Comparative evaluation of iterative and non-iterative methods to ground coordinate determination from single aerial images

Abstract

The single-ray backprojection problem refers to the process of determining ground coordinates of pixels in a single aerial image with the support of a digital surface model or a digital elevation model. Several methods have been employed to solve this problem. The iterative photogrammetric (IP) method, based on the inverse collinearity equations, is widely used in photogrammetry. The ray-tracing (RT) method, which is popular in computer graphics, computes the coordinates by intersecting the view ray with the surface. A third one is an iterative ray-tracing (IRT) method, which finds the intersection point by extending the view ray towards the surface by a certain step once a time until it hits the surface. Since the methods become diversified, there is a need to compare and evaluate them. This paper analyzes the principles of these three methods, tests them using a variety of data sets, and provides a comprehensive comparison on their strategies, parameter selection, divergence, occlusion-compliance, precision, robustness, and efficiency. The major difference of these methods is in the strategy of computing the intersection between the view ray and the surface, and this leads to their varied performance. It is found that the IP method is the most computationally efficient and can produce precise coordinates for simple surfaces, but it may surfer from the divergence and occlusion-induced problems for complicated ones. The rigorous RT method is precise, occlusion-compliant and parameter-free, but it is computationally intensive. The IRT method is intermediate in terms of efficiency. If the initial step is small enough, it can adequately address the occlusion-induced problem and produce satisfactory coordinates for complicated surfaces. This comparison provides a guide to method selection for the single-ray backprojection problem.