1. Comparison of Image Registration Methods David Grimm Joseph Handfield Mahnaz Mohammadi Yushan Zhu March 18, 2004

2. Registration task:  Match two or more images taken:  at different times  with different sensors  from different view points  with different filters

3. Outline of this Methodology  Point Mapping  Fourier Methods  Geometric Transformation (matrices)  Subimage Processing Pixel Correlation  Multispectral Imaging, an example  Evaluation Methods  Colorimetric Evaluation

4. Point Mapping  Currently widely used (benchmark)  Standard technique for registering images misaligned by an unknown transformation  Requires “control points” to be found in the images  Intrinsic or extrinsic  Can be done either manually or automatically

5. Point Mapping (cont)  Mathematically relates the coordinate systems of the images  Higher order equations for more complicated transforms are possible

6. Fourier Methods  Very robust for images with correlated noise  Particularly images taken under differing illumination conditions  Good for images that have been rigidly misaligned (rotation, translation, etc.)

7. Fourier Methods (cont)  Phase difference in Fourier Transforms of 2 images correlates to a translation (Shift Theorem)  Rotation is a shift in polar coordinates

8. Geometric Registration  This picture gives multiple similar image transformations that we can encounter in registering an image  There are matrices that can register tiles with nonuniformity

9. Transform Matrices

10. 3D Transform matrix

11. Subimage Processing  Using landmark image patches of the full image reduces search data size to register images in a shorter time and increased accuracy.  Edge detection algorithms aid programs in automatic subimage selection, picking clearly discernable features and matching correlation values.

12. Subimage Example Subimage ↓ Squares of approximate correlation

13. Evaluation Methods  Correlation  Colorimetric  Only applicable if original scene is available

14. Correlation  Basic statistical approach to registration  Measurement of degree of similarity between images  Note: By itself, cross correlation is not a registration method  Correlation theorem

15. Correlation (Cont.) For a template T and image I: Cross-correlation function: A related measure correlation coefficient:

16. 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

17. Correlation theorem (Cont.)  The transformation whose cross-correlation is the largest specifies how two images optimally registered  There is a computational cost with increasing the number of transformations  So, measures are often computed on features instead of the whole image  Noisy images must be pre-filtered before cross- correlation ( Matched filter technique)

18. Color Multispectral Imaging, An example

19. Colorimetric evaluation as measurement of accuracy  Registration of the gray images  Synthesized sRGB image using gray images  In situ spectral reflectance measurement of the original image  Calculate color-difference between the synthesized and the original image  Smaller color-difference, better registration