Real-Time Nonlinear Shape Interpolation
Real-Time Nonlinear Shape Interpolation
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DOI：
10.1145/2729972
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发表时间：
2015-05
期刊：
影响因子：
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通讯作者：
C. V. Tycowicz;Christian Schulz;H. Seidel;K. Hildebrandt
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文献类型：
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作者：
C. V. Tycowicz;Christian Schulz;H. Seidel;K. Hildebrandt
我们介绍了一个实时非线性插值的一组形状的计划。该方案利用了形状插值问题的结构，特别是所有可能的插值形状的集合是高维形状空间中的低维对象的事实。插值形状被定义为形状空间上的非线性目标泛函的最小值。我们的方法是构造一个简化的优化问题，近似其未简化的对应，可以在毫秒内解决。为了实现这一点，我们限制优化的低维子空间，是专门设计的形状插值问题。的子空间的建设是基于两个组成部分：一个公式计算的衍生物的插值形状和一个Krylov型序列相结合的衍生物和Hessian的目标功能。为了使计算成本为解决减少优化问题的独立的分辨率的例子形状，我们结合联合收割机的降维方案的有效近似减少非线性目标功能和它的梯度。在我们的实验中，我们获得的速率为每秒20- 100插值形状，即使是最大的例子，每个例子形状有500 k个顶点。
We introduce a scheme for real-time nonlinear interpolation of a set of shapes. The scheme exploits the structure of the shape interpolation problem, in particular the fact that the set of all possible interpolated shapes is a low-dimensional object in a high-dimensional shape space. The interpolated shapes are defined as the minimizers of a nonlinear objective functional on the shape space. Our approach is to construct a reduced optimization problem that approximates its unreduced counterpart and can be solved in milliseconds. To achieve this, we restrict the optimization to a low-dimensional subspace that is specifically designed for the shape interpolation problem. The construction of the subspace is based on two components: a formula for the calculation of derivatives of the interpolated shapes and a Krylov-type sequence that combines the derivatives and the Hessian of the objective functional. To make the computational cost for solving the reduced optimization problem independent of the resolution of the example shapes, we combine the dimensional reduction with schemes for the efficient approximation of the reduced nonlinear objective functional and its gradient. In our experiments, we obtain rates of 20--100 interpolated shapes per second, even for the largest examples which have 500k vertices per example shape.