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Found 22 papers, 4 papers with code
Do the receptive fields in the primary visual cortex span a variability over the degree of elongation of the receptive fields?
This paper presents results of combining (i) theoretical analysis regarding connections between the orientation selectivity and the elongation of receptive fields for the affine Gaussian derivative model with (ii) biological measurements of orientation selectivity in the primary visual cortex, to investigate if (iii) the receptive fields can be regarded as spanning a variability in the degree of elongation.
Discrete approximations of Gaussian smoothing and Gaussian derivatives
With close connections to previous axiomatic treatments of continuous and discrete scale-space theory, we consider three main ways discretizing these scale-space operations in terms of explicit discrete convolutions, based on either (i) sampling the Gaussian kernels and the Gaussian derivative kernels, (ii) locally integrating the Gaussian kernels and the Gaussian derivative kernels over each pixel support region and (iii) basing the scale-space analysis on the discrete analogue of the Gaussian kernel, and then computing derivative approximations by applying small-support central difference operators to the spatially smoothed image data.
Joint covariance property under geometric image transformations for spatio-temporal receptive fields according to the generalized Gaussian derivative model for visual receptive fields
The influence of natural image transformations on receptive field responses is crucial for modelling visual operations in computer vision and biological vision.
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 covariance and a cascade property with a simplifying kernel over temporal scales.
Orientation selectivity properties for the affine Gaussian derivative and the affine Gabor models for visual receptive fields
This paper presents a theoretical analysis of the orientation selectivity of simple and complex cells that can be well modelled by the generalized Gaussian derivative model for visual receptive fields, with the purely spatial component of the receptive fields determined by oriented affine Gaussian derivatives for different orders of spatial differentiation.
Covariance properties under natural image transformations for the generalized Gaussian derivative model for visual receptive fields
This paper presents a theory for how geometric image transformations can be handled by a first layer of linear receptive fields, in terms of true covariance properties, which, in turn, enable geometric invariance properties at higher levels in the visual hierarchy.
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 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.
Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales
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.
Ranked #1 on
Scale Generalisation
on MNIST Large Scale dataset
Scale-covariant and scale-invariant Gaussian derivative networks
This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade.
Inability of spatial transformations of CNN feature maps to support invariant recognition
In this paper, we prove that spatial transformations of CNN feature maps cannot align the feature maps of a transformed image to match those of its original, for general affine transformations, unless the extracted features are themselves invariant.
Understanding when spatial transformer networks do not support invariance, and what to do about it
This enables the use of more complex features when predicting transformation parameters.
Exploring the ability of CNNs to generalise to previously unseen scales over wide scale ranges
The ability to handle large scale variations is crucial for many real world visual tasks.
The problems with using STNs to align CNN feature maps
Spatial transformer networks (STNs) were designed to enable CNNs to learn invariance to image transformations.
Provably scale-covariant continuous hierarchical networks based on scale-normalized differential expressions coupled in cascade
This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant.
Provably scale-covariant networks from oriented quasi quadrature measures in cascade
This article presents a continuous model for hierarchical networks based on a combination of mathematically derived models of receptive fields and biologically inspired computations.
Dynamic texture recognition using time-causal and time-recursive spatio-temporal receptive fields
We propose a new family of video descriptors based on regional statistics of spatio-temporal receptive field responses and evaluate this approach on the problem of dynamic texture recognition.
Dense scale selection over space, time and space-time
This paper presents a methodology for performing dense scale selection, so that hypotheses about local characteristic scales in images, temporal signals and video can be computed at every image point and every time moment.
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.
Discrete approximations of the affine Gaussian derivative model for visual receptive fields
The affine Gaussian derivative model can in several respects be regarded as a canonical model for receptive fields over a spatial image domain: (i) it can be derived by necessity from scale-space axioms that reflect structural properties of the world, (ii) it constitutes an excellent model for the receptive fields of simple cells in the primary visual cortex and (iii) it is covariant under affine image deformations, which enables more accurate modelling of image measurements under the local image deformations caused by the perspective mapping, compared to the more commonly used Gaussian derivative model based on derivatives of the rotationally symmetric Gaussian kernel.
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.
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.
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.
