lecture 32: photometric stereo, part 2 cs4670: computer vision noah snavely
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Lecture 32: Photometric stereo, Part 2
CS4670: Computer VisionNoah Snavely
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BRDF’s can be incredibly complicated…
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Shape from shading
Suppose
You can directly measure angle between normal and light source• Not quite enough information to compute surface shape• But can be if you add some additional info, for example
– assume a few of the normals are known (e.g., along silhouette)
– constraints on neighboring normals—“integrability”
– smoothness
• Hard to get it to work well in practice– plus, how many real objects have constant albedo?
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Photometric stereo
N
L1L2
V
L3
Can write this as a matrix equation:
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Solving the equations
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More than three lightsGet better results by using more lights
What’s the size of LTL?
Least squares solution:
Solve for N, kd as before
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Example
Recovered albedo Recovered normal field
Forsyth & Ponce, Sec. 5.4
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Computing light source directionsTrick: place a chrome sphere in the scene
• the location of the highlight tells you where the light source is
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Depth from normals
Get a similar equation for V2• Each normal gives us two linear constraints on z• compute z values by solving a matrix equation
V1
V2
N
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Example
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LimitationsBig problems
• doesn’t work for shiny things, semi-translucent things• shadows, inter-reflections
Smaller problems• camera and lights have to be distant• calibration requirements
– measure light source directions, intensities– camera response function
Newer work addresses some of these issues
Some pointers for further reading:• Zickler, Belhumeur, and Kriegman, "
Helmholtz Stereopsis: Exploiting Reciprocity for Surface Reconstruction."
IJCV, Vol. 49 No. 2/3, pp 215-227. • Hertzmann & Seitz, “
Example-Based Photometric Stereo: Shape Reconstruction with General, Varying BRDFs.” IEEE Trans. PAMI 2005
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Finding the direction of the light source
P. Nillius and J.-O. Eklundh, “Automatic estimation of the projected light source direction,” CVPR 2001
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Application: Detecting composite photos
Fake photo
Real photo
Which is the real photo?
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Questions?