Temporal scale selection in time-causal scale space
When designing and developing scale selection mechanisms for generating hypotheses about characteristic scales in signals, it is essential that the selected scale levels reflect the extent of the underlying structures in the signal. This paper presents a theory and in-depth theoretical analysis about the scale selection properties of methods for automatically selecting local temporal scales in time-dependent signals based on local extrema over temporal scales of scale-normalized temporal derivative responses. Specifically, this paper develops a novel theoretical framework for performing such temporal scale selection over a time-causal and time-recursive temporal domain as is necessary when processing continuous video or audio streams in real time or when modelling biological perception. For a recently developed time-causal and time-recursive scale-space concept defined by convolution with a scale-invariant limit kernel, we show that it is possible to transfer a large number of the desirable scale selection properties that hold for the Gaussian scale-space concept over a non-causal temporal domain to this temporal scale-space concept over a truly time-causal domain. Specifically, we show that for this temporal scale-space concept, it is possible to achieve true temporal scale invariance although the temporal scale levels have to be discrete, which is a novel theoretical construction.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Temporal Causal Prior-Data Fitted Networks for Panel Data with Learned Reliability Signals
Estimating causal effects in industrial time series requires handling temporal dynamics, time-varying treatments, and unobserved confounders. Existing causal foundation models (CausalPFN, CausalFM) operate only on static…
A time-causal and time-recursive analogue of the Gabor transform
This paper presents a time-causal analogue of the Gabor filter, as well as a both time-causal and time-recursive analogue of the Gabor transform, where the proposed time-causal representations obey both temporal scale co…
A time-causal and time-recursive scale-covariant scale-space representation of temporal signals and past time
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 simplificati…
Time-causal and time-recursive spatio-temporal receptive fields
We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, based on a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equi…
Separable time-causal and time-recursive spatio-temporal receptive fields
We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or e…