Idealized computational models for auditory receptive fields

This paper presents a theory by which idealized models of auditory receptive fields can be derived in a principled axiomatic manner, from a set of structural properties to enable invariance of receptive field responses under natural sound transformations and ensure internal consistency between spectro-temporal receptive fields at different temporal and spectral scales. For defining a time-frequency transformation of a purely temporal sound signal, it is shown that the framework allows for a new way of deriving the Gabor and Gammatone filters as well as a novel family of generalized Gammatone filters, with additional degrees of freedom to obtain different trade-offs between the spectral selectivity and the temporal delay of time-causal temporal window functions. When applied to the definition of a second-layer of receptive fields from a spectrogram, it is shown that the framework leads to two canonical families of spectro-temporal receptive fields, in terms of spectro-temporal derivatives of either spectro-temporal Gaussian kernels for non-causal time or the combination of a time-causal generalized Gammatone filter over the temporal domain and a Gaussian filter over the logspectral domain. For each filter family, the spectro-temporal receptive fields can be either separable over the time-frequency domain or be adapted to local glissando transformations that represent variations in logarithmic frequencies over time. Within each domain of either non-causal or time-causal time, these receptive field families are derived by uniqueness from the assumptions. It is demonstrated how the presented framework allows for computation of basic auditory features for audio processing and that it leads to predictions about auditory receptive fields with good qualitative similarity to biological receptive fields measured in the inferior colliculus (ICC) and primary auditory cortex (A1) of mammals.Comment: 55 pages, 22 figures, 3 table

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 equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about (i) parameterizing the intermediate temporal scale levels, (ii) analysing the resulting temporal dynamics, (iii) transferring the theory to a discrete implementation, (iv) computing scale-normalized spatio-temporal derivative expressions for spatio-temporal feature detection and (v) computational modelling of receptive fields in the lateral geniculate nucleus (LGN) and the primary visual cortex (V1) in biological vision. We show that by distributing the intermediate temporal scale levels according to a logarithmic distribution, we obtain much faster temporal response properties (shorter temporal delays) compared to a uniform distribution. Specifically, these kernels converge very rapidly to a limit kernel possessing true self-similar scale-invariant properties over temporal scales, thereby allowing for true scale invariance over variations in the temporal scale, although the underlying temporal scale-space representation is based on a discretized temporal scale parameter. We show how scale-normalized temporal derivatives can be defined for these time-causal scale-space kernels and how the composed theory can be used for computing basic types of scale-normalized spatio-temporal derivative expressions in a computationally efficient manner.Comment: 39 pages, 12 figures, 5 tables in Journal of Mathematical Imaging and Vision, published online Dec 201

SIGNAL TRANSFORMATIONS FOR IMPROVING INFORMATION REPRESENTATION, FEATURE EXTRACTION AND SOURCE SEPARATION

Questa tesi riguarda nuovi metodi di rappresentazione del segnale nel dominio tempo-frequenza, tali da mostrare le informazioni ricercate come dimensioni esplicite di un nuovo spazio. In particolare due trasformate sono introdotte: lo Spazio di Miscelazione Bivariato (Bivariate Mixture Space) e il Campo della Struttura Spettro-Temporale (Spectro-Temporal Structure-Field). La prima trasformata mira a evidenziare le componenti latenti di un segnale bivariato basandosi sul comportamento di ogni componente frequenziale (ad esempio a fini di separazione delle sorgenti); la seconda trasformata mira invece all'incapsulamento di informazioni relative al vicinato di un punto in R^2 in un vettore associato al punto stesso, tale da descrivere alcune propriet\ue0 topologiche della funzione di partenza. Nel dominio dell'elaborazione digitale del segnale audio, il Bivariate Mixture Space pu\uf2 essere interpretato come un modo di investigare lo spazio stereofonico per operazioni di separazione delle sorgenti o di estrazione di informazioni, mentre lo Spectro-Temporal Structure-Field pu\uf2 essere usato per ispezionare lo spazio spettro-temporale (segregare suoni percussivi da suoni intonati o tracciae modulazioni di frequenza). Queste trasformate sono studiate e testate anche in relazione allo stato del'arte in campi come la separazione delle sorgenti, l'estrazione di informazioni e la visualizzazione dei dati. Nel campo dell'informatica applicata al suono, queste tecniche mirano al miglioramento della rappresentazione del segnale nel dominio tempo-frequenza, in modo tale da rendere possibile l'esplorazione dello spettro anche in spazi alternativi, quali il panorama stereofonico o una dimensione virtuale che separa gli aspetti percussivi da quelli intonati.This thesis is about new methods of signal representation in time-frequency domain, so that required information is rendered as explicit dimensions in a new space. In particular two transformations are presented: Bivariate Mixture Space and Spectro-Temporal Structure-Field. The former transform aims at highlighting latent components of a bivariate signal based on the behaviour of each frequency base (e.g. for source separation purposes), whereas the latter aims at folding neighbourhood information of each point of a R^2 function into a vector, so as to describe some topological properties of the function. In the audio signal processing domain, the Bivariate Mixture Space can be interpreted as a way to investigate the stereophonic space for source separation and Music Information Retrieval tasks, whereas the Spectro-Temporal Structure-Field can be used to inspect spectro-temporal dimension (segregate pitched vs. percussive sounds or track pitch modulations). These transformations are investigated and tested against state-of-the-art techniques in fields such as source separation, information retrieval and data visualization. In the field of sound and music computing, these techniques aim at improving the frequency domain representation of signals such that the exploration of the spectrum can be achieved also in alternative spaces like the stereophonic panorama or a virtual percussive vs. pitched dimension

Scale-space theory for auditory signals

We show how the axiomatic structure of scale-space theory can be applied to the auditory domain and be used for deriving idealized models of auditory receptive fields via scale-space principles. For defining a time-frequency transformation of a purely temporal signal, it is shown that the scale-space framework allows for a new way of deriving the Gabor and Gammatone filters as well as a novel family of generalized Gammatone filters with additional degrees of freedom to obtain different trade-offs between the spectral selectivity and the temporal delay of time-causal window functions. Applied to the definition of a second layer of receptive fields from the spectrogram, it is shown that the scale-space framework leads to two canonical families of spectro-temporal receptive fields, using a combination of Gaussian filters over the logspectral domain with either Gaussian filters or a cascade of first-order integrators over the temporal domain. These spectro-temporal receptive fields can be either separable over the time-frequency domain or be adapted to local glissando transformations that represent variations in logarithmic frequencies over time. Such idealized models of auditory receptive fields respect auditory invariances, can be used for computing basic auditory features for audio processing and lead to predictions about auditory receptive fields with good qualitative similarity to biological receptive fields in the inferior colliculus (ICC) and the primary auditory cortex (A1).QC 20150407</p