CS4670/5760: Computer Vision
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1 CS4670/5760: Computer Vision Kavita Bala! Lecture 28: Photometric Stereo Thanks to ScoC Wehrwein
2 Announcements PA 3 due at 1pm on Monday PA 4 out on Monday HW 2 out on weekend Next week: MVS, sfm
3 Last Time: Two- View Stereo
4 Last Time: Two- View Stereo Key Idea: use feature motion to understand shape!
5 Today: Photometric Stereo Key Idea: use pixel brightness to understand shape!
6 Today: Photometric Stereo Key Idea: use pixel brightness to understand shape!
7 Photometric Stereo What results can you get?! Input (1 of 12)! Normals (RGB colormap) Normals (vectors) Shaded 3D rendering! Textured 3D rendering!
8
9 Modeling Image FormaTon Now we need to reason about: How light interacts with the scene How a pixel value is related to light energy in the world Track a ray of light all the way from light source to the sensor!
10 DirecTonal LighTng Key property: all rays are parallel Equivalent to an infinitely distant point source
11 LamberTan Reflectance Image intensity! Image intensity! Surface Light normal! direction! cos(angle between N and L)!
12 Materials - Three Forms Ideal diffuse (Lambertian) Ideal specular Directional diffuse Kavita Bala, Computer Science, Cornell University
13 Reflectance Three Forms Ideal diffuse (Lambertian) Ideal specular Directional diffuse Kavita Bala, Computer Science, Cornell University
14 Ideal Diffuse ReflecTon CharacterisTc of multple scacering materials An idealizaton but reasonable for mace surfaces Basis of most radiosity methods Kavita Bala, Computer Science, Cornell University
15 Lambert s Law Ideal Diffuse Kavita Bala, Computer Science, Cornell University
16 Ideal Specular ReflecTon Calculated from Fresnel s equatons Exact for polished surfaces Basis of early ray- tracing methods Kavita Bala, Computer Science, Cornell University
17 LamberTan Reflectance 1. Reflected energy is proportonal to cosine of angle between L and N (incoming) 2. Measured intensity is viewpoint- independent (outgoing)!
18 LamberTan Reflectance: Incoming 1. Reflected energy is proportonal to cosine of angle between L and N
19 LamberTan Reflectance: Incoming 1. Reflected energy is proportonal to cosine of angle between L and N
20 LamberTan Reflectance: Incoming 1. Reflected energy is proportonal to cosine of angle between L and N Light hitting surface is proportional to the cosine!
21 LamberTan Reflectance: Outgoing 1. Radiance (what we see) is viewpoint- independent!
22 LamberTan Reflectance: Outgoing 1. Radiance (what the eye sees) is viewpoint- independent!
23 LamberTan Reflectance: Outgoing 1. Measured intensity is viewpoint- independent!
24 LamberTan Reflectance: Outgoing 1. Measured intensity is viewpoint- independent! Radiance! (what eye sees)! A cos (θ)!
25 Image FormaTon Model: Final 1. Diffuse albedo: what fracton of incoming light is reflected? Introduce scale factor 2. Light intensity: how much light is arriving? Compensate with camera exposure (global scale factor) 3. Camera response functon Assume pixel value is linearly proportonal to incoming energy (perform radiometric calibraton if not)!
26 A Single Image: Shape from Shading Assume is 1 for now. What can we measure from one image? is the angle between N and L Add assumptons: A few known normals (e.g. silhoueces) Smoothness of normals! In practce, SFS doesn t work very well: assumptons are too restrictve, too much ambiguity in nontrivial scenes.
27 MulTple Images: Photometric Stereo N L 1! L 3! L 2! V Write this as a matrix equaton:
28 Solving the EquaTons 28
29 Solving the EquaTons When is L nonsingular (invertble)? >= 3 light directons are linearly independent, or: All light directon vectors cannot lie in a plane. What if we have more than one pixel? Stack them all into one big system. 29
30 More than Three Lights Solve using least squares (normal equatons): Equivalently use SVD Given G, solve for N and as before.
31 More than one pixel Previously: 1 x # images! I 1 x 3! 3 x # images! N! L! =! *!
32 More than one pixel Stack all pixels into one system: p x # images! I =! p x 3! 3 x # images! N! *! L! Solve as before.
33 Depth Map from Normal Map We now have a surface normal, but how do we get depth? orthographic projection! V 2! N V 1! Assume a smooth surface Get a similar equaton for V 2 Each normal gives us two linear constraints on z compute z values by solving a matrix equaton! 33
34 Determining Light DirecTons Trick: Place a mirror ball in the scene. The locaton of the highlight is determined by the light source directon. 34
35 Real- World HDR LighTng Environments Funston Beach Eucalyptus Grove Uffizi Gallery Grace Cathedral Lighting Environments from the Light Probe Image Gallery: Kavita Bala, Computer Science, Cornell University
36 Mirrored Sphere Kavita Bala, Computer Science, Cornell University
37 Kavita Bala, Computer Science, Cornell University
38 Acquiring the Light Probe Kavita Bala, Computer Science, Cornell University
39 Assembling the Light Probe Kavita Bala, Computer Science, Cornell University
40 Extreme HDR Image Series 1 sec f/4 1/4 sec f/4 1/30 sec f/4 1/30 sec f/16 1/250 sec f/16 1/1000 sec f/16 1/8000 sec f/16 Kavita Bala, Computer Science, Cornell University
41 Extreme HDR Image Series sun closeup 1 sec f/4 1/4 sec f/4 1/30 sec f/4 1/30 sec f/16 1/250 sec f/16 1/1000 sec f/16 Kavita Bala, Computer Science, Cornell University 1/8000 sec f/16 only image that does not saturate!
42 HDRI Sky Probe Kavita Bala, Computer Science, Cornell University
43 Determining Light DirecTons For a perfect mirror, the light is reflected across N: So the light source directon is given by: 43
44 Determining Light DirecTons For a sphere with highlight at point H: Compute N: R = directon of the camera from C = 44
45 Results from Athos Georghiades 45
46 Results Input (1 of 12)! Normals (RGB colormap) Normals (vectors) Shaded 3D rendering! Textured 3D rendering!
47 QuesTons?
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