1、由明暗度提取外形信息朱俊 0220080198一 实验内容1 由图像的明暗度提取外形信息二 实验原理1 Shape From Shading维理解是通过物体表面的明暗度 Shading 分布去提取得到物体外形2Shading 信息的一种表达方法。人们把明暗度分布的图像称为外现图像（extrinsic image） ，把 表达称为内在图像（intrinsic image） ，表示这是排21除了光线的影响后直接反映出物体外形的图像。2 约束方程从外现图像到内在图像所要做的工作就是解图像辉度约束方程：I(x,y)=R(p,q)即 1)(),( 220ssqpIyxI其中 为入射光的强度， 为物体表面
2、反射系数03 迭代求解 )1,()1,(),1(),1(4),( , ),(),(1),(),( , N1 yxqyxqxqyxqyxq ppppp RqyxIyxqpp NNNNNNN 三 实验步骤首先用 matlab 生成一个灰度的球，具体操作如下：sphere；生成一个球colormap gray;使得彩色的球变成灰度的axis off;去掉多余的坐标轴 axis equal;使得椭球变成圆球shading flat;和 shading interp 使得圆球表面光滑光线入射角为默认的 0 度，入射光强度和球表面的反射系数未知。得到的球如图所示：23202320)1()(qpIRPIss
3、代入初始 p，q0，则显然迭代结果也是 0代入初始 p，q无穷，则 和 也为无穷，迭代结果也不收敛pR因此需要进行坐标变换，使边界值为有限值。所以采用高斯球系统将球投影到 fg 平面，可得关系： 221,qpgf把原来的迭代公式转化为： jiNNN jigRyxfRyxIgyx ffff ,1 ,),(),(),(),(),( , 四 实验结果迭代的开始点，在遮合边界上 fi,j0=2， gi,j0=2，里面点为 fi,j0=0， gi,j0=0，把图压缩成 1919 的，则迭代结果为：0,0 0,0 0,0 0,0 0,0 0,0 0,0 -0.434,-1.952 -0.221,-1.98
4、8 0.000,-2.000 0.221,-1.988 0.434,-1.952 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 -0.894,-1.789 -0.474,-1.156 -0.339,-1.344 -0.171,-1.376 -0.000,-1.384 0.171,-1.376 0.338,-1.344 0.474,-1.156 0.894,-1.789 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 -1.162,-1.627 -0.741,-1.257 -0.506,-1.106 -0.333,-1.1
5、22 -0.167,-1.140 -0.000,-1.146 0.166,-1.140 0.332,-1.121 0.505,-1.105 0.739,-1.254 1.162,-1.627 0,0 0,0 0,0 0,0 0,0 0,0 0,0 -1.414,-1.414 -0.932,-1.102 -0.687,-0.994 -0.515,-0.978 -0.349,-0.999 -0.178,-1.023 -0.000,-1.030 0.177,-1.023 0.349,-0.999 0.513,-0.975 0.687,-0.993 0.932,-1.102 1.414,-1.414
6、0,0 0,0 0,0 0,0 0,0 -1.627,-1.162 -1.122,-0.927 -0.858,-0.838 -0.693,-0.834 -0.542,-0.863 -0.378,-0.901 -0.195,-0.931 -0.000,-0.943 0.195,-0.931 0.378,-0.900 0.542,-0.863 0.692,-0.834 0.858,-0.838 1.122,-0.927 1.627,-1.162 0,0 0,0 0,0 0,0 -1.736,-0.992 -1.092,-0.711 -0.869,-0.673 -0.724,-0.696 -0.58
7、3,-0.744 -0.417,-0.799 -0.220,-0.842 -0.000,-0.858 0.219,-0.842 0.417,-0.799 0.583,-0.744 0.724,-0.696 0.869,-0.673 1.092,-0.711 1.736,-0.992 0,0 0,0 0,0 -1.873,-0.702 -1.327,-0.575 -1.037,-0.510 -0.891,-0.518 -0.768,-0.554 -0.635,-0.610 -0.464,-0.670 -0.245,-0.709 -0.001,-0.720 0.243,-0.708 0.464,-
8、0.670 0.635,-0.610 0.769,-0.555 0.891,-0.518 1.037,-0.510 1.325,-0.574 1.873,-0.702 0,0 0,0 -1.940,-0.485 -1.273,-0.359 -1.038,-0.338 -0.919,-0.356 -0.814,-0.392 -0.685,-0.440 -0.494,-0.479 -0.251,-0.489 -0.001,-0.483 0.248,-0.486 0.494,-0.478 0.686,-0.440 0.817,-0.394 0.919,-0.357 1.038,-0.338 1.27
9、2,-0.359 1.940,-0.485 0,0 0,0 -1.985,-0.248 -1.277,-0.178 -1.055,-0.171 -0.939,-0.182 -0.846,-0.205 -0.716,-0.231 -0.494,-0.242 -0.232,-0.229 -0.001,-0.230 0.230,-0.228 0.493,-0.242 0.715,-0.232 0.847,-0.206 0.942,-0.183 1.055,-0.171 1.274,-0.177 1.985,-0.248 0,0 0,0 -2.000,0.000 -1.278,-0.000 -1.06
10、0,-0.001 -0.950,-0.002 -0.859,-0.003 -0.722,-0.005 -0.480,-0.006 -0.230,-0.007 -0.000,-0.007 0.229,-0.007 0.479,-0.007 0.719,-0.006 0.859,-0.004 0.950,-0.003 1.060,-0.001 1.281,-0.000 2.000,0.000 0,0 0,0 -1.985,0.248 -1.274,0.176 -1.055,0.169 -0.939,0.179 -0.846,0.199 -0.713,0.221 -0.490,0.228 -0.23
11、0,0.214 -0.000,0.214 0.229,0.214 0.488,0.226 0.713,0.220 0.846,0.198 0.939,0.178 1.055,0.168 1.274,0.176 1.985,0.248 0,0 0,0 -1.940,0.485 -1.272,0.358 -1.037,0.336 -0.915,0.352 -0.811,0.386 -0.682,0.430 -0.488,0.462 -0.245,0.466 0.000,0.457 0.246,0.466 0.488,0.461 0.685,0.430 0.812,0.385 0.916,0.351
12、 1.037,0.336 1.272,0.358 1.940,0.485 0,0 0,0 -1.873,0.702 -1.324,0.573 -1.033,0.507 -0.887,0.515 -0.767,0.551 -0.632,0.603 -0.459,0.658 -0.241,0.694 0.001,0.702 0.242,0.693 0.461,0.657 0.633,0.601 0.764,0.547 0.888,0.514 1.036,0.508 1.325,0.573 1.873,0.702 0,0 0,0 0,0 -1.736,0.992 -1.086,0.707 -0.86
13、6,0.670 -0.724,0.695 -0.579,0.739 -0.414,0.792 -0.217,0.834 0.001,0.849 0.219,0.833 0.416,0.790 0.581,0.737 0.724,0.693 0.866,0.669 1.087,0.707 1.736,0.992 0,0 0,0 0,0 0,0 -1.627,1.162 -1.121,0.926 -0.855,0.836 -0.686,0.829 -0.537,0.859 -0.373,0.893 -0.192,0.925 0.001,0.938 0.194,0.924 0.375,0.891 0
14、.540,0.856 0.689,0.827 0.856,0.836 1.121,0.926 1.627,1.162 0,0 0,0 0,0 0,0 0,0 -1.414,1.414 -0.927,1.097 -0.679,0.990 -0.508,0.979 -0.345,0.997 -0.176,1.018 0.000,1.024 0.177,1.017 0.347,0.991 0.511,0.967 0.682,0.985 0.929,1.098 1.414,1.414 0,0 0,0 0,0 0,0 0,0 0,0 0,0 -1.162,1.627 -0.735,1.257 -0.50
15、8,1.148 -0.332,1.130 -0.166,1.136 -0.000,1.139 0.165,1.132 0.330,1.112 0.500,1.091 0.735,1.246 1.162,1.627 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 -0.894,1.789 -0.556,1.448 -0.349,1.379 -0.172,1.368 -0.001,1.366 0.168,1.359 0.333,1.324 0.465,1.132 0.894,1.789 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 -0.632,1.897 -0.434,1.952 -0.221,1.988 0.000,2.000 0.221,1.988 0.434,1.952 0,0 0,0 0,0 0,0 0,0 0,0 0,0
