a standard SIFT descriptor, by setting each histogram bin to its rank in a sorted array of bins. The Euclidean distance between SIFT-Rank descriptors is invariant to arbitrary monotonic changes in histogram bin values, and is related to Spearman's rank correlation coefficient. Applications Object recognition using SIFT features Given SIFT's ability to find distinctive keypoints that are invariant to location, scale and rotation, and robust to affine transformations (changes in scale, rotation, shear, and position) and changes in illumination, they are usable for object recognition. The steps are given below. First, SIFT features are obtained from the input image using the algorithm described above. These features are matched to the SIFT feature database obtained from the training images. This feature matching is done through a Euclidean-distance based nearest neighbor approach. To increase robustness, matches are rejected for those keypoints for which the ratio of the nearest neighbor distance to the second-nearest neighbor distance is greater than 0.8. This discards many of the false matches arising from background clutter. Finally, to avoid the expensive search required for finding the Euclidean-distance-based nearest neighbor, an approximate algorithm called the best-bin-first algorithm is used. This is a fast method for returning the nearest neighbor with high probability, and can give speedup by factor of 1000 while finding nearest neighbor (of interest) 95% of the time. Although the distance ratio test described above discards many of the false matches arising from background clutter, we still have matches that belong to different objects. Therefore, to increase robustness to object identification, we want to cluster those features that belong to the same object and reject the matches that are left out in the clustering process. This is done using the Hough transform. This will identify clusters of features that vote for the same object pose. When clusters of features are found to vote for the same pose of an object, the probability of the interpretation being correct is much higher than for any single feature. Each keypoint votes for the set of object poses that are consistent with the keypoint's location, scale, and orientation. Bins that accumulate at least 3 votes are identified as candidate object/pose matches. For each candidate cluster, a least-squares solution for the best estimated affine projection parameters relating the training image to the input image is obtained. If the projection of a keypoint through these parameters lies within half the error range that