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SIFT-Rank: Ordinal Description for Invariant Feature Correspondence

SIFT-Rank: Ordinal Description for Invariant Feature Correspondence. Matthew Toews and WilliamWells III Harvard Medical School, Brigham and Women’s Hospital. Outline. Outline Introductions Conversion Definitions of correlation Experiments Results Advantages & Disadvantages

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SIFT-Rank: Ordinal Description for Invariant Feature Correspondence

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  1. SIFT-Rank: Ordinal Description for Invariant Feature Correspondence Matthew Toews and WilliamWells III Harvard Medical School, Brigham and Women’s Hospital

  2. Outline • Outline • Introductions • Conversion • Definitions of correlation • Experiments • Results • Advantages & Disadvantages • Conclusion

  3. Introductions • SIFT : • We use Euclidean Distance for calculating relationships between features • Efficient for calculating but invalid for nonlinear monotonic deformations (illumination changes, sensor saturation) Different viewpoint

  4. Introductions • Ordinal description compares sets of data in an ordered array, instead of the original data • Rank-Ordering is a normalized representation which is invariant under arbitrary monotonic deformations a (possibly non-linear) operator T : X → X∗ is said to be a monotone operator if

  5. Conversion • Converting raw data to rank-order • Let X=(x1,x2,x3,….,xn) be the input vector, R is output array, and xi ≠ xj ……………………………………………….(*) • ri=|{xk|xk<=xi}| (number of elements that is not larger than ith item in X array)

  6. Conversion • The output vector (r1,r2,r3,…rn) • numbers in array are between 1 to n • The norm of the output vector is • The Euclidean Distance between two vectors is between • Example: array(150,255,100,23,66,90) reduced to array(5,6,4,1,2,3)

  7. Definitions of correlation coefficients 1. (Faster) 2. (*): When element in array is not unique (many zero elements occur usually in SIFT descriptor) use Pearson's correlation coefficient instead: all normalize data to [-1,1]

  8. Experiments • SIFT • SIFT-Rank • GLOH • GLOH-Rank • PCA-SIFT • PCA-SIFT-Rank R=6,11,15

  9. Experiments • Using same dataset, software as (Performance evaluation for local descriptors[15]): • Zoom/Rotation • Viewpoint • Illumination • Blur • JPEG compression noise • Result: successfully matched the pictures

  10. Experiments more prominent linear trend in d) due to rank-ordering

  11. Results • Little change for GLOH -> GLOH-Rank • Better for SIFT -> SIFT-Rank • Worse for PCA-SIFT -> PCA-Rank • SIFT-Rank outperform others

  12. Advantages & Disadvantages • Suitable in high dimensional representations • Normalized vector values (conquer monotonic deformation) • Need to recalculate for O(N log N) sorting when image lattice is changed • Ill-suited for popular dimension reduction methods

  13. Conclusion • Rank ordering do no significant improve on GLOH but detrimental on PCA-SIFT • May be faster on GLOH and PCA-SIFT by applying Rank ordering before PCA compression • Ordinal description may be important consideration in the future • Currently investigating appliance for large databases

  14. The End

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