A New Approach to Through-the-Lens Camera Control
A New Approach to Through-the-Lens Camera Control
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通过镜头控制相机的新方法
DOI：
10.1006/gmip.1996.0022
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
S. Hong
中科院分区：
文献类型：
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作者：
M. Kyung;Myung;S. Hong
本文介绍了由M. Gleicher和A. Witkin [计算机] Graphics 26（2），1992，331-340]，提供了一种强大的用户界面，用于控制3D计算机图形和动画中的虚拟相机。他们的技术是基于局部反演的非线性透视观察变换。然而，在给定m个图像控制点的情况下，雅可比矩阵是一个非常复杂的2 m × 8矩阵，而且雅可比矩阵的秩最多可以为7，因此它至少有一个冗余列。对于m ≥ 4的过约束情形，由于其2 m × 2 m方阵的秩最多为7，所以拉格朗日方程总是奇异的.所有这些复杂性都是由于去除了表示摄像机旋转的单位四元数（qw，qx，qy，qz）∈ S3的约束q2 w + q2 x + q2 y + q2 z = 1而产生的。在本文中，我们解释的问题作为一个目标跟踪问题，并制定它作为一个约束的非线性反演问题。然后通过对虚拟相机的配置空间上定义的切向量场进行积分来解决该问题。矢量场由雅可比矩阵方程的最小二乘解给出。雅可比矩阵的行和列加权方案提供了一种方便的方法来控制所需的最小二乘解和相关的向量场。单位四元数空间S3的李群结构使我们能够导出一个简单的2 m × 7雅可比矩阵，这提高了整个算法的计算效率和数值稳定性。对于m ≥ 4的过约束情形，利用一种时间复杂度为O（m）的有效投影方法求解雅可比矩阵方程（在最小二乘意义下）.
Abstract The through-the-lens camera control technique originally proposed by M. Gleicher and A. Witkin [Comput. Graphics26(2), 1992, 331–340], provides a powerful user interface for the control of the virtual camera in 3D computer graphics and animation. Their techique is based on locally inverting the nonlinear perspective viewing transformation. However, givenmimage control points, the Jacobian matrix is derived as a quite complex 2m× 8 matrix; furthermore, the Jacobian matrix always has at least one redundant column since its rank can be 7 at most. For the overconstrained case ofm≥ 4, the Lagrange equation is always singular since its 2m× 2msquare matrix has rank 7 at most. All these complications result from removing the constraintq2w+q2x+q2y+q2z= 1 for unit quaternions (qw,qx,qy,qz) ∈S3which represent the camera rotations. In this paper, we interpret the problem as a target tracking problem and formulate it as a constrianed nonlinear inversion problem. The problem is then solved by integrating a tangent vector field defined on the configuration space of the virtual camera. The vector field is given by the least-squares solutions of the Jacobian matrix equations. The row and column weighting scheme for the Jacobian matrix provides a convenient way to control the desired least-squares solutions and the associated vector field. The Lie group structure of the unit quaternion spaceS3enables us to derive a simple 2m× 7 Jacobian matrix, which improves both the computational efficiency and numerical stability of the overall algorithm. For the overconstrained case ofm≥ 4, the Jacobian matrix equation is solved (in the least-squares sense) by using an efficient projection method withO(m) time complexity.