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When the subpixel disparity between the source and target images is required, the cost function or the target image has to be interpolated. While cost-based interpolation is easier to implement, multiple works have shown that image-based interpolation can increase the accuracy of the disparity estimate. In this paper we review closed-form formulae for subpixel disparity computation for one dimensional matching, e.g., rectified stereo matching, for the standard cost functions used in patch-based matching. We then propose new formulae to generalize to high-dimensional search spaces, which is necessary for unrectified stereo matching and optical flow. We also compare the image-based interpolation formulae with traditional cost-based formulae, and show that image-based interpolation brings a significant improvement over the cost-based interpolation methods for two dimensional search spaces, and small improvement in the case of one dimensional search spaces. The zero-mean normalized cross correlation cost function is found to be preferable for subpixel alignment. A new error model, based on very broad assumptions is outlined in the Supplementary Material to demonstrate why these image-based interpolation formulae outperform their cost-based counterparts and why the zero-mean normalized cross correlation function is preferable for subpixel alignement.<\/jats:p>","DOI":"10.1007\/s11263-025-02457-9","type":"journal-article","created":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T10:30:18Z","timestamp":1747650618000},"page":"5958-5975","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generalized Closed-Form Formulae for Feature-Based Subpixel Alignment in Patch-Based Matching"],"prefix":"10.1007","volume":"133","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5395-1967","authenticated-orcid":false,"given":"Laurent Valentin","family":"Jospin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4758-7510","authenticated-orcid":false,"given":"Hamid","family":"Laga","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farid","family":"Boussaid","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6603-3257","authenticated-orcid":false,"given":"Mohammed","family":"Bennamoun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,19]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Ana Sovi\u0107 Kr\u017ei\u0107 and Damir Ser\u0161i\u0107. 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