What Do Planar Shadows Tell About Scene Geometry?

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What Do Planar Shadows Tell About Scene Geometry?

• Idan Shatz

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The Texts

• 3d photography on your desk
• Jean-Yves Bouguet and Pietro Perona
• What do planar shadows tell about scene geometry?
• Jean-Yves Bouguet, Markus Weber and Pietro Perona

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3D fax

• What is a (simple) fax machine?

Scanning (2D image)
Transmitting (Data 0-1)
Printing (2D image)
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3D fax

• We would like the same for 3D objects

Scanning (3D object)
Transmitting (Data 0-1)
Creating (3D object)
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Scanning 3D objects

• Getting a collection of 3D vertexes
• (X,Y,Z)
• that well cover the object

(X,Y,Z)
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How?

• Many methods
• Shooting lasers beams
• Stereo Vision
• Or
• Shadows
• Simple
• Cheap
• Accurate

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The Idea
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The Math
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The Topics

• First Paper
• Calibrations
• Camera
• Light Source
• Scanning
• Spatial temporal shadows location
• Example

• Second Paper
• Removing the Reference Plane
• Shadows Properties
• Dual Space
• The Math
• Error Estimation
• Examples

Conclusions Future work
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Light Source Calibration
The only tools we need to calibrate the
position and direction of the light source S
is a panicle (with known length)
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Light Source Calibration
IF the Reference Plane Is Known Then,
The Direction can berecovered From one
Image.
The Position can be recovered From Two
Images.
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The scanning process
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Shadow Position
Light Source
Reference Top row
Reference bottom row
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Shadow Position(Spatial-Temporal)
The Position of The shadow, Both IN Spatial and
Temporal, IS done is a sub-pixel resolution
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Example
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Example
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Shadow properties
If two points On a Shadow Line Have Known
Positions
All Points On The Shadow Could Be Recovered
All SHADOWS That INTERSECT BOTH SHADOWS
Could Be Recovered
IF Two Shadows ARE Known
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The Idea
Scan the Object with Shadows that Intersect
Building a Net OF Shadows
Find The Position Of Intersection Points (Up to 3
scalars)
IF 3 Points ARE Known Then The 3 Scalars Are
Known
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The Dual Space
A PLANE IS a Vector IN the Dual Space

• A Line On the Image Plane
• Is Represented
• as a Vector

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The Math

• ALL SHADOWS PLANES
• INCLUDE S
• INTRESCT WITH OTHERS

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The Math
If we are Given a Non-Trivial Solution

• The Matrix B
• Has a Rank
• of 2N-1

The Matrix A Has a Rank of 2N-3
Then
Is Also a Solution
Find The NON-Trivial Solution With SVD.
The Solution is a Eigenvector associated with the
unique zero eigenvalue
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Error Estimation
Find The NON-Trivial Solution With SVD.
Minimize The Error Function
Each Intersection Point Can Be recovered From TWO
Planes
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Example 1/2
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Example 2/2
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Conclusions

• Very Simple and Cheap method.
• However, Good Results
• Error of 0.5mm First Paper
• Error of 3mm Second Paper

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Conclusions

• It seems that Reference Plane Helps.
• Its removal havent
• The error increases
• We still need 3 measurements.
• However
• Intersecting shadows could minimize the
  reconstruction error.

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Future work

• Working with two light sources
• And integrate the results.
• Use Stickers of known shape and size