时间信号与过去时间的一种时间因果且时间递归的尺度协变尺度空间表示
A time-causal and time-recursive scale-covariant scale-space representation of temporal signals and past time
AI总结：
本文提出一种时间因果且时间递归的尺度协变时间尺度空间理论，通过时间因果极限核实现无需未来信息的多尺度时间平滑与过去记忆，适用于连续现象建模和实时信号处理。
摘要：
本文概述了一种对时间信号进行时间平滑的理论，使得：（i）在较粗时间尺度上的时间平滑信号保证构成任何较细时间尺度（包括原始信号）上相应时间平滑信号的简化，并且（ii）时间平滑过程既是时间因果的又是时间递归的，即它不需要访问未来信息，并且除了所得到的平滑时间尺度空间表示本身之外，不需要其他关于过去的时间记忆缓冲。对于满足这一性质的线性和平移不变时间平滑算子类别的特定参数设置子集，本文展示了如何额外获得时间尺度协变性，从而保证如果时间输入信号被一个均匀缩放因子重新缩放，那么重新缩放后的时间信号所得到的时间尺度空间表示将仅仅构成原始输入信号的时间尺度空间表示的重新缩放，并辅以沿时间尺度维度的平移。由此得到的满足这一性质的时间因果极限核构成了一种规范的时间核，用于在实时场景中处理时间信号，此时常规高斯核因其对来自未来的信息的非因果访问而无法使用，并且我们也不能额外要求时间平滑过程包含超出时间平滑过程本身所含信息的关于过去的补充记忆，而这种方式同时也充当了过去的多尺度时间记忆。该理论普遍适用于：（i）对多个时间尺度上的连续时间现象进行建模，以及（ii）对实测时间信号进行实时数字处理。
英文摘要：
This article presents an overview of a theory for performing temporal smoothing on temporal signals in such a way that: (i) temporally smoothed signals at coarser temporal scales are guaranteed to constitute simplifications of corresponding temporally smoothed signals at any finer temporal scale (including the original signal) and (ii) the temporal smoothing process is both time-causal and time-recursive, in the sense that it does not require access to future information and can be performed with no other temporal memory buffer of the past than the resulting smoothed temporal scale-space representations themselves. For specific subsets of parameter settings for the classes of linear and shift-invariant temporal smoothing operators that obey this property, it is shown how temporal scale covariance can be additionally obtained, guaranteeing that if the temporal input signal is rescaled by a uniform scaling factor, then also the resulting temporal scale-space representations of the rescaled temporal signal will constitute mere rescalings of the temporal scale-space representations of the original input signal, complemented by a shift along the temporal scale dimension. The resulting time-causal limit kernel that obeys this property constitutes a canonical temporal kernel for processing temporal signal in real-time scenarios when the regular Gaussian kernel cannot be used because of its non-causal access to information from the future and we cannot additionally require the temporal smoothing process to comprise a complementary memory of the past beyond the information contained in the temporal smoothing process itself, which in this way also serves as a multi-scale temporal memory of the past. This theory is generally applicable for both: (i) modelling continuous temporal phenomena over multiple temporal scales and (ii) digital processing of measured temporal signals in real time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
