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Termes IGN > mathématiques > analyse numérique > optimisation (mathématiques) > programmation linéaire > méthode itérative de Newton-Raphson
méthode itérative de Newton-RaphsonSynonyme(s)Méthode du paraboloïde |
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Evaluation of the Newton-Raphson method for three-point resection in photogrammetry / S.M. Easa in SaLIS Surveying and land information science, vol 67 n° 1 (March 2007)
[article]
Titre : Evaluation of the Newton-Raphson method for three-point resection in photogrammetry Type de document : Article/Communication Auteurs : S.M. Easa, Auteur Année de publication : 2007 Article en page(s) : pp 33 - 42 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Photogrammétrie numérique
[Termes IGN] méthode itérative de Newton-Raphson
[Termes IGN] relèvement
[Termes IGN] relèvement photogrammétriqueRésumé : (Auteur) Three-point resection in photogrammetry (based on measured distances between three object points and the corresponding image coordinates) has been a viable approach because it does not require data on the object coordinates. Many iterative and closed-form solutions of the problem have been developed. The problem may have up to four solutions for the distances between the exposure station and the objects. Due to the complexity of the closed-form solutions, a simple method involving Newton-Raphson (N-R) search has recently been suggested for determining the unique (correct) solution for the Grunert's quartic polynomial. The N-R method, however, may not converge to the unique solution. This paper first describes the geometry of the three-point resection and the difficulties with the N-R method. A new Excel-based method that identifies all four solutions of the quartic polynomial is then presented. The method does not require initial estimates of the roots. Situations in which the N-R method is useful are highlighted. Application examples are used to illustrate the issues and concepts addressed. The proposed method, which provides insights into space resection, should be of interest to both researchers and educators. Copyright SaLIS Numéro de notice : A2007-211 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article DOI : sans Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=83654
in SaLIS Surveying and land information science > vol 67 n° 1 (March 2007) . - pp 33 - 42[article]Réservation
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Code-barres Cote Support Localisation Section Disponibilité 121-07011 RAB Revue Centre de documentation En réserve L003 Disponible The 3-point resection problem in photogrammetry / W. Tan in Surveying and land information science, vol 64 n° 3 (01/09/2004)
[article]
Titre : The 3-point resection problem in photogrammetry Type de document : Article/Communication Auteurs : W. Tan, Auteur Année de publication : 2004 Article en page(s) : pp 177 - 179 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Photogrammétrie numérique
[Termes IGN] convergence
[Termes IGN] itération
[Termes IGN] méthode itérative de Newton-Raphson
[Termes IGN] photogrammétrie numérique
[Termes IGN] relèvementRésumé : (Auteur) This paper provides a simple solution to the three-point resection problem in photogrammetry. it is based on Grunert's (1841) closed form solution but uses the Newton-Raphson iteration procedure, and its desirable property of quadratic convergence, to solve the quartic equation. The proposed solution is superior to closed-form solution with multiple roots. Although four-point closed form formulas also exist to define a unique solution, they are quite complex. Numéro de notice : A2004-603 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article DOI : sans Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=27119
in Surveying and land information science > vol 64 n° 3 (01/09/2004) . - pp 177 - 179[article]Réservation
Réserver ce documentExemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 121-04031 SL Revue Centre de documentation Revues en salle Disponible