Image Registration  Mapping of Evolution

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# Image Registration Mapping of Evolution - PowerPoint PPT Presentation

Image Registration  Mapping of Evolution. Registration Goals. I 2 (x,y)=g(I 1 (f(x,y)) f() – 2D spatial transformation g() – 1D intensity transformation. Assume the correspondences are known Find such f() and g() such that the images are best matched. Spatial Transformations. Rigid

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### Image Registration Mapping of Evolution

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
Spatial Transformations
• Rigid
• Affine
• Projective
• Perspective
• Global Polynomial
• Spline
Rigid Transformation
• Rotation(R)
• Translation(t)
• Similarity(scale)
Affine Transformation
• Rotation
• Translation
• Scale
• Shear

No more preservation of lengths and angles

Parallel lines are preserved

Perspective Transformation(2)
• (xo,yo,zo)  world coordinates
• (xi,yi)  image coordinates
• Flat plane tilted with respect to the camera requires Projective Transformation
Projective Transformation
• (xp,yp)  Plane Coordinates
• (xi,yi)  Image Coordinates
• amn coefficients from the equations of the scene and the image planes
Complex Transformations

Global Polynomial Transformation(splines)

Methods of Registration
• Correlation
• Fourier
• Point Mapping
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.

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.
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

Point Mapping Registration
• Control Points
• Point Mapping with Feedback
• Global Polynomial
Control Points

Intrinsic

Markers within

the Image

Extrinsic

Manually or Automatically selected

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

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
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

Global Polynomial Transformation(2)
• When is polynomial transformation bad?
• Splines approximate polynomial transformations(B-spline, TP-spline)
Characteristics of Registration Methods
• Feature Space
• Similarity Metrics
• Search Strategy
Robust Multi-Sensor Image Alignment

Irani & Anandan

Direct Method(vs. Feature Based)

Multi Sensor Images

EO IR

Find features

Loss of important information

Original Image (Intensity Map)

Assume global statistical correlation

Often violated

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
Multi Sensor Image Representation(2)

Goal: Suppress non-common information & capture the common scene details

Solution: High pass energy images

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

Directional Derivative Energy Images
• Filter with Gaussian
• Apply directional derivative filter to the original image in 4 directions
• Square the resultant images
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
Behavior of Normalized Correlation with Energy Images
• NC=1

Two images are linearly related

• NC<1(high)

Two images are not linearly related, yet local fluctuations are low

• NC<1(low)≈0

Incorrect displacements

Global Alignment with Local Correlation(1)

a, b – original images

{ai,bi} – directional derivatives (i=1..4)

p=(p1…p6)Taffine

(u,v) – shift from one image to another

Si(x,y)(u,v) – correlation surface at a pixel(x,y)

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)

Solving for M(p)

Newton’s 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.
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)
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 det|H(u)|
Results

EO image

IR image

Composite before Alignment

Composite after Alignment

IR image

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