PCA-SIFT Details

PCA-SIFT was introduced as an improvement for SIFT. The implementation only differs in the 4th step (keypoint descriptor). PCA-SIFT uses Principal Component Analysis (PCA) instead of a histogram to normalize the gradient patch. Hence, the feature vector is significantly smaller than the standard SIFT feature vector.

It differs from the original SIFT implementation in its forth stage. By reducing the 128 element of the original SIFT using PCA, results in a significant space benefit.

Another difference is the input vector is created by concatenating the horizontal and vertical gradient maps for 41x41 patch centered at the keypoint. Producing 2x39x39 = 3042 vector elements. The fewer components of PCA-SIFT requires less storage therefore, resulting in faster matching. The dimensionality of this feature space is arbitrary chosen as n=20, which results in a significant space benefit.

TO DO: add more detail

Principal Component Analysis

Principal component analysis has several disadvantages including

• Translation variant
• Scale variant
• Background variant
• Lighting variant

The first principal component accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible. Although PCA is used as a tool in exploratory data analysis and making predictive models, its strength is also considered its weakness. This is because of its non-parametric analysis. Since there are no parameters to tweak, the answer of PCA is unique and independent of the users experience. Thus, the answer may not be optimal in all cases.

The basic idea of PCA is given a set of variables, find a set of variables with less redundancy, this gives a good representation for regression analysis. Since redundancy is computed via correlation, it is required for reducing the scale space between vector elements

In Matlab PCA is done via the following function:

[COEFF, SCORE] = princomp(X);

EXAMPLES TO FOLLOW:
TO DO