Fixing Implicit Derivatives: Trust-Region Based Learning of Continuous Energy Functions
Fixing Implicit Derivatives: Trust-Region Based Learning of Continuous Energy Functions
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发表时间：
2019-09
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通讯作者：
Chris Russell;M. Toso;N. Campbell
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作者：
Chris Russell;M. Toso;N. Campbell
我们提出了一种学习连续能量函数的新技术，我们称之为维伯格学习。逆问题的一种常见方法是将其转化为能量最小化问题，其中找到的最小成本解决方案用作隐藏参数的估计器。我们的新方法通过将最小值描述为优化方法的固定点，正式表征了控制能量函数形状的权重与最小值位置之间的依赖性。这允许使用基于梯度的端到端训练来集成深度学习和经典的逆问题方法。我们展示了如何应用我们的方法在跟踪器融合和多视图 3D 重建的各种应用中获得最先进的结果。
We present a new technique for the learning of continuous energy functions that we refer to as Wibergian Learning. One common approach to inverse problems is to cast them as an energy minimisation problem, where the minimum cost solution found is used as an estimator of hidden parameters. Our new approach formally characterises the dependency between weights that control the shape of the energy function, and the location of minima, by describing minima as fixed points of optimisation methods. This allows for the use of gradient-based end-to- end training to integrate deep-learning and the classical inverse problem methods. We show how our approach can be applied to obtain state-of-the-art results in the diverse applications of tracker fusion and multiview 3D reconstruction.