Exploitation of Linear Features in Surveying and Photogrammetry

Abstract

Modeling of linear features, particularly straight lines and circles, in two-dimensional (2D) and three-dimensional (3D) spaces, is developed, with specific consideration of independent descriptors. This is followed by the derivation of the four-, six-, and eight-parameter 2D transformations in terms of the line and circle parameters, as well as 3D linear transformation. Minimum configuration, redundant cases, and restrictions regarding special cases are carefully noted and are compared to the cases of using points only. Many useful geometric constraints between linear features, which provide significant information, are identified and corresponding equations are developed. Constraints involving relative geometric information relating features to each other are considered in addition to those constraints relating features to the reference coordinate system. Finally, the standard point-based photogrammetric collinearity equations are replaced by those based on correspondence between image and object linear features. Results are presented describing experiments where the coordinates of points are perturbed using Gaussian random noise to emulate real data. Several thoughts are listed regarding the future applications of this research in practice.