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Tony Lindeberg

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Neurons and Cognition Computer Vision eess.SP Machine Learning Neural and Evolutionary Computing Sound

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preprint2026arXiv

Direction and speed selectivity properties for spatio-temporal receptive fields according to the generalized Gaussian derivative model for visual receptive fields

This paper gives an in-depth theoretical analysis of the direction and speed selectivity properties of idealized models of the spatio-temporal receptive fields of simple cells and complex cells, based on the generalized Gaussian derivative model for visual receptive fields. According to this theory, the receptive fields are modelled as velocity-adapted affine Gaussian derivatives for different image velocities and different degrees of elongation. By probing such idealized receptive field models of visual neurons to moving sine waves with different angular frequencies and image velocities, we characterize the computational models to a structurally similar probing method as is used for characterizing the direction and speed selective properties of biological neurons. By comparison to results of neurophysiological measurements of direction and speed selectivity for biological neurons in the primary visual cortex, we find that our theoretical results are consistent with (i) velocity-tuned visual neurons that are sensitive to particular motion directions and speeds, and (ii) different visual neurons having broader vs. sharper direction and speed selective properties. Our theoretical results in combination with results from neurophysiological characterizations of motion-sensitive visual neurons are also consistent with a previously formulated hypothesis that the simple cells in the primary visual cortex ought to be covariant under local Galilean transformations, so as to enable processing of visual stimuli with different motion directions and speeds.

preprint2026arXiv

Encoding and Decoding Temporal Signals with Spiking Bandpass Wavelets

Spike-based encodings are sparse and energy-efficient, but have largely been formulated probabilistically, disconnected from most signal processing literature. We recast spike encoders as time-causal wavelet frames with quantitative bandwidths and reconstruction error bounds. The proposed wavelets preserve the sparsity and locality of spiking representations, with reconstruction up to spike quantization and time discretization. We demonstrate reconstruction on ECG and audio datasets, achieving a normalized RMSE comparable to continuous wavelet transforms. The spiking wavelets map directly to neuromorphic hardware.

preprint2022arXiv

Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales

The ability to handle large scale variations is crucial for many real world visual tasks. A straightforward approach for handling scale in a deep network is to process an image at several scales simultaneously in a set of scale channels. Scale invariance can then, in principle, be achieved by using weight sharing between the scale channels together with max or average pooling over the outputs from the scale channels. The ability of such scale channel networks to generalise to scales not present in the training set over significant scale ranges has, however, not previously been explored. In this paper, we present a systematic study of this methodology by implementing different types of scale channel networks and evaluating their ability to generalise to previously unseen scales. We develop a formalism for analysing the covariance and invariance properties of scale channel networks, and explore how different design choices, unique to scaling transformations, affect the overall performance of scale channel networks. We first show that two previously proposed scale channel network designs do not generalise well to scales not present in the training set. We explain theoretically and demonstrate experimentally why generalisation fails in these cases. We then propose a new type of foveated scale channel architecture}, where the scale channels process increasingly larger parts of the image with decreasing resolution. This new type of scale channel network is shown to generalise extremely well, provided sufficient image resolution and the absence of boundary effects. Our proposed FovMax and FovAvg networks perform almost identically over a scale range of 8, also when training on single scale training data, and do also give improved performance when learning from datasets with large scale variations in the small sample regime.

preprint2017arXiv

Normative theory of visual receptive fields

This article gives an overview of a normative computational theory of visual receptive fields, by which idealized functional models of early spatial, spatio-chromatic and spatio-temporal receptive fields can be derived in an axiomatic way based on structural properties of the environment in combination with assumptions about the internal structure of a vision system to guarantee consistent handling of image representations over multiple spatial and temporal scales. Interestingly, this theory leads to predictions about visual receptive field shapes with qualitatively very good similarity to biological receptive fields measured in the retina, the LGN and the primary visual cortex (V1) of mammals.

preprint2015arXiv

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 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 parameterizing the intermediate temporal scale levels, analysing the resulting temporal dynamics and transferring the theory to a discrete implementation in terms of recursive filters over time.

preprint2015arXiv

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.

preprint2014arXiv

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.

preprint2012arXiv

Invariance of visual operations at the level of receptive fields

Receptive field profiles registered by cell recordings have shown that mammalian vision has developed receptive fields tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time. This article presents a theoretical model by which families of idealized receptive field profiles can be derived mathematically from a small set of basic assumptions that correspond to structural properties of the environment. The article also presents a theory for how basic invariance properties to variations in scale, viewing direction and relative motion can be obtained from the output of such receptive fields, using complementary selection mechanisms that operate over the output of families of receptive fields tuned to different parameters. Thereby, the theory shows how basic invariance properties of a visual system can be obtained already at the level of receptive fields, and we can explain the different shapes of receptive field profiles found in biological vision from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.