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. 2022 Sep 30;12:16459. doi: 10.1038/s41598-022-20816-1

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Image registration results with the single homography method. (a) Frame 20 is used as the start frame of scene 1. (b) Frame 220 with small perspective changes, instrument movement, and organ deformation in relation to frame 20. (c) Frame 430 shows occlusions from an instrument and organ deformation due to manipulation compared with frame 20. (d)–(i) Semitransparent overlay of the transformed start frame 20 and the current frames 220 (left column, red) and 430 (right column, yellow) for ORB1000 (d, e), A-KAZE (f, g), and MG-DHNN (h, i). Green crosses indicate the ground truth and blue crosses the estimated position of the annotated points. White arrows highlight large registration errors and non-overlapping regions are shown in greyscale. The normalized RE averaged over the annotations of the shown frame are 0.1 for d, f, and g; 0.26 for e; 0.13 for h and i.