Fast LoG SIFT Keypoint Detector

Scale-invariant feature transform (SIFT) is a classical computer vision technique for scale-invariant keypoint detection and feature extraction. SIFT exhibits invariance to various transformations such as scale, rotation, noise, and illumination, making it applicable in a wide range of applications like object recognition, image matching and stitching, environment mapping, navigation, robotics, camera calibration, and more. A key contribution of SIFT is its utilization of the Difference-of-Gaussian (DoG) feature pyramid, which approximates the scale-space response of the Laplacian-of-Gaussian (LoG) filter. The DoG feature pyramid is computed by taking the separable Gaussian filtering and stacking the difference of Gaussian blurred images. In this paper, we propose a novel approach called “Fast LoG” filtering, which offers direct computation of the LoG filter to model the scale-space response solution. The “Fast LoG” filter is achieved by decomposing the LoG filter into two separable filters via SVD, and the scale-space response is computed by a direct polynomial fitting and differentiation, which is analytically more accurate. The polynomial fitting and differentiation only happen after the LoG peak strength thresholding, therefore the overall complexity is low compared with the DoG-based SIFT. The experimental results show that the keypoint generated by the Fast LoG method matches the SIFT keypoints, and per-pixel filtering complexity is lower.