Chap 5 Geometric Operations课件.pptVIP

Chap 5 Geometric Operations;Chap 5 Geometric Operations;Chap 5 Geometric Operations;Consider: 设: 输入图像大小为(w, h)，输出图像大小为(W, H) 根据(W,H)和(w,h)大小比较，可以将图像的比例变换分为：拉伸和压缩 比例变换的步骤 设：输出图像中点(x,y)与输入图像中点(a,b)相对应，则它们满足以下公式：x=a*W/w,y=b*H/h f(x,y)=f(a,b);“See geometric_operation.m” Problems: 拉伸时，按公式：x=a*W/w, y=b*H/h，则输出图像中有一些像素无法与输入图像中的像素对应起来。 压缩时，按公式：x=a*W/w, y=b*H/h，输入图像中多个像素点会与输出图像中的1个像素点对应。;5.1 Grey-level Interpolation;5.1 Grey-level Interpolation;5.1 Grey-level Interpolation;5.1 Grey-level Interpolation;First-Order (Bilinear Interpolation) What is “Bilinear (双线性)”? Linear Expression “...which is of first degree in its variable (or variables).” ? y=x+1, y=x*x+x+1 This is a linear expression.;First-Order (Bilinear Interpolation) Bilinear (双线性) “A mathematical expression is bilinear if it is linear WRT (With Respect To, 关于) each of 2 variables or positions.” Note: “Bilinear” does not mean that it is the simple superposition (重叠) of linear expressions.;Consider: 已知：f(0,0), f(0,1), f(1,0), f(1,1) 试用双线性插值方法求：f(x,y), 其中，0?x?1, 0?y?1。 Note: for sake of discussion, normalize to unit size, 0x1, 0y1 ;First-Order (Bilinear Interpolation) Solution is overdetermined (超定的) for a plane since we have four points. Use hyperbolic (双曲线的) Paraboloid (抛物面的) f(x,y)=ax+by+cxy+d ;First-Order (Bilinear Interpolation) f(x,y)=ax+by+cxy+d Simpler methods of computing is using constituent (成分，组成) equations;Example of bilinear interpolation 设: f(0,0)=2,f(1,0)=3,f(0,1)=1,f(1,1)=4 则: f(x,y)=x-y+2xy+2;The steps of Bilinear interpolation Step1: 定义双线性方程组 f(x,y)=ax+by+cxy+d Step2: 代入已知4点的值， 求解方程组 Step3: 求f(x,y);Drawback of Bilinear Interpolation : 在几何运算中，双线性插值的平滑作用可能使细节产生退化，尤其在进行放大处理时，这种影响更为明显。 在其他应用中，双线性插值的斜率不连续会产生不希望的结果。 这两种情况都可通过高阶插值得到修正，当然需要增加计算量。;Matlab example;5.2 Spatial Transformations;Simple Transformation Coordinate Translation Coordinate Scaling Coordinate Rotation Compound Transformation Geometric calibration (校正) General Transformation (Image Wa