数字图像处理第3章课件

DigitalImageProcessing,3rded.第三章灰度变换与空间滤波灰度变换：g(x,y)=T[f(x,y)]其中：f/g分别是I/O图像；T是f的上的操作，与(x,y)的邻域有关图像坐标系DigitalImageProcessing,3rded.当邻域为1*1时，T有最简单形式——点运算反差增强的灰阶转换函数DigitalImageProcessing,3rded.crsrcsrLs)1lg(1反转增强暗部增强亮部其中c,r和γ为正数3.2一些基本灰度转换函数DigitalImageProcessing,3rded.rLs1a.原照片b.反转照片,其中小病变和乳房组织更清晰DigitalMammogram数字乳房X线照片例一DigitalImageProcessing,3rded.Fourier频谱图及其Log转换图例二[0到1,500,000]线性压到8bit[0,255],突出显示最大的变换系数,牺牲小的变换系数。[0到1,500,000]用常用对数Lg压到[0到6.2].c=1增强显示小的变换系数,突出细节。DigitalImageProcessing,3rded.指数幂变换crs其中c和γ为正常数，图中c=1。γ1的效果与γ1的效果相反。DigitalImageProcessing,3rded.许多图像外设都采用指数γ校正。比如CRT显示器的响应有γ=[1.8,2.5],而LCD显示器的γ=2.2γ=1/2.5=0.4DigitalImageProcessing,3rded.指数幂转换也用于通用的反差增强处理原图γ=0.6γ=0.4γ=0.2crsc=1例三a，增强暗部DigitalImageProcessing,3rded.例三b，增强亮部原图γ=3.0γ=4.0γ=5.0crsc=1DigitalImageProcessing,3rded.3.2.4分段线性变换函数变换函数的图形原图变换图二值化扩展中间灰度，压缩两边DigitalImageProcessing,3rded.灰度级分层DigitalImageProcessing,3rded.位平面分层8bit图像的位平面表示，各个平面的重要性不同。DigitalImageProcessing,3rded.左上图的8个位图（二值图,第0到第7个比特）DigitalImageProcessing,3rded.使用最显著的2,3,4个比特面的效果DigitalImageProcessing,3rded.DigitalImageProcessing,3rded.3.3HistogramProcessing直方图处理4种基本的图像类型低调/暗图像高调/亮图像低反差图像高反差图像DigitalImageProcessing,3rded.灰度变换函数TT非单调,多r对一sT严格单调,1对1映射,可逆DigitalImageProcessing,3rded.ProbabilityDensityFunctionDigitalImageProcessing,3rded.3.3.1HistogramEqualization直方图均衡一个单值单调上升的灰度变换函数。12,1,0)()(00LknnrprTskjjkjjrkk灰度变换函数采用的是累积概率分布函数：DigitalImageProcessing,3rded.直方图均衡的表解例：64×64*23bits灰度图象n=64×64,灰度级范围[0，L-1],输入灰度值为lk,出现的频数为nk,归一化灰度值rk=lk/(L-1),概率p(rk)=nk/n,累计概率分布Sk=T(rk)=p(r0)+p(r1)+…+p(rk),输出灰度值sk=lk’=[Sk*(L-1)],DigitalImageProcessing,3rded.输入灰度值为lk,出现的频数为nk,归一化灰度值rk=lk/(L-1),概率p(rk)=nk/n,累计概率分布Sk=T(rk)=p(r0)+p(r1)+…+p(rk),输出灰度值sk=lk’=[Sk*(L-1)],DigitalImageProcessing,3rded.64*64*3比特的直方图和PDF直方图是离散的/近似的PDFDigitalImageProcessing,3rded.直方图均衡后的灰度级数量(动态范围)并没有减少，减少的是非零频数的灰度级数。DigitalImageProcessing,3rded.DigitalImageProcessing,3rded.直方图均衡的关键：累计频数作为转换函数DigitalImageProcessing,3rded.3.3.2HistogramMatching(Specification)规定的直方图规定化的直方图DigitalImageProcessing,3rded.规定的直方图规定化得到的直方图DigitalImageProcessing,3rded.一张火星卫星的图像DigitalImageProcessing,3rded.直方图均衡上图的直方图均衡效果——总体上偏亮DigitalImageProcessing,3rded.直方图规定化(1)是手工定义直方图的累计频数；(2)是(1)的反函数。将(2)应用于右下图的效果如图c.DigitalImageProcessing,3rded.3.3.3LocalEnhancement3*3子图做均衡(a)原图(b)整体直方图均衡(c)局部直方图均衡DigitalImageProcessing,3rded.3.3.4用直方图统计量进行图像增强钨丝缠绕的扫描电镜图像(SEM)DigitalImageProcessing,3rded.otherwiseyxfDkDkMkmyxfEyxgGSGGSxyxy,),(,),(),(210且当xyxyStststsSrprm),(,,)(xyxyStstssttsSrpmr),(,2,2)(][p(r)是对应灰度值r的归一化的局部直方图分量，S表示某邻域；k[0,1],M,D是整图的均值,方差(b)(a)(c)实验数据：K0=0.4K1=0.02K2=0.4E=4.0DigitalImageProcessing,3rded.比较原图：虽然亮部不变，只有一些暗部被增强，但也包括一些不该增强的。本例的思想可以举一反三，用于其它局部增强。DigitalImageProcessing,3rded.3.4BasicsofSpatialFiltering掩模/模板掩模下的子图DigitalImageProcessing,3rded.线性滤波的通式（3.4-1）aasbbttysxftswyxg),(),(),(m*n是滤波器的大小,a=(m-1)/2,b=(n-1)/2∑∑--),(aasbbttsw==使用时，g(x,y)要除以比例因子点(x,y)周围像素的加权和DigitalImageProcessing,3rded.模板卷积•图象f(x,y)大小N×N•模板(filtermask,template),m×m相关：模板T(i,j)1010),(),(),(),(mimjjyixfjiTyxfTyxg其中x=1,2,…N-m+1;y=1,2,…N-m+1．当m=3时，)2,2()2,2()1,()1,0(),()0,0(),(yxfTyxfTyxfTyxgDigitalImageProcessing,3rded.卷积：aaibbjjyixfjiWyxfyxwyxg),(),(),(),(),(当m,n为奇数（2a+1)和(2b+1)时：演示：lectures_2D_3_linear_filtering_1up.pdf模板w(i,j),m×nDigitalImageProcessing,3rded.DigitalImageProcessing,3rded.DigitalImageProcessing,3rded.3.4.3线性滤波器的向量表示:点积zwzwzwzwRT992211zwzwzwzwRTmnmn2211wzDigitalImageProcessing,3rded.3.5平滑空间滤波器两个平滑滤波器DigitalImageProcessing,3rded.平均滤波器大小从3、5、9、15到35的平滑效果DigitalImageProcessing,3rded.太空望远镜图像平滑二值化DigitalImageProcessing,3rded.3.5.2Order-StatisticsFilter排序统计量滤波器+椒盐噪声均值滤波中值滤波需要用Photoshop实例演示，LinearfilteringinMatlabhelp？DigitalImageProcessing,3rded.3.6SharpeningSpatialFilters3.6.1Foundation)()1(xfxfxf)(2)1()1(22xfxfxfxf锐化DigitalImageProcessing,3rded.一段信号的一阶和二阶微分DigitalImageProcessing,3rded.3.6.2利用二阶微分作图像增强——Laplacian算子22222yfxff2222),(),(),(),(),(凸形凹形yxfyxfyxfyxfyxg),(4)]1,()1,(),1(),1([2yxfyxfyxfyxfyxff用Laplacian算子做增强：其中：),(2-),1-(),1(∂∂22yxfyxfyxfxf++=),(2-)1-,()1,(∂∂22yxfyxfyxfyf++=DigitalImageProcessing,3rded.)76.3(),(),(),(),(),(2222凸形凹形yxfyxfyxfyxfyxgDigitalImageProcessing,3rded.3.6.3Unsharpmasking&high-boostfiltering钝化/非锐化?DigitalImageProcessing,3rded.),(),(),(yxfyxfyxgmask),(yxf),(yxf),(),(),(yxgyxfyxgmask),(),(),(yxgkyxfyxgmaskk1Unsharpmasking&high-boostfilteringunsharpmaskinghigh-boostfilteringDigitalImageProcessing,3rded.在Matlab中定义特定类型的２维滤波器H=FSPECIAL(TYPE)类型：•'average'averagingfilter•'disk'circularaveragingfilter•'gaussian'Gaussianlowpassfilter•'laplacian'filterapproximatingthe2-DLaplacianoperator•'log'LaplacianofGaussianfilter•'motion'motionfilter•'prewitt'Prewitthorizontaledge-emphasizingfilter•'sobel'Sobelhorizontaledge-emphasizingfilter•'unsharp'unsharpcontrastenhancementfilterDigitalImageProcessing,3rded.例：•I=imread('moon.tif');•h=fspecial('laplacian');•I1=imfilter(I,h);•h=fspecial('unsharp');%'laplacian'•I2=imfil