Image Registration ? Mapping of Evolution

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Image Registration ?Mapping of Evolution
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Registration Goals
I2(x,y)g(I1(f(x,y))f() 2D spatial
transformationg() 1D intensity transformation

• Assume the correspondences are known
• Find such f() and g() such that the images are
  best matched

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Spatial Transformations

• Rigid
• Affine
• Projective
• Perspective
• Global Polynomial
• Spline

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Rigid Transformation

• Rotation(R)
• Translation(t)
• Similarity(scale)

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Affine Transformation

• Rotation
• Translation
• Scale
• Shear

No more preservation of lengths and
angles Parallel lines are preserved
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Perspective Transformation (Planar Homography)
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Perspective Transformation(2)

• (xo,yo,zo) ? world coordinates
• (xi,yi) ? image coordinates
• Flat plane tilted with respect to the camera
  requires Projective Transformation

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Projective Transformation

• (xp,yp) ? Plane Coordinates
• (xi,yi) ? Image Coordinates
• amn ? coefficients from the equations of the
  scene and the image planes

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Complex Transformations
Global Polynomial Transformation(splines)
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Methods of Registration

• Correlation
• Fourier
• Point Mapping

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Correlation Based Techniques

• Given a two images T I, 2D normalized
  correlation function measures the similarity for
  each translation in an image patch

Correlation must be normalized to avoid
contributions from local image intensities.
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Correlation Theorem

• Fourier transform of the correlation of two
  images is the product of the Fourier transform of
  one image and the complex conjugate of the
  Fourier transform of the other.

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Fourier Transform Based Methods

• Phase-Correlation
• Cross power spectrum
• Power cepstrum
• All Fourier based methods are very efficient,
  only only work in cases of rigid transformation

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Point Mapping Registration

• Control Points
• Point Mapping with Feedback
• Global Polynomial

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Control Points
Extrinsic Manually or Automatically selected

• Intrinsic
• Markers within
• the Image

After the control points have been determined,
cross correlation, convex hull edges and other
common methods are used to register the sets of
control points
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Point mapping with Feedback

• Clustering example determine the optimal spatial
  transformation between images by an evaluation of
  all possible pairs of feature matches.
• Initialize a point in cluster space for each
  transformation
• Use the transformation that is closest to the
  best cluster
• Too many points, thus use a subset

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Global Polynomial Transformation(1)

• Use a set of patched points to generate a single
  optimal transformation
• Bi-Variate transformation

(x,y) reference image (u,v) working image
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Global Polynomial Transformation(2)

• When is polynomial transformation bad?
• Splines approximate polynomial transformations(B-s
  pline, TP-spline)

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Characteristics of Registration Methods

• Feature Space
• Similarity Metrics
• Search Strategy

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Feature Spaces
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Similarity Metrics
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Search Strategies
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• Robust Multi-Sensor Image Alignment
• Irani Anandan
• Direct Method(vs. Feature Based)

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Multi Sensor Images
EO IR
Find features
Loss of important information
Original Image (Intensity Map)
Assume global statistical correlation
Often violated
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Multi Sensor Image Representation(1)

• Same Modality Camera Sensors ? enough correlated
  structure at all resolution levels
• Different Modality Camera Sensors ? primary
  correlation only in high resolution levels

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Multi Sensor Image Representation(2)

• Goal Suppress non-common information capture
  the common scene details
• Solution High pass energy images

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Laplacian Energy Images

• Apply the Laplacian high pass filter to the
  original images
• Square the results ? NO contrast reversal
• BUT
• The Laplacian is directionally invariant

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Directional Derivative Energy Images

• Filter with Gaussian
• Apply directional derivative filter to the
  original image in 4 directions
• Square the resultant images

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Alignment Algorithm

• Do not assume global correlation, use only local
  correlation information
• Use Normalized Correlation as a similarity
  measure
• Thus, no assumptions about the original data

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Behavior of Normalized Correlation with Energy
Images

• NC1
• Two images are linearly related
• NClt1(high)
• Two images are not linearly related, yet local
  fluctuations are low
• NClt1(low)0
• Incorrect displacements

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Global Alignment with Local Correlation(1)

• a, b original images
• ai,bi directional derivatives (i1..4)
• p(p1p6)T ?affine
• (u,v) shift from one image to another
• Si(x,y)(u,v) correlation surface at a
  pixel(x,y)

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Global Alignment with Local Correlation(2)
Goal Find the parametric transformation p, which
maximizes the sum of all normalized correlation
values.? global similarity M(p)
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Solving for M(p)

• Newtons method is used to solve for M(p)

The quadratic approximation of M around p is
obtained by combining the quadratic
approximations of each of the local correlation
surfaces S around local displacement.
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Steps of the Algorithm

• Construct a Laplacian resolution pyramid
• Compute a local normalized-correlation surface
  around a given displacement
• Compute the parametric refinement
• Update p
• Start over(process terminates at the highest
  resolution level of the last image)

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Outlier Rejection

• Due to the different modalities of the
• sensors, the number of outliers may be very
• large
• Accept pixels based on concavity of the
  correlation surface
• Weigh the contribution of a pixel by detH(u)

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Results
EO image
IR image
Composite before Alignment
Composite after Alignment
IR image
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Acknowledgements

• I would like to thank Compaq for making awful
  computers
• Professor Belongie for reviewing the slides