Rank SIFT


Rank SIFT algorithm is the revised SIFT 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 is a training image sequence and is a key point obtained by SIFT detector. The following equation determines the rank of in the key point set. Larger value of corresponds to the higher rank of.
where is the indicator function, is the homography transformation from to, and is the threshold.
Suppose is the feature descriptor of key point defined above. So can be labeled with the rank of in the feature vector space. Then the vector set containing labeled elements can be used as a training set for the Ranking SVM problem.



The learning process can be represented as follows:
The obtained optimal 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 is the feature vector of a key point and the elements of is the corresponding rank of in. is defined as follows:
After transforming original feature vector to the ordinal descriptor, 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 and, it can be proved that
The Kendall's Tau also refers to Kendall tau rank correlation coefficient.
In the above case, the Kendall's Tau between and is