cs.CVApr 8, 2026

Mathematical Analysis of Image Matching Techniques

Authors: Oleh Samoilenko

Organizations: Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

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Abstract

Image matching is a fundamental problem in Computer Vision with direct applications in robotics, remote sensing, and geospatial data analysis. We present an analytical and experimental evaluation of classical local feature-based image matching algorithms on satellite imagery, focusing on the Scale-Invariant Feature Transform (SIFT) and the Oriented FAST and Rotated BRIEF (ORB). Each method is evaluated through a common pipeline: keypoint detection, descriptor extraction, descriptor matching, and geometric verification via RANSAC with homography estimation. Matching quality is assessed using the Inlier Ratio - the fraction of correspondences consistent with the estimated homography. The study uses a manually constructed dataset of GPS-annotated satellite image tiles with intentional overlaps. We examine the impact of the number of extracted keypoints on the resulting Inlier Ratio.

Figures & tables

Figure 1: Satellite Image Dataset. The images are sampled such that the neighbouring images have overlapping regions, enable evaluation of the image matching and alignment algorithms. A collection of the satellite images is retrieved by utilizing the Google Maps Static API [ 1 ] .
Figure 2: Difference of the Gaussians [ 14 ] is computed by subtracting the scale-space representation of an input image at different levels of the Gaussian blurring resulting in a pyramid of images, which is utilized for detecting the scale-invariant keypoints.
Figure 3: The FAST feature detection [ 4 ] . As example, the Bresenham circle of the radius 3 with the center at CC is presented. The highlighted squares are the pixels adopted in the feature detection.
Figure 4: Keypoint matches with the Brute Force. Initial keypoint correspondences between two images using a Brute Force Matcher on SIFT descriptors, including outliers. Images are retrieved by utilizing the Google Maps Static API [ 1 ] .
Figure 5: The keypoint matches between two images after applying the RANSAC filtering. The RANSAC rejects outliers and retains only geometrically consistent matches (inliers), leading to a much cleaner and structurally meaningful correspondence set. Images are retrieved by utilizing the Google Maps Static API [ 1 ] .
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