ERROR DISTRIBUTION EVALUATION OF THE THIRD VANISHING POINT BASED ON RANDOM STATISTICAL SIMULATION

Abstract. POS, integrated by GPS / INS (Inertial Navigation Systems), has allowed rapid and accurate determination of position and attitude of remote sensing equipment for MMS (Mobile Mapping Systems). However, not only does INS have system error, but also it is very expensive. Therefore, in this paper error distributions of vanishing points are studied and tested in order to substitute INS for MMS in some special land-based scene, such as ground façade where usually only two vanishing points can be detected. Thus, the traditional calibration approach based on three orthogonal vanishing points is being challenged. In this article, firstly, the line clusters, which parallel to each others in object space and correspond to the vanishing points, are detected based on RANSAC (Random Sample Consensus) and parallelism geometric constraint. Secondly, condition adjustment with parameters is utilized to estimate nonlinear error equations of two vanishing points (V_X, V_Y). How to set initial weights for the adjustment solution of single image vanishing points is presented. Solving vanishing points and estimating their error distributions base on iteration method with variable weights, co-factor matrix and error ellipse theory. Thirdly, under the condition of known error ellipses of two vanishing points (V_X, V_Y) and on the basis of the triangle geometric relationship of three vanishing points, the error distribution of the third vanishing point (V_Z) is calculated and evaluated by random statistical simulation with ignoring camera distortion. Moreover, Monte Carlo methods utilized for random statistical estimation are presented. Finally, experimental results of vanishing points coordinate and their error distributions are shown and analyzed.