Use of generalised Procrustes analysis for the photogrammetric block adjustment by independent models |
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| Institution: | 1. Programa de Pós-graduação em Análise de Bacias e Faixas Móveis, Universidade do Estado do Rio de Janeiro (UERJ), Faculdade de Geologia, Rua São Francisco Xavier, 524, Maracanã, 20550-013, Rio de Janeiro, RJ, Brazil;2. Universidade Federal do Triângulo Mineiro (UFTM), Instituto de Ciências Exatas, Naturais e Educação (ICENE), Av. Randolfo Borges Jr. 1400, Univerdecidade, 38064-200, Uberaba, MG, Brazil;3. Universidade Federal do Triângulo Mineiro (UFTM), Complexo Cultural e Científico de Peirópolis (CCCP), Centro de Pesquisas Paleontológicas “Llewellyn Ivor Price” (CPPLIP), Uberaba, MG, Brazil;4. Museu de Paleontologia “Prof. Antonio Celso de Arruda Campos”, Centro de Artes, Praça do Centenário, 15910-000, Monte Alto, SP, Brazil;5. Museu de Paleontologia “Pedro Candolo”, Estação Cultura, Praça Farmacêutico Bruno Garisto, 15890-000, Uchoa, SP, Brazil;1. Department of Mathematics, Science Faculty, Taibah University, Al Madinah Al Munawwarah, P.O. Box 30097, Zip Code 41477, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Moulay Ismail University, Meknes, Morocco;3. Department of Pure Mathematics, P.O. Box 1159, Ferdowsi University of Mashhad, Mashhad 91775, Iran;4. Department of Information Science, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan;1. Oak Ridge Institute of Science and Education, Ecosystems Research Division, 960 College Station Road, Athens, GA, USA;2. US Environmental Protection Agency, Ecosystems Research Division, 960 College Station Road, Athens, GA, USA;1. Institute of Agrochemistry and Food Technology (IATA), Spanish Council for Scientific Research (CSIC), Agustí Escardino 7, 46980, Paterna, Valencia, Spain;2. Department of Organic Chemistry, University of Valencia, Doctor Moliner 50, 46100, Burjassot, Valencia, Spain |
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| Abstract: | The paper reviews at first some aspects of the generalised Procrustes analysis (GP) and outlines the analogies with the block adjustment by independent models. On this basis, an innovative solution of the block adjustment problem by Procrustes algorithms and the related computer program implementation are presented and discussed.The main advantage of the new proposed method is that it avoids the conventional least squares solution. For this reason, linearisation algorithms and the knowledge of a priori approximate values for the unknown parameters are not required. Once the model coordinates of the tie points are available and at least three control points are known, the Procrustes algorithms can directly provide, without further information, the tie point ground coordinates and the exterior orientation parameters.Furthermore, some numerical block adjustment solutions obtained by the new method in different areas of North Italy are compared to the conventional solution. The very simple data input process, the less memory requirements, the low computing time and the same level of accuracy that characterise the new algorithm with respect to a conventional one are verified with these tests.A block adjustment of 11 models, with 44 tie points and 14 control points, takes just a few seconds on an Intel PIII 400 MHz computer, and the total data memory required is less than twice the allocated space for the input data. This is because most of the computations are carried out on data matrices of limited size, typically 3×3. |
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