類型的邊緣檢測子：Sobel, Prewitt, Roberts, Laplacian of a Gaussian (LoG), Zero crossings and Canny，前三種的模板見下圖： 另一個(gè)強(qiáng)有力的邊緣檢測器：Canny Edge Detector (Canny 1986)，其算法的基本步驟如下：(1) First, the ima

9、ge is smoothed using a Gaussian filter with a specified standard deviation s(2) The local gradient, g(x, y) = Gx2+Gy21/2, and edge direction, q(x, y) = tan-1(Gy /Gx), are computed at each point. Any of the first three techniques can be used to computer the Gx and Gy. An edge point is defined to be a

10、 point whose strength is locally maximum in the direction of the gradient.(3) The edge points give rise to ridges in the gradient magnitude image. The algorithm then tracks along the top of these ridges and sets to zero all pixels that are not actually on the ridge top so as to give a thin line, a p

11、rocess known as nonmaximal suppression. The ridge pixels are the thresholded using thresholds, T1 and T2, with T1 < T2. Ridge pixels with values greater than T2 are said to be “strong” edge pixels and pixels between T1 and T2 “weak” edge pixels.(4) Finally, the algorithm performs edge linking by

12、incorporating the weak pixels that are 8-connected to strong pixels.注意：Edge function does not compute edges at ±450. To compute edges we need to specify the mask and use imfilter. 4Hough變換In practice, the resulting pixels produced by the methods discussed in the previous sections seldom charact

13、erize an edge completely because of noise, breaks from nonuniform illumination, and other effects that introduce spurious discontinuities. Hough Transform is one type of linking procedure to find and link line segments for assembling edge pixels into meaningful edges.About the principle of Hough tra

14、nsform, please refer to page 586 in textbook.Instance of Hough transform:% constructing an image containing 5 isolated foreground pixels in several locaitons:f = zeros(101, 101);f(1, 1) = 1, f(101, 1) = 1, f(1, 101) = 1, f(101, 101) = 1, f(51, 51) = 1;H, theta, rho = hough(f); % hough transformimsho

15、w(theta, rho, H, , 'notruesize');axis on, axis normal;xlabel('theta'), ylabel('rho');圖象分割圖像分割是將圖像劃分成若干個(gè)互不相交的小區(qū)域的過程， 小區(qū)域是某種意義下具有共同屬性的像素的連通集合。如不同目標(biāo)物體所占的圖像區(qū)域、 前景所占的圖像區(qū)域等。連通是指集合中任意兩個(gè)點(diǎn)之間都存在著完全屬于該集合的連通路徑。單色（灰度）圖像的分割通常是基于圖像強(qiáng)度的兩個(gè)基本特征：灰階值的不連續(xù)性和灰度區(qū)域的相似性。第一類方法主要是基于圖像灰階值的突然變換（如邊緣）來分割圖像，而

16、第二類方法主要是把圖像的某個(gè)子區(qū)域與某預(yù)定義的標(biāo)準(zhǔn)進(jìn)行比較，以二者之間的相似性指標(biāo)為指導(dǎo)來劃分圖像區(qū)域：如閾值化技術(shù)、面向區(qū)域的方法、形態(tài)學(xué)分水嶺分割算法等。1.雙峰法先給出原圖的直方圖，再定出閾值(門限)T，一般取兩個(gè)峰值間的谷值。2.P參數(shù)法這種方法用于目標(biāo)所占圖像面積已知的情況。設(shè)目標(biāo)在最簡單圖像f(i , j) 中所占的面積s0與圖像面積s之比為P = s0/ s，則背景所占面積比為1-P = (s - s0) / s。一般來說，低灰度值為背景，高灰度值為目標(biāo)。如果統(tǒng)計(jì)圖像f(i , j)灰度值不大于某一灰度t的像元數(shù)和圖像總像元數(shù)之比為1-p時(shí)，則以t為閾值。3自適應(yīng)全局閾值（單閾值

17、）算法步驟如下：1、 初始化閾值T (一般為原圖像所有像素平均值)。2、 用T分割圖像成兩個(gè)集合：G1 和G2，其中G1包含所有灰度值小于T的像素，G2包含所有灰度值大于T的像素。3、 計(jì)算G1中像素的平均值m1及G2中像素的平均值m2。4、 計(jì)算新的閾值：T （m1m2）/2 。5、 如果新閾值跟原閾值之間的差值小于一個(gè)預(yù)先設(shè)定的范圍，停止循環(huán)，否則繼續(xù)24步。全局單閾值分割只適用于很少的圖像。對一般圖像采用局部閾值法或多閾值法會得到更好的效果4. 最大類間方差法 (OTSU)設(shè)有M-1個(gè)閾值：0k1k2KM-1L-1。將圖像分割成M個(gè)灰度值的類Cj， （Cjkj-1+1, , kj；j=1

18、, 2, , M ; k0=0, kM=L），則各類Cj的發(fā)生概率j和平均值j為 (3-1) (3-2)式中, (0)=0，(0)=0。 由此可得各類的類間方差為 (3-3)將使上式的2值為最大的閾值組(k1, k2， , kM1)， 作為M值化的最佳閾值組。若取M為2，即分割成2類，則可用上述方法求出二值化的閾值。三實(shí)驗(yàn)提示1.MATLAB的圖像處理工具箱中提供的edge函數(shù)可以實(shí)現(xiàn)檢測邊緣的功能，其語法格式如下：BW = edge (I,sobel)BW = edge (I,sobel, thresh,direction)BW = edge (I, Roberts)BW = edge (I

19、, log)BW = edge (I, log, thresh, sigma)BW = edge (I, canny)BW = edge (I,canny, thresh, sigma)這里BW = edge(I,'sobel')采用Sobel算子進(jìn)行邊緣檢測。BW = edge(I,'sobel',direction)可以指定算子方向，即：direction= horizontal ，為水平方向；direction= vertical ， 為垂直方向；direction= both ， 為水平和垂直兩個(gè)方向。BW = edge(I,'canny'

20、;,thresh,sigma)和BW = edge(I,'log',thresh,sigma)分別為用canny算子和拉普拉斯高斯算子進(jìn)行邊緣檢測。選項(xiàng)log和canny的Sigma默認(rèn)值分別為2.0和1.0。例：用三種算子進(jìn)行邊緣檢測。I=imread('eight.tif');imshow(I)BW1=edge(I,'roberts');figure ,imshow(BW1),title('用Roberts算子')BW2=edge(I,'sobel');figure,imshow(BW2),title('

21、;用Sobel算子 ')BW3=edge(I,'log');figure,imshow(BW3),title('用拉普拉斯高斯算子') 2也可以通過，如拉普拉斯模板（有好幾個(gè)）：i=imread('w01.tif')I=doubole(i);h=0,1,0;1,-4,0;0,1,0j= conv2(I,h,same);k=I-j;imshow(k, );3I>T 結(jié)果為一個(gè)邏輯值矩陣，I中大于T的值對應(yīng)的位置為1（真），其余位置為0（假）。I(I> T) 表示I 中所有大于T的值組成的向量。255* (I>T) + 0*

22、(I<=T) 可將I中大于T的像素值設(shè)為255，小于等于T的像素值設(shè)為0。四、練習(xí)1 點(diǎn)、線和邊緣檢測111 點(diǎn)檢測 點(diǎn)檢測模板w：-1-1-1-18-1-1-1-1檢測方法： g=abs(imfilter(double(f), w)>=T練習(xí)1f=imread(moon.tif);w=-1 -1 -1; -1 8 -1; -1 -1 -1;g=abs(imfilter(double(f), w);T=max(g(:);T=T*0.5;g=g>=T;imshow(f); figure, imshow(g);線檢測水平模板、+45度模板、垂直模板、-45度模板。練習(xí)2f=imr

23、ead(circbw.tif);imshow(f);w=2 -1 -1; -1 2 -1; -1 -1 2;g=abs(imfilter(double(f), w);figure,imshow(g);使用edge函數(shù)的邊緣檢測語法：g,t=edge(f, method, parameter)說明：g是一個(gè)邏輯數(shù)組，其值為：在f中檢測到邊緣的位置為1，其他位置為零；t是edge是用的閾值；method為邊緣監(jiān)測器方法，可選為： sobel, prewit, roberts, log(LoG), zerocoss, canny等；parameter包含兩部分：T為指定的閾值，第二部分為dir（檢測

24、邊緣的首選方向： horizontal, vertical, both），或sigma（標(biāo)準(zhǔn)方差），或H（指定的濾波函數(shù)）。練習(xí)3f=imread(rice.tif);imshow(f);gsobel,t=edge(f, sobel);figure, imshow(gsobel);glog,t=edge(f, log);figure, imshow(glog);gcanny,t=edge(f, canny);figure, imshow(gcanny);22 使用Hough變換的線檢測練習(xí)4設(shè)計(jì)與實(shí)現(xiàn)一個(gè)基于Hough變換的直線檢測器。23 閾值處理231 全局閾值處理語法：T=graythr

25、esh(f)說明：T是閾值，歸一化為0至1之間的值。232 局部閾值處理通過一個(gè)形態(tài)學(xué)頂帽算子并對得到的結(jié)果使用graythresh來計(jì)算。練習(xí)5f=imread(moon.tif);imshow(f);T=graythresh(f);g=f>=T;figure, imshow(g);24 基于區(qū)域的分割241 區(qū)域生長 242 區(qū)域分裂和合并練習(xí)6設(shè)計(jì)與實(shí)現(xiàn)一個(gè)基于區(qū)域生長的分割程序。25 使用分水嶺變換的分割練習(xí)7f=imread(cell.tif);imshow(f);g=im2bw(f, graythresh(f);figure,imshow(g);gc=g;D=bwdist(g

26、c);L=watershed(-D);w=L= =0;g2=g&w;figure,imshow(g2);26 分割后處理語法：BW2 = bwfill(BW1,c,r,n)說明：填充二進(jìn)制圖像的背景色。（形態(tài)學(xué)處理）練習(xí)8BW1 =1 0 0 0 0 0 0 01 1 1 1 1 0 0 01 0 0 0 1 0 1 01 0 0 0 1 1 1 01 1 1 1 0 1 1 11 0 0 1 1 0 1 01 0 0 0 1 0 1 01 0 0 0 1 1 1 0BW2 = bwfill(BW1,3,3,8)I = imread('blood1.tif');BW3

27、= im2bw(I);BW4 = bwfill(BW3,'holes');imshow(BW3)figure, imshow(BW4)語法：bwareaopen說明：二進(jìn)制圖像區(qū)域打開，清除小物體。五. 部分參考程序和參考結(jié)果1房屋輪廓描繪代碼：f = imread('Fig1006(a)(building).tif');gv, t = edge(f, 'sobel', 'vertical'); % using threshold computed automatically, here t = 0.0516subplot(231

28、);imshow(f, );title('the original image');subplot(232);imshow(gv, );title('vertical edge with threshold determined automatically');gv1 = edge(f, 'sobel', 0.15, 'vertical'); % using a specified threshold.subplot(233);imshow(gv1, );title('vertical edge with a specif

29、ied threshold');gboth = edge(f, 'sobel', 0.15); % edge detection of two directionssubplot(234);imshow(gboth, );title('horizontal and vertical edge');% edge detection of 450 direction using imfilter functionw45 = -2 -1 0; -1 0 1; 0 1 2;g45 =imfilter(double(f), w45, 'replicate&

30、#39;);T = 0.3*max(abs(g45(:);g45 = g45 >= T;subplot(235);imshow(g45, );title('edge at 45 with imfilter');wm45 = 0 1 2; -1 0 1; -2 -1 0;g45 =imfilter(double(f), wm45, 'replicate');T = 0.3*max(abs(g45(:);g45 = g45 >= T;subplot(236);imshow(g45, );title('edge at -45 with imfilt

31、er');另一個(gè)實(shí)驗(yàn)：為比較三種檢測方法的相對性能：Sobel, LoG 和 Canny edge detectors，和為了改善檢測效果所需使用的技巧。% using the default thresholdf = imread('Fig1006(a)(building).tif');gs_default, ts = edge(f, 'sobel'); % ts = 0.074gl_default, tl = edge(f, 'log'); % tl = 0.002 and the default sigma = 0.2gc_defa

32、ult, tc = edge(f, 'canny'); % tc = 0.0189 0.047 and the default sigma = 0.1% using the optimal threshold acquired by manual testgs_best = edge(f, 'sobel', 0.05);gl_best = edge(f, 'log', 0.003, 2.25);gc_best = edge(f, 'canny', 0.04 0.1, 1.5); The left column in above f

33、igure shows the edge images obtained using the default syntax for the sobel, log and canny operator respectively, whereas the right column are the results using optimal threshold and sigma values obtained by try.2Hough變換用于線檢測從而增強(qiáng)邊緣的連續(xù)性2.1 Hough transform for peak detectionPeak detection is the first

34、 step in using Hough transform for line detection and linking. However, finding a meaningful set of distinct peaks in a Hough transform can be challenging. Because of the quantization in space of the digital image and in parameter space of the Hough transform, as well as the fact that edges in typic

35、al images are not perfectly straight, Hough transform peaks tend to lie in more than one Hough transform cell. One strategy to overcome this problem is following:(1) find the HT cell containing the highest value and record its location;(2) suppress (set to zero) HT cells in the immediate neighborhoo

36、d of the maximum;(3) repeat until the desired number of peaks has been found, or until a specified threshold has been reached.function%HOUGHPEAKS Detect peaks in Hough transform.% R, C, HNEW = HOUGHPEAKS(H, NUMPEAKS, THRESHOLD, NHOOD) detects% peaks in the Hough transform matrix H. NUMPEAKS specifie

37、s the% maximum number of peak locations to look for. Values of H below% THRESHOLD will not be considered to be peaks. NHOOD is a% two-element vector specifying the size of the suppression% neighborhood. This is the neighborhood around each peak that is% set to zero after the peak is identified. The

38、elements of NHOOD% must be positive, odd integers. R and C are the row and column% coordinates of the identified peaks. HNEW is the Hough transform% with peak neighborhood suppressed. % If NHOOD is omitted, it defaults to the smallest odd values >=% size(H)/50. If THRESHOLD is omitted, it default

39、s to% 0.5*max(H(:). If NUMPEAKS is omitted, it defaults to 1. =2.2 HT for line detection and linkingFor each peak, the first step is to find the location of all nonzero pixels in the image that contributed to that peak. This purpose can be implemented by the following function:function%HOUGHPIXELS C

40、ompute image pixels belonging to Hough transform bin.% R, C = HOUGHPIXELS(F, THETA, RHO, RBIN, CBIN) computes the% row-column indices (R, C) for nonzero pixels in image F that map% to a particular Hough transform bin, (RBIN, CBIN). RBIN and CBIN% are scalars indicating the row-column bin location in

41、 the Hough% transform matrix returned by function HOUGH. THETA and RHO are% the second and third output arguments from the HOUGH function. The pixels associated with the locations found using houghpixles must be grouped into line segments, which is programmed into the following function:function%HOU

42、GHLINES Extract line segments based on the Hough transform.% LINES = HOUGHLINES(F, THETA, RHO, RR, CC, FILLGAP, MINLENGTH)% extracts line segments in the image F associated with particular% bins in a Hough transform. THETA and RHO are vectors returned by% function HOUGH. Vectors RR and CC specify th

43、e rows and columns% of the Hough transform bins to use in searching for line% segments. If HOUGHLINES finds two line segments associated with% the same Hough transform bin that are separated by less than% FILLGAP pixels, HOUGHLINES merges them into a single line% segment. FILLGAP defaults to 20 if omitted. Merged line%