{"schema_version":"1.0","canonical_url":"https://patentable.app/patents/US-9646361","patent":{"patent_number":"US-9646361","title":"Initialization independent approaches towards registration of 3D models with 2D projections","assignee":null,"inventors":[],"filing_date":"2015-12-10T00:00:00.000Z","publication_date":"2017-05-09T00:00:00.000Z","cpc_codes":["G06T","G06T","G06T","G06T","G06T","G06T","G06T"],"num_claims":21,"abstract":"A method of registering a 3-dimensional (3D) model of a coronary artery tree with 2-dimensional (2D) images includes solving for matrices R, Pi, i=1, . . . , N, that minimize a cost function Σi=1N∥ΨiRX−IiPi∥2,1 subject to constraints that R∈conv(SO(3)), Pi∈[0,1]n×m, and Pi1≦1, 1TPi=1, for i∈{1, N}, where N is a number of 2D images, R is a rotation matrix, conv(SO(3)) denotes a convex hull of the special orthogonal group in 3 dimensions, X denotes a 3D centerline model of a coronary artery tree, Ii denotes the ith 2D image, Ψi denotes a transformation between the 3D centerline model X and the ith 2D image Ii, 1 is an all-ones vector, Pi is a permutation matrix, and rounding a solution R to a nearest orthogonal matrix R* in SO(3), where R* aligns the 3D centerline model X of the coronary artery tree with 2D fluoroscopic images acquired during a percutaneous coronary intervention procedure."},"analysis":{"summary":null,"layman_explanation":null,"technical_analysis":null,"business_analysis":null,"faqs":null,"topics":[],"tech_cluster":null},"seo":{"title":"Initialization independent approaches towards registration of 3D models with 2D projections","description":"A method of registering a 3-dimensional (3D) model of a coronary artery tree with 2-dimensional (2D) images includes solving for matrices R, Pi, i=1, . . . , N, that minimize a cost function Σi=1N∥ΨiR","keywords":[]},"attribution":{"source":"Patentable","source_url":"https://patentable.app","canonical_url":"https://patentable.app/patents/US-9646361","license":"CC-BY-4.0-like","license_terms":"AI-generated analysis on this page (summary, layman_explanation, technical_analysis, business_analysis, faqs) may be reused with attribution and a visible link back to the canonical URL above. Patent abstracts, claims, and bibliographic data are USPTO public domain.","required_link":"https://patentable.app/patents/US-9646361","citation_suggestion":"Patentable. \"Initialization independent approaches towards registration of 3D models with 2D projections\" (US-9646361). https://patentable.app/patents/US-9646361","copyright_holder":"Nomic Interactive Technology LLC"},"links":{"html":"https://patentable.app/patents/US-9646361","json":"https://patentable.app/api/llm-context/US-9646361","site":"https://patentable.app","llms_txt":"https://patentable.app/llms.txt"},"generated_at":"2026-06-06T15:33:08.208Z"}