Enhanced SIFT Algorithm Implementation with Harris Operator and Dimensionality Reduction

The standard SIFT algorithm produces an excessive number of feature points with substantial false detections and uneven distribution, which inadequately represents image characteristics. Each feature point carries a 128-dimensional descriptor vector, and the algorithm involves extensive Gaussian convolution operations, resulting in substantial computational overhead and slow registration speeds. To address these issues, we propose replacing the feature detection and localization stage with the Harris corner detector. In code implementation, this involves using Harris corner response function calculations instead of Difference-of-Gaussian (DoG) extremum detection. The Harris operator computes corner responses using image gradients and autocorrelation matrices, providing more stable and evenly distributed feature points. This modification enhances algorithm speed and robustness by reducing sensitivity to noise while maintaining good localization accuracy. Additionally, we implement dimensionality reduction of feature vectors while preserving rotation and scale invariance properties. This can be achieved through principal component analysis (PCA) applied to the standard SIFT descriptors or by designing compact binary descriptors. The implementation would involve calculating covariance matrices of training descriptors and projecting original 128-dimensional vectors to lower-dimensional spaces (e.g., 64 or 32 dimensions). This optimization significantly reduces memory requirements and matching complexity while maintaining distinctive power. From the analysis above, we observe that SIFT algorithm exhibits several limitations in feature extraction: excessive feature point quantity, numerous false detections, and uneven spatial distribution. The 128-dimensional feature descriptors combined with extensive Gaussian convolution operations create substantial computational burden, leading to slow registration performance. Our solution integrates Harris operator for improved feature detection and implements descriptor dimensionality reduction techniques. The Harris corner detection implementation involves computing image derivatives Ix and Iy, constructing the second-moment matrix, and applying corner response thresholding. For dimensionality reduction, we maintain rotational and scale invariance by normalizing feature orientations and implementing scale-space processing while reducing descriptor dimensions through feature selection or transformation methods. These enhancements collectively improve algorithm efficiency without compromising key invariant properties.