computer vision: photometric...
TRANSCRIPT
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Last Lecture
• Single View Modeling
Vermeer’s Music LessonReconstructions by Criminisi et al.
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Today
• Photometric Stereo
• Separate Global and Direct Illumination
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Photometric Stereo
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Photometric Stereo
Readings• R. Woodham, Photometric Method for Determining Surface Orientation from
Multiple Images. Optical Engineering 19(1)139-144 (1980). (PDF)
Merle Norman Cosmetics, Los Angeles
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Diffuse reflection
Simplifying assumptions
• I = Re: camera response function f is the identity function:
– can always achieve this in practice by solving for f and
applying f -1 to each pixel in the image
• Ri = 1: light source intensity is 1
– can achieve this by dividing each pixel in the image by Ri
image intensity of P
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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
L1
L2
V
L3
Can write this as a matrix equation:
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Solving the equations
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More than three lights
Get 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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Computing light source directions
Trick: place a chrome sphere in the scene
• the location of the highlight tells you where the light source is
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For a perfect mirror, light is reflected about N
Recall the rule for specular reflection
otherwise0
if RVi
e
RR
We see a highlight when V = R
• then L is given as follows:
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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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What if we don’t have mirror ball?
• Hayakawa, Journal of the Optical Society of America,
1994, Photometric stereo under a light source with
arbitrary motion.
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Limitations
Big 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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Aaron Hertzmann
University of Toronto
Example-based Photometric Stereo
Steven M. Seitz
University of Washington
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Shiny things
“Orientation consistency”
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same surface normal
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Virtual views
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Velvet
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Virtual Views
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Brushed Fur
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Brushed Fur
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Virtual Views
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0.9 + 0.6 + 0.2 + 2.0 + 2.1 + 2.1
=
= + +
= + +
Linear combinations of materials
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0.9
0.6
0.2
2.0
2.1
2.1
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Virtual views
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photometric stereo laser scanlaser scan photometric stereo
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Problem definition
Estimate 3D shape by varying illumination, fixed camera
Operating conditions
• any opaque material
• distant camera, lighting
• reference object available
• no shadows, interreflections, transparency
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Fast Separation of Direct and Global Images
Using High Frequency Illumination
Shree K. Nayar
Gurunandan G. Krishnan
Columbia University
SIGGRAPH Conference
Boston, July 2006
Support: ONR, NSF, MERL
Michael D. Grossberg
City College of New York
Ramesh Raskar
MERL
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source
surface
P
Direct and Global Illumination
A
A : Direct
B
B : Interrelection
C
C : Subsurface
D
participating medium
D : Volumetrictranslucentsurface
E
E : Diffusion
camera
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Fast Separation of Direct and Global Images
• Create Novel Images of the Scene
• Enhance Brightness Based Vision Methods
• New Insights into Material Properties
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],[],[],[ icLicLicL gd
direct globalradiance
Direct and Global Components: Interreflections
surface
i
camera
source
P
g jiLjiAicL ],[],[],[
j
BRDF and geometry
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High Frequency Illumination Pattern
surface
camera
source
fraction of activated source elements
],[],[],[ icLicLicL gd
+
i
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High Frequency Illumination Pattern
surface
fraction of activated source elements
camera
source
],[],[],[ icLicLicL gd
+ -],[],[ icLicL g)1(
i
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:2
1min2LLg
Separation from Two Images
direct global
,minmax LLLd
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Other Global Effects: Subsurface Scattering
translucent surface
camera
source
i
j
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Other Global Effects: Volumetric Scattering
surface
camera
source
participating medium
i
j
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Diffuse Interreflections
SpecularInterreflections
Volumetric Scattering
SubsurfaceScattering
Diffusion
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Scene
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Scene
Direct Global
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Real World Examples:
Can You Guess the Images?
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Eggs: Diffuse Interreflections
Direct Global
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Wooden Blocks: Specular Interreflections
Direct Global
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Novel Images
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Mirror Ball: Failure Case
Direct Global
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Photometric Stereo using Direct Images
Bowl
Shape
Source 1 Source 2 Source 3
Direct
Global
Nayar et al., 1991
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Variants of Separation Method
• Shadow of Line Occluder
• Shadow of Mesh Occluders
• Coded Structured Light
• Shifted Sinusoids
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Stick
Building Corner
Shadow
minLLg
direct global
,minmax LLLd
3D from Shadows:
Bouguet and Perona 99
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Direct Global
Building Corner
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Shower Curtain: Diffuser
Shadow
Mesh
minLLg
direct global
,minmax LLLd
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Direct Global
Shower Curtain: Diffuser
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Kitchen Sink: Volumetric Scattering
Volumetric Scattering:
Chandrasekar 50, Ishimaru 78
Direct Global
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Peppers: Subsurface Scattering
Direct Global
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Hand
Direct Global
Skin: Hanrahan and Krueger 93,
Uchida 96, Haro 01, Jensen et al. 01,
Cula and Dana 02, Igarashi et al.
05, Weyrich et al. 05
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Hands
Afric. Amer.
Female
Chinese
Male
Spanish
Male
Direct Global
Afric. Amer.
Female
Chinese
Male
Spanish
Male
Afric. Amer.
Female
Chinese
Male
Spanish
Male
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Tea Rose Leaf
Direct Global
Leaf Anatomy: Purves et al. 03
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Translucent Rubber Balls
Direct Global
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Face: Without and With Makeup
GlobalDirect
GlobalDirectWithout Makeup
With Makeup
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Blonde Hair
Hair Scattering: Stamm et al. 77,
Bustard and Smith 91, Lu et al. 00
Marschner et al. 03
Direct Global
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Pebbles: 3D Texture
Direct Global
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Pink Carnation
GlobalDirect
Spectral Bleeding: Funt et al. 91
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Summary
• Fast and Simple Separation Method
• Wide Variety of Global Effects
• No Prior Knowledge of Material Properties
• Implications:
• Generation of Novel Images
• Enhance Computer Vision Methods
• Insights into Properties of Materials
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http://www1.cs.columbia.edu/CAVE/projects/separation/separation.php