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However, accurate depth estimation in colonoscopy remains highly challenging due to specular highlights and low-texture areas. This study aims to improve monocular depth estimation in colonoscopy by incorporating surface normal information.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We propose a self-supervised deep learning method for relative depth estimation that integrates surface normal information through a cross-attention mechanism. Surface normals are first predicted by an existing normal estimation model and then used as auxiliary geometric priors. The depth estimation network employs cross-attention to adaptively fuse normal features with image features, enabling spatially selective geometric refinement.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>Quantitative and qualitative comparisons show that the proposed method outperforms state-of-the-art self-supervised methods on SimCol3D, C3VD, and real colonoscopy data. The proposed method generates more realistic depth maps, preserving mucosal folds and lumen geometry. Ablation studies verify that the cross-attention module is crucial for effectively exploiting normal information for accurate depth estimation.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>By leveraging cross-attention to fuse predicted surface normals with image features, the proposed method enhances monocular depth estimation accuracy and robustness in colonoscopy. This approach provides a general and lightweight strategy for incorporating geometric priors into self-supervised frameworks, offering potential benefits for downstream tasks such as 3D reconstruction and endoscopic navigation.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1007\/s11548-026-03720-1","type":"journal-article","created":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T11:26:16Z","timestamp":1786620376000},"page":"1621-1629","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Self-supervised monocular depth estimation for colonoscopy using normal-guided cross-attention"],"prefix":"10.1007","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-1841-375X","authenticated-orcid":false,"given":"Yahui","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stamatia","family":"Giannarou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel S.","family":"Elson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,13]]},"reference":[{"key":"3720_CR1","unstructured":"Bhat SF, Alhashim I, Wonka P (2021) Adabins: depth estimation using adaptive bins. 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