单幅图像深度重建:基于单眼线索的深度重建Shape From Shading

1 .第九章 单幅图像深度重建 Depthmap Reconstruction Based on Monocular cues 

2 .深度图 

3 . 章节安排  基于单眼线索的深度重建  Shape From Shading  Shape From Vanishing Point  Shape From Defocus  Shape From Texture 

4 .Shape From Shading 

5 . What is Shading?  Well… not shadow…  We can’t reconstruct shape from one shadow… 

6 . What is Shading?  Variable levels of darkness  Gives a cue for the actual 3D shape  There is a relation between intensity and shape 

7 . Shading Examples  These circles differ only in grayscale intensity  Intensities give a strong “feeling” of scene structure 

8 .What determines scene radiance? n 

9 .

10 . Surface Normal Convenient notation for surface orientation A smooth surface has a tangent plane at every point We can model the surface using the normal at every point 

11 . The Shape From Shading Problem  Given a grayscale image  And albedo  And light source direction  Reconstruct scene geometry  Can be modeled by surface normals 

12 . Lambertian Surface  Appears equally bright from all viewing directions  Reflects all light without absorbing  Matte surface, no “shiny” spots  Brightness of the surface as seen from camera is linearly correlated to the amount of light falling on the surface Here we will discuss only n Lambertian surfaces under point-source illumination 

13 . Some Notations: Surface Orientation 

14 . Some Notations: Surface Orientation 

15 .Reflectance Map 

16 . Reflectance Map • Lambertian case I cos  i n s   pps  qqs 1 R  p, q  2 2 2 2 p  q 1 p  q 1 S S Reflectance Map Iso-brightness contour (Lambertian) cone of constant  i 

17 . Reflectance Map • Lambertian case iso-brightness contour q 0.8 0.9 1.0 R  p, q  0.7  pS , q S  p  i 90  ppS  qqS 1 0 0.3 0.0 Note: R p, q  is maximum when  p, q   pS , qS  

18 . Reflectance Map Example • Brightness as a function of surface orientation Lambertian iso-brightness contour q surface 0 .8 0.9 1.0 R p, q  0.7  pS , qS  p  i 90  ppS  qqS  1 0 0.3 0.0 

19 . Reflectance Map of a Glossy Surface  Brightness as a function of surface orientation Surface with diffuse and glossy components 

20 . Reflectance Map Examples  Brightness as a function of surface orientation 

21 .Graphics with a 3D Feel 

22 .Shape From Shading? q p 

23 . Shape From Shading!  Use more images  Photometric stereo  Shape from shading  Introduce constraints  Solve locally  Linearize problem 

24 . Photometric Stereo  Take several pictures of same object under same viewpoint with different lighting q p 1 S , q1S  p 

25 . Photometric Stereo  Take several pictures of same object under same viewpoint with different lighting q p 1 S , q1S  p p 2 S 2 , qS  

26 . Photometric Stereo  Take several pictures of same object under same viewpoint with different lighting q p 1 S , q1S  p p 2 S 2 , qS  p 3 S , q 3S  

27 . Photometric Stereo Lambertian case:   kc  I  kc cos  i n s  1    n Image irradiance: s2 s3 I1 n s1 s1 v I 2 n s 2 I 3 n s 3 • We can write this in matrix form: I  1  s T   I    s T  n 1  2  2  I 2   T s 3  

28 .改变光源所获得的同一个球的五幅图像 

29 .g  x, y 