Accurata 3D Registration Optimization Based On Graphics Simulation Method

Three-dimensional registration is one of the key technologies in the field of Augmented Reality.Its purpose is to achieve the geometrical consistency between the virtual world and the real world,and its essence is to obtain the position and direction of the target object in the image relative to the camera,named the pose of the target object.For the solution of the three-dimensional registration problem,it is generally converted into the optimization problem of the objective function,and then the optimization problem is solved by the Levenberg-Marquardt algorithm[1].The core of the algorithm is to obtain the first derivative of the objective function,the Jacobian matrix,to determine the direction in which the algorithm iterates.According to the different conditions of the objective function and its derivative function,the solution method of Jacobian matrix can be divided into three types:When the objective function and its derivative function can be analytically solved,the analytical method is usually used to directly determine the first derivative;when the target When the function can be parsed and the derivative function is unresolvable,it can be approximated from a defined point of view by means of numerical sampling to obtain the approximate value of the derivative.When the objective function is not analytically expressed,the 3D model data of the target object can be used to render the image through graphics.The method simulates the function value under the corresponding parameters,and then uses the numerical method to approximate the solution.This method is called the graphic simulation method.In this paper,we first define the objective function based on contour matching when the three-dimensional model of target object is known,and use L-M algorithm to solve it.Since the objective function is not parsable,this paper uses a graphical simulation method to obtain its first derivative.However,the method of graphic simulation is based on pixels.Therefore,there is a lower limit of accuracy.In the refined iteration process,due to the small step size,the maximum error of the derivative approximation is often caused,and the optimization process converges to the target.The local extremum of the function causes a large error.To solve this problem,this paper proposes a refined optimization method combining analytical incremental estimation with random sampling estimation.During each iteration,according to the differences in the features of the position and orientation in the pose parameters,the corresponding derivative components are calculated using the analytical incremental estimation method and the random sampling estimation method,respectively,to ensure that the incremental reprojection point is always a contour point.At the same time,the precision of discrete sampling is achieved at the floating-point level,which simulates a smooth expression for the objective function.This can greatly reduce the local extremum interference caused by the resolution of the image and improve the accuracy of the algorithm.In order to verify the fine-tuning method based on graph simulation proposed in this paper,we conducted several sets of comparative experiments.The results of quantitative and qualitative comparison show that this method can converge quickly and overcome the local extremum problem well.