Eigenvalue-Based Approaches for Solving an Ill-Posed Problem Arising in Sensor Orientation

Abstract

Sensor orientation is an essential step for georeferencing of images, establishing the coordinate transformation between the image and ground spaces. This orientation is mainly carried out by the sensor dependent or independent models, and the desired georeferencing accuracy is achieved with the adjusted orientation elements using ancillary data. Independently of the orientation model, an ill-posed problem is occurred in the adjustment process, caused by the ill-conditioned Jacobian matrix which is differentiated through the orientation elements. However, this challenge is mitigated by various approaches such as regularization, matrix inversion, or elimination methods. In this work, three different types of orientation models were exposed on Zonguldak test site characterizing mountainous urban and dense forest areas: 1) sensor-dependent orientation model for handling of SPOT 5 HRG panchromatic stereo images and 2) sensor-dependent and 3) sensor-independent rational function model (RFM) for Pleiades 1A and SPOT 6 panchromatic mono images. The main finding of this work is that eigenvalue-based approaches, i.e., Tikhonov regularization using eigenvalue and Moore–Penrose (pseudo) inversing, provide the best numerical solutions among the approaches initially investigated by the authors. The novelty of this article is that two eigenvalue-based approaches investigated in this article are never preferred to solve ill-posed problem in different sensor orientation cases.