十几何变换.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,几何运算,平移,旋转,放大缩小,反转,延展,几何变形,实 例,平移，旋转,三维的平移,点击图片,播放视频,PROBLEM,SOLUTION,f,(,x,y,),g,(,x,y,),Nearest neighbour,Bilinear,Bicubic,.,Nearest Neighbour(Zero order),:,Example:From which input pixel(1,2,3 or 4)would you get the gray level of the output pixel?,1,2,34,1,Interpolation methods,:,f,(,x,y,),g,(,x,y,),Bilinear(First-Order)Interpolation,:,Gray level at non-integer coordinates found by interpolating values of four(4)neighbouring pixels using,bilinear,function.,x,y,g(,x,y,),f,(,x,y,),Bilinear vs Nearest Neighbour,:,Original,Nearest Neighbour,Bilinear,几何运算,线性内插,双线性内插,双线性内插,P118 Eq.(2),双线性方程,双线性内插,p.118,上海交大学生作品,透,视,F0108201,张丹枫作品,透,视,透,视,透,视,点击图片 播放,FLASH,可按,Alt+F4,退出,FLASH,E.g.,image warping,近朱者赤,点击图片,播放视频,变形的脸,变形的狗嘴,点击图片,播放视频,几何运算,几何校正用于校正：,透视失真,枕形失真,桶形失真,Geometric calibration,E.g.,barrel distortion(shown below);pin-cushion distortion,Correct by imaging a known grid pattern and designing a warping function based on known pattern and imaged pattern.,Image rectification,E.g.,polar scans in ultrasound:convert from(,r,)coordinate system to(,x,y,),r,Image rectification(contd),Original image:,After rectification:,几何校正,P118 Eq.(19),双线性空,间变换方程,f,x,y,),g,(,x,y,),g,(,x,y,),Gray-Level Interpolation,(1)Forward Mapping,-compute new coordinates,-,then“spread”gray level over four neighbouring pixels using interpolation,(2),Backward Mapping,E.g.,for translation,-,(,i,j,),could in general fall between non-integer coordinates,-obtain gray-level at coordinates,(,i,j,),using interpolation,f,(,x,y,),g,(,x,y,),Many input pixels may map outside border of output image,Each output pixel may be addressed many times,with many input pixels contributing to final gray level(esp.for demagnification),Forward mapping is,wasteful,:,f,(,x,y,),g,(,x,y,),Backward mapping is,more practical,:,In backward mapping,gray level of each output pixel is determined by,one interpolation,step between,exactly 4,input pixels,f,(,x,y,),g,(,x,y,),Backward mapping is more practical,although calculating inverse operation may be difficult.,p.122,p.126,p.127,p.128,p.123,Control Point,pp.120-121,平移,放大 变换公式,旋转,The aspect of the organ models deformation,Control Point,Data Fusion System for Supporting the Surgery,Time sequential image of walking,Control PointPosition Marker,4-,dimensional musculoskeletal model,点击图片,播放视频,一个广告的制作过程,控制点的运用,怎样让骷髅动得更逼真？,点击图片 播放,FLASH,可按,Alt+F4,退出,FLASH,点击图片 播放,FLASH,可按,Alt+F4,退出,FLASH,点击图片 播放,FLASH,可按,Alt+F4,退出,FLASH,几何变换之大集成,图象配准,没配准的后果,欲盖弥彰的配准,Image registration,E.g.,may image a tumor at two different instants in time and may want to check if it is growing.,E.g.,Surveying land:Image 1 shows an area of Mojave desert;2 shows adjacent area3 formed by registering overlapping regions and stitching images together.,1,2,3,Multispectral Tissue Classification,T,1,T,2,3,D Histogram,Segmented,Image,配准,配准,点击图片 播放,FLASH,可按,Alt+F4,退出,FLASH,图象变形(,Image morphing),p.137 Figure 8-17,点击图片,播放视频,Image morphing,Note,we are warping from one image to a,different,image.Compare with Einstein example.,-used in motion pictures&animation,反过来变换，岂不更好？,点击图片,播放视频,点击图片,播放视频,哭笑不得的表情是怎样生成的？,点击图片,播放视频,返老还童不是梦（在屏幕上）,成 长,制图学应用,对准地球按住鼠标左键移动,点击图片 播放,FLASH,可按,Alt+F4,退出,FLASH,Terms,Geometric correction,Geometric calibration:,几何校正,Spatial transformation:,空间变换,Interpolation:,内插，插值,Nearest neighbor interpolation:,最近邻点,内插,Bilinear interpolation:,双线性内插,Extrapolation:,外插,Terms,Zoom in:,放大,Zoom out:,缩小,Hyperbolic paraboloid:,双曲抛物面,Image rectification:,图象矫正,Image registration:,图象定位，图象配准,Cartography:,制图学,Projection:,投影,Terms,Image morphing:,图象变形,Control point:,控制点,Control grid:,控制栅格,Polynomial warping:,多项式卷绕,