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The method calculates the affine parameters consistent with the epipolar geometry from the point coordinates and the scales and rotations which the feature detector obtains. The proposed closed-form solver returns a single solution and is extremely fast, i.e., 0.5\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\upmu $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03bc<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>seconds on average. Possible applications include estimating the homography from a single upgraded correspondence and, also, estimating the surface normal for each correspondence found in a pre-calibrated image pair (e.g., stereo rig). As the second contribution, we propose a minimal solver that estimates the relative pose of a vehicle-mounted camera from a single SIFT correspondence with the corresponding surface normal obtained from, e.g., upgraded ACs. The proposed algorithms are tested both on synthetic data and on a number of publicly available real-world datasets. Using the upgraded features and the proposed solvers leads to a significant speed-up in the homography, multi-homography and relative pose estimation problems with better or comparable accuracy to the state-of-the-art methods.<\/jats:p>","DOI":"10.1007\/s11263-023-01802-0","type":"journal-article","created":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T07:02:41Z","timestamp":1685602961000},"page":"2316-2332","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["On Making SIFT Features Affine Covariant"],"prefix":"10.1007","volume":"131","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8736-0222","authenticated-orcid":false,"given":"Daniel","family":"Barath","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,6,1]]},"reference":[{"issue":"2","key":"1802_CR1","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s11554-014-0446-6","volume":"14","author":"KA Acharya","year":"2018","unstructured":"Acharya, K. 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