Mutlak Yöneltmenin Doğrudan Çözümü İçin Gauss-Helmert Modeli

Yıl 2023, Cilt: 5 Sayı: 2, 66 - 73, 31.12.2023

Ozan Arslan

https://doi.org/10.53030/tufod.1385445

Öz

Mutlak yöneltme, fotogrametri, bilgisayarlı görü (computer vision) ve robot biliminde eski ve temel görevlerden biridir. Fotoğraf çiftlerinden geliştirilen stereo modelin görüntü koordinat sisteminden nesne koordinat sistemine dönüşümünün elde edilmesini içerir. Mutlak yöneltmeye yönelik geleneksel çözüm, dönüşüm parametrelerinin iyi bir yaklaşımını gerektiren bir doğrusallaştırma sürecini işleten sayısal (nümerik) yinelemeli en küçük kareler çözümüdür. Bu çalışmada ise mutlak yöneltmenin çözümü için üç boyutlu benzerlik dönüşümünde kullanılan ve ‘doğrudan’ çözüm sağlayan Gauss-Helmert Modeli üzerinde durulmuştur. Önerilen doğrudan çözüm yönteminin performansını test etmek üzere; literatürde özellikleri bilinen bir koordinat veri seti sayısal uygulama ve analizler için kullanılmıştır. Geleneksel GMM yöntemiyle kestirilen dönüşüm parametreleri ve doğruluk değerleri, doğrudan çözüm sağlayan GHM modeliyle elde edilen sonuçlarla karşılaştırılmıştır.
Genel olarak dönme açılarının nispeten küçük olduğu mutlak yöneltme problemlerinde doğrudan çözüm yöntemlerinin kullanılması uygun bir tercih olabilir. Örnek sayısal deneylerde GHM modelinin daha az zaman gereksinimiyle, daha duyarlı dönüşüm parametreleri üretebileceği gösterilmiştir.

Anahtar Kelimeler

Mutlak yöneltme, En küçük kareler, Koordinat dönüşümü, Gauss-Helmert modeli

Gauss-Helmert Model for Direct Solution to Absolute Orientation

Öz

Absolute orientation is an old and fundamental task in photogrammetry, computer vision and robotics. It involves obtaining the transformation of the stereo model developed from pairs of photographs from the image coordinate system to the object coordinate system. The traditional solution for absolute orientation is a numerical iterative least squares solution, which operates a linearisation process that requires a good approximation of the transformation parameters. In this study, we focus on the Gauss-Helmert model, which is used in three-dimensional similarity transformation for solving absolute orientation and provides a 'direct' solution. In order to test the performance of the proposed direct solution method, a coordinate data set with known properties in the literature is used for numerical implementation and analyses. The transformation parameters and accuracy values estimated by the conventional GMM method are compared with the results obtained by the direct solution GHM model. In general, for absolute orientation problems where the rotation angles are relatively small, the use of direct solution methods may be an appropriate choice. Numerical experiments have shown that the GHM model can produce more accurate transformation parameters with less time requirement.

Anahtar Kelimeler

Absolute orientation, least squares, coordinate transformation, Gauss-Helmert model

Kaynakça

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