Rank SIFT

Rank SIFT algorithm is the revised SIFT (Scale-invariant feature transform) algorithm which uses ranking techniques to improve the performance of the SIFT algorithm. In fact, ranking techniques can be used in key point localization or descriptor generation of the original SIFT algorithm.
SIFT With Ranking Techniques.
Ranking the Key Point.
Ranking techniques can be used to keep certain number of key points which are detected by SIFT detector.
Suppose formula_1 is a training image sequence and formula_2 is a key point obtained by SIFT detector. The following equation determines the rank of formula_2 in the key point set. Larger value of formula_4 corresponds to the higher rank of formula_2.
formula_6
where formula_7 is the indicator function, formula_8 is the homography transformation from formula_9 to formula_10, and formula_11 is the threshold.
Suppose formula_12 is the feature descriptor of key point formula_13 defined above. So formula_12 can be labeled with the rank of formula_13 in the feature vector space. Then the vector set formula_16 containing labeled elements can be used as a training set for the Ranking SVM problem.
The learning process can be represented as follows:
formula_17
The obtained optimal formula_18 can be used to order the future key points.
Ranking the Elements of Descriptor.
Ranking techniques also can be used to generate the key point descriptor.
Suppose formula_19 is the feature vector of a key point and the elements of formula_20 is the corresponding rank of formula_12 in formula_22. formula_23 is defined as follows:
formula_24
After transforming original feature vector formula_25 to the ordinal descriptor formula_26, the difference between two ordinal descriptors can be evaluated in the following two measurements.
The Spearman correlation coefficient also refers to Spearman's rank correlation coefficient.
For two ordinal descriptors formula_26 and formula_28, it can be proved that
formula_29
The Kendall's Tau also refers to Kendall tau rank correlation coefficient.
In the above case, the Kendall's Tau between formula_30 and formula_31 is
formula_32
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