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The nearest neighbors are defined as the keypoints with minimum Euclidean distance from the given descriptor vector.The probability that a match is correct can be determined by taking the ratio of distance from the closest neighbor to the distance of the second closest.
To perform reliable recognition, it is important that the features extracted from the training image be detectable even under changes in image scale, noise and illumination.
However, in practice SIFT detects and uses a much larger number of features from the images, which reduces the contribution of the errors caused by these local variations in the average error of all feature matching errors.
SIFT can robustly identify objects even among clutter and under partial occlusion, because the SIFT feature descriptor is invariant to uniform scaling, orientation, illumination changes, and partially invariant to affine distortion.
For example, if only the four corners of a door were used as features, they would work regardless of the door's position; but if points in the frame were also used, the recognition would fail if the door is opened or closed.
Similarly, features located in articulated or flexible objects would typically not work if any change in their internal geometry happens between two images in the set being processed.