Extended Abstract
Introduction
Analyzing the image blocks captured before and after geometrical changes is known as the conventional approach for detecting them in photogrammetric applications. Developed methods can be categorized into 1- comparison of 3D models generated via the image blocks and 2- direct comparison of single images. The occurrence of radiometric differences in the geometrically changed areas can increase their discrimination and facilitate their detection. However, the occurrence of geometric changes without sensible radiometric effects is a special type of change that its identification is faced with more challenges. Slight displacement of the objects in the scene, small landslides, subsidence or uplift, the effects of local pressure and tension on objects in the industrial procedures and etc. are some examples of geometric changes that do not have a noticeable radiometric appearance in the images.
In the absence of incorrect observations, simultaneous triangulation of image blocks captured before and after geometric changes is a simple and effective way of reaching to detection of changes. In other words, by identifying the corresponding points in the fixed regions of the scene in the image blocks, the simultaneous triangulation of the image blocks captured in both epochs can align them in a unique object coordinate system. Thus, it can be possible to generate two independent and co-registered 3D models for identifying the occurred changes. However, maintaining the radiometric similarity of the changed areas leads to the identification of wrong-matched points when using automatic image matching methods.
The inclusion of an unknown 3D position for each wrong-matched point in the changed areas leads to a defect in the design of the mathematical model for the bundle adjustment. These defects result in incorrect generation of the 3D models, large and systematic errors in the residuals of observations, and incorrect estimation of the extrinsic parameters of images. The remedy to this defect is to assign two distinct unknown 3D positions for each wrong-matched point before and after changes in the bundle adjustment. Lack of prior knowledge of the wrong-matched points located in the changed areas is the cause of this problem. In this article, an iterative solution is proposed to identify and correct the effects of the wrong-matched points in the process of simultaneous bundle adjustment.
Materials and Methods
In the proposed method, at first, all the confident radiometrically matched points among all images taken before and after the geometric changes are detected via the well-known feature-based image matching methods. Their matched positions, then, are again accurately rectified and verified by the least squares image matching method. The matched points identified after refinement are classified into two categories. 1- The matched points that have been detected only in the images of one image block and 2- The matched points that have been detected at least in two images in each image block. Among the points of the second category, there probably are matched points that are geometrically changed between two epochs, but their radiometric similarities have made to incorrectly identified as the matched points between two image blocks. In this paper, these were called the wrong-matched points which are iteratively identified and their corresponding mathematical models are corrected in the triangulation process.
To do so, three different bundle adjustments are performed as the first step. Independent triangulation of the image blocks captured before and after the geometric changes and the simultaneous bundle adjustment of both blocks via the initially detected matched points of the first and second categories are the first three triangulations. Due to the existence of wrong-matched points, the initial simultaneous triangulation has a defect in the design of the mathematical model, which is gradually and in an iterative process, the wrong-matched points located in the changed areas would be identified.
Identification of the wrong-matched points is done using the relative comparisons on their residual vectors. The comparisons are designed in two consecutive statistical tests. The main idea of this method has been inspired by the well-known Baarda test in the detection of gross errors in the observations of geodetic networks. By gradual identification of the wrong-matched points, their corresponding mathematical model will be modified in the bundle adjustment.To do so, the unknown values of the 3D coordinates of these points are separated for the time before and after the change epochs.This action by modification of the mathematical model in the bundle adjustments brings back the relative equilibrium in the estimation of the residual vector of observations.
 
Results and Discussion
Implementation and comparison of the proposed method with a conventional geometric approach in identifying the incorrectly matched points (using robust estimation of the epipolar geometry) have shown the adequacy and superiority of the proposed method. The proposed method, on average in more than 11 different experiments, was able to achieve an average accuracy of 85.8% in identifying the changed points. Meanwhile, the proposed method shows a 34.5% improvement compared to the conventional geometric approach based on epipolar geometry.
               
Conclusions and suggestions
The proposed method is an effective solution for identifying the geometrically changed points in the simultaneous triangulation of image blocks before and after geometric changes when the changed areas have a stable radiometric similarity. This method is more sensitive to the occurred changes than the conventional method of identifying incorrect correspondences based on epipolar geometry. Iterative adjustment of the observations’weight matrix through the Variance Components Estimation (VCE) techniques in order to detect and eliminate the effects of wrong-matched points can be considered a future research topic in this field.