论文标题
时间信号和过去时间的时期和时间恢复量表的比例空间表示
A time-causal and time-recursive scale-covariant scale-space representation of temporal signals and past time
论文作者
论文摘要
本文概述了一种理论，该理论在时间信号上执行时间平滑的方式：（i）确保时间平滑的时间平滑信号可以保证构成对相应的时间平滑信号的简化，以简化任何较好的时间平滑的信号（包括原始信号）和（包括时间平滑过程），并且（ii）均可访问时间，而不是需要时间访问时间，而不是访问时间，而不是访问时间，而不是访问时间范围，则在不适合时间范围内，而不是在范围内进行访问，则在范围内进行了访问，并且在范围内进行了访问，并且在范围内进行了访问，并且在范围内均能访问，而不是在范围内进行，并且是在范围内进行的。除了由此产生的平滑时间尺度表示本身，没有其他过去的时间内存缓冲区。 对于遵守该属性的线性和转变的时间平滑操作员的类别的特定子集，请显示如何额外获得时间尺度的协方差，并保证，如果均匀标度的时间范围内的临时输入信号归为均匀标度，则可以构成序列信号的临时信号的范围标准范围，以下均等范围，该信号的时间范围均可构成。与沿时间尺度维度的转变相辅相成。服从该属性的随之而来的时间因极限内核构成了一个规范的时间内核，用于在实时场景中处理时间信号，当时无法使用常规高斯内核，因为它的非伴侣访问其未来的信息，我们不能额外地需要临时的辅助过程，以使其在此范围内构成平稳的辅助记忆。过去的多尺度时间内存。 该理论通常适用于两者：（i）在多个时间尺度上对连续的时间现象进行建模，以及（ii）实时测量时间信号的数字处理。
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.
