Estimation of Camera Parameters from a Single Moving Camera using Quaternion-based Interpolation of 3D Trajectory

This paper presents a new quaternion-based method to estimate the camera parameters in a single video stream to interpolate 3D trajectory of the moving camera with camera parameters. We assume that the camera looks at three fixed points while translating and rotating in 3D space. To estimate the camera parameters, we get a set of nonlinear equations derived from a geometric perspective camera model. We have a large number of image frames to find each camera parameters while the number of unknown camera model parameters cannot be determined from a single frame. In order to solve this problem, we used interpolation to approximate camera movement in both translation and rotation. This was done using the concept of control node set at the specific frame in the video stream. The camera movement is based on acceleration level control while satisfying physical constraints. The control node is the set of variables used to determine acceleration-based interpolated equation used for data fitting. In this process, we used quaternion to interpolate orientation of the camera. The acceleration-based data fitting problem is solved using nonlinear parameter optimization solver, GRG2. Our experimental results show that this approach to estimate camera parameters and 3D trajectory of the camera moment is robust enough to handle image sequences of a common scene without sudden change in camera moment.

1. Introduction

Estimation of the camera parameters from consecutive images taken from a single moving camera with common scene is one of the hardest problems in augmented reality, and camera interpolation to produce smooth and natural scene with three dimensional artificial object embedded is very important in computer animation. In this paper, we propose a new method for estimation of the changes in camera parameters, both in orientation and displacement, in a movie sequence. We have a single camera moving, and the moving condition may differ according to each scene. The target has three points in the scene. We do not have any information in terms of camera and three target points. If the camera is moving at constant velocity, we need three images to identify relative position/orientation of three target points in terms of camera. Possibly we can compute displacement/angular velocities between the target and the camera. If the camera is moving at constant acceleration, we need 4 images to compute all values involved in the scene. If the camera is moving at varying acceleration, there is no analytic solution, but we have to rely on approximate solution. This work is an extension of our early work in object tracking[13]. Figure 1. Architecture of the Proposed Method