Discrete exterior calculus for variational problems in computer vision and graphics
Discrete exterior calculus for variational problems in computer vision and graphics
复制标题
计算机视觉和图形中变分问题的离散外微积分
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
J. Marsden
中科院分区：
文献类型：
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作者：
M. Desbrun;A. N. Hirani;J. Marsden
本文演示了如何离散外部演算（DEC）工具可能是有用的计算机视觉和图形。变分方法提供了与力学的联系。我们的DEC的发展包括离散微分形式，离散向量场和这些操作。这种离散微积分的发展，当与离散力学和其他最近的工作的方法相结合时，很可能在计算机视觉等领域有很好的应用，它提供了丰富的各种各样的具有挑战性的变分问题要解决计算。作为一个具体的例子，我们考虑的模板匹配的问题，并显示如何从离散外部演算的数值方法开始发挥重要作用，在求解平均模板匹配的方程。我们还展示了一些例子应用程序使用变分问题从计算机图形学和力学证明，制定问题的离散和使用离散方法的解决方案，可以导致有效的算法。
The paper demonstrates how discrete exterior calculus (DEC) tools may be useful in computer vision and graphics. A variational approach provides a link with mechanics. Our development of DEC includes discrete differential forms, discrete vector fields and the operators acting on these. This development of a discrete calculus, when combined with the methods of discrete mechanics and other recent work is likely to have promising applications in a field like computer vision which offers such a rich variety of challenging variational problems to be solved computationally. As a specific example we consider the problem of template matching and show how numerical methods derived from a discrete exterior calculus are starting to play an important role in solving the equations of averaged template matching. We also show some example applications using variational problems from computer graphics and mechanics to demonstrate that formulating the problem discretely and using discrete methods for solution can lead to efficient algorithms.