Projective Geometry in Photogrammetry
Date Issued
2007
Date
2007
Author(s)
Cheng, Chieh-Wen
DOI
zh-TW
Abstract
The collinearity equation is commonly used to estimate the best result when determining orientation parameters. This method is rigorous, but because it belongs to systems of non-linear equations, it is necessary to use parameter approximations and the iteration process to get convergent results. Projective geometry provides an alternative method for representing and transforming geometric entities, and transfers the complicated non-linear problems in photogrammetry into simple linear cases. The results can then be treated as the approximations for the rigorous non-linear system. Projective geometry also produces estimates of orientation parameters and epipolar images that are of similar quality as the results yielded by using the common collinearity and coplanarity methods. It is a possible substitute procedure, which supports automated calculation, to the collinearity and coplanarity methods for photogrammetry issues.
This study consists of two parts. The first part is a comparative study between using the collinearity method and the projective geometry method to determine orientation parameters and intersecting ground points. The second part is a comparative study between using the coplanarity method and the projective geometry method to solve epipolar geometry. The first part tested, via simulated experiments, several factors that would affect the results in determining the orientation parameters and the coordinates of ground points, such as the accuracy of control points, the accuracy of observations, the number of control points, and the distribution of control points. Actual aerial and close-range photos were used to execute the resection, intersection and epipolar image solving process. After analyzing the data, the feasibility of the projective geometry in photogrammetry was verified.
Subjects
射影幾何
核線幾何
基本矩陣
基礎矩陣
直接線性轉換
共線式
共面式
Projective geometry
Epipolar geometry
Essential matrix
Fundamental matrix
Direct linear transform
Collinarity equation
Coplanarity equation
Type
thesis
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