Temporal scale selection in time-causal scale space

Abstract

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.

44 pages, 15 figures, 10 tables in Journal of Mathematical Imaging and Vision, 2017

References in corpus (5)

• Action Recognition with Trajectory-Pooled Deep-Convolutional Descriptors
• Time-causal and time-recursive spatio-temporal receptive fields
• Invariance of visual operations at the level of receptive fields
• Idealized computational models for auditory receptive fields
• Separable time-causal and time-recursive spatio-temporal receptive fields

Cited by in corpus (7)

• Normative theory of visual receptive fields
• Dense scale selection over space, time and space-time
• A time-causal and time-recursive scale-covariant scale-space representation of temporal signals and past time
• Unified theory for joint covariance properties under geometric image transformations for spatio-temporal receptive fields according to the generalized Gaussian derivative model for visual receptive fields
• Covariant spatio-temporal receptive fields for spiking neural networks
• Orientation selectivity properties for the affine Gaussian derivative and the affine Gabor models for visual receptive fields
• A time-causal and time-recursive analogue of the Gabor transform