标题： 方向得分应该很容易 显示英文标题

标题： Orientation Scores should be a Piece of Cake

摘要： 我们通过公理化方法推导出一种用于方向评分的波浪小波族，从位置空间$\mathbb{R}^2$提升到位置和方向空间$\mathbb{R}^2\times S^1$，具有快速重建特性，且最小化位置-方向不确定性。 随后，我们证明这些最小不确定性状态可以很好地由蛋糕波浪小波近似：对于标准参数，蛋糕波浪小波的不确定性差距小于 1.1，并且在极限情况下，我们证明不确定性差距趋向于最小值 1。 接下来，我们完善了之前的理论论证，说明在 (PDE-)G-CNN 中不需要训练提升层，而是可以使用蛋糕波浪小波。 最后，我们通过实验表明，这样可以减少网络复杂性并提高 (PDE-)G-CNN 的可解释性，而对模型性能的影响仅是轻微的。 显示英文摘要

摘要： We axiomatically derive a family of wavelets for an orientation score, lifting from position space $\mathbb{R}^2$ to position and orientation space $\mathbb{R}^2\times S^1$, with fast reconstruction property, that minimise position-orientation uncertainty. We subsequently show that these minimum uncertainty states are well-approximated by cake wavelets: for standard parameters, the uncertainty gap of cake wavelets is less than 1.1, and in the limit, we prove the uncertainty gap tends to the minimum of 1. Next, we complete a previous theoretical argument that one does not have to train the lifting layer in (PDE-)G-CNNs, but can instead use cake wavelets. Finally, we show experimentally that in this way we can reduce the network complexity and improve the interpretability of (PDE-)G-CNNs, with only a slight impact on the model's performance.