A COMPARISON STUDY BETWEEN COLLINEARITY CONDITION, COPLANARITY CONDITION, AND DIRECT LINEAR TRANSFORMATION (DLT) METHOD FOR CAMERA EXTERIOR ORIENTATION PARAMETERS DETERMINATION

Khalid L A El-Ashmawy

doi:10.3846/20296991.2015.1051335

Abstract

The present work emphasizes on using collinearity condition, coplanarity condition and DLT method for determining the camera exterior orientation parameters. The derivation of the mathematical formulation based on each suggested methods is explained. The comparison of the results of the methods was performed based on accuracy aspects using mathematical and actual photogrammetric data. The used data shows that the suggested methods are suitable for camera exterior orientation parameters determination for a block of photographs of any size. The results of this investigation prove that the accuracy of using coplanarity equations is slightly better than using collinearity equations or DLT method. Although the results of the DLT method are less accurate than those of using collinearity or coplanarity equation, DLT method is essential when the necessary information for the collinearity or coplanarity model is not available. This paper shows the necessity for the mathematical photogrammetric data for testing the photogrammetric studies.

Highlights

With regard to a single photograph, its exterior orientation consists of two separable sets of parameters
Undoubtedly the most flexible approach to block formation and adjustment and to photogrammetry in general is through the use of the bundles of rays produced by individual photographs
∆ is the correction vector to the current values set for the unknowns in the iterative solution; B is the matrix of the partial derivatives of Equation

Summary

Introduction

With regard to a single photograph, its exterior orientation (with respect to the object space) consists of two separable sets of parameters. The results of the bundle adjustment of the block of photographs are camera exterior orientation parameters of each photograph and a listing of the object space coordinates of the measured new points as well as their statistical precision. ∆ is the correction vector to the current values set for the unknowns (camera interior orientation parameters, camera exterior orientation parameters of each photo and object space coordinates of points) in the iterative solution;. More details for the determination of the initial values of camera exterior orientation parameters and the object space coordinates of pass and/or tie points can be found in El-Ashmawy (1999). ∆ is the correction vector to the current values set for the unknowns (camera interior orientation parameters, camera exterior orientation parameters of the left and right photos and object space coordinates of points) in the iterative solution;. For starting the least squares iterative solution, the computation of the initial values of unknowns is essential and explained in (El-Ashmawy, Azmi 2003)

Determination of camera exterior orientation parameters using the DLT method

Developing and testing the necessary softwares

Strips

Method

Findings

Conclusions