Camera Calibration from Planar Patterns

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Camera Calibration fromPlanar Patterns
(courtesy Jean-Yves Bouguet, Intel)
Mitul Saha

• Homework 2 Help Session

CS223b
Stanford University
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Camera Calibration
Object Space
Image Space
M
m
m Camera Projection Matrix M
A R t
extrinsics
camera intrinsics
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Camera Calibration
Object Space
Image Space
M
m
m Camera Projection Matrix M

• Camera calibration is about
• finding the camera intrinsics
• But, why do we need them?

A R t
extrinsics
camera intrinsics
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Camera Calibration

• Common approach

Non-planar pattern
Planar pattern
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Camera Calibration from Planar Patterns

• ICCV Zhang99 Flexible Calibration by Viewing a
  Plane From Unknown Orientations

m Camera Projection Matrix M
A R t
Minimize
estimate A R t M
observed
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Camera Calibration from Planar Patterns

• ICCV Zhang99 Flexible Calibration by Viewing a
  Plane From Unknown Orientations

m Camera Projection Matrix M
A R t

• Two steps
• Find an initial solution
• for A R t
• Minimize the objective function
• using the initial solution

Minimize
estimate A R t M
observed
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Camera Calibration from Planar Patterns

• Finding an initial solution
• First step
• Estimate the image homography matrix H for each
  image

Minimize
Initial solution for minimization
L
x is the eigenvector of LTL with smallest
eigenvalue
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Camera Calibration from Planar Patterns

• Finding an initial solution
• First step
• Estimate the image homography matrix H for each
  image
• Second step
• Solve for b in the linear system

V b 0
b is the eigenvector of VTV with smallest
eigenvalue
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Camera Calibration from Planar Patterns

• Finding an initial solution
• First step
• Estimate the image homography matrix H for each
  image
• Second step
• Solve for b in the linear system
• b yields the intrinsic parameter matrix A.
• Rotation matrix r1 r2 r3 and translation t
  is computed from

V b 0
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Camera Calibration from Planar Patterns

• Finding an initial solution
• First step
• Estimate the image homography matrix H for each
  image
• Second step
• Solve for b in the linear system
• b yields the intrinsic parameter matrix A.
• Rotation matrix r1 r2 r3 and translation t
• But the computed rotation matrix does not satisfy
  the properties of rotation matrix RTRRRTI.
• One can it enforce by minRnew - R,
• U D V
  SVD(R),
• Rnew
  UVT

V b 0
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Camera Calibration from Planar Patterns
m Camera Projection Matrix M
A R t

• Two steps
• Find an initial solution
• for A R t
• Minimize the objective function
• using the initial solution

Minimize
use lsqnonlin in Matlab
estimate A R t M
observed