scholarly journals Provably Scale-Covariant Continuous Hierarchical Networks Based on Scale-Normalized Differential Expressions Coupled in Cascade

2019 ◽  
Vol 62 (1) ◽  
pp. 120-148
Author(s):  
Tony Lindeberg
Keyword(s):  
Wide Class ◽  
Functional Model ◽  
Receptive Fields ◽  
Scale Space ◽  
Biologically Inspired ◽  
Hierarchical Networks ◽  
Reduced Representation ◽  
Complex Cells ◽  
Scale Covariance ◽  
Linear And Nonlinear

Abstract This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds for a wide class of networks defined from linear and nonlinear differential expressions expressed in terms of scale-normalized scale-space derivatives. Then, we present a more detailed development of one example of such a network constructed from a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed, and we give explicit proofs of how the resulting representation allows for scale and rotation covariance. A prototype application to texture analysis is developed, and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.

scholarly journals Biologically inspired computational modeling of motion based on middle temporal area

2018 ◽  
Vol 9 (1) ◽  
pp. 60-71 ◽  
Author(s):  
Fernanda da C. e C. Faria ◽  
Jorge Batista ◽  
Helder Araújo
Keyword(s):  
Receptive Fields ◽  
Biologically Inspired ◽  
Significant Information ◽  
Temporal Area ◽  
Middle Temporal ◽  
Complex Cells ◽  
Motion Computation ◽  
Reciprocal Connections ◽  
Middle Temporal Area ◽  
Last Stage

Abstract This paper describes a bio-inspired algorithm for motion computation based on V1 (Primary Visual Cortex) andMT (Middle Temporal Area) cells. The behavior of neurons in V1 and MT areas contain significant information to understand the perception of motion. From a computational perspective, the neurons are treated as two dimensional filters to represent the receptive fields of simple cells that compose the complex cells. A modified elaborated Reichardt detector, adding an output exponent before the last stage followed by a re-entry stage of modulating feedback from MT, (reciprocal connections of V1 and MT) in a hierarchical framework, is proposed. The endstopped units, where the receptive fields of cells are surrounded by suppressive regions, are modeled as a divisive operation. MT cells play an important role for integrating and interpreting inputs from earlier-level (V1).We fit a normalization and a pooling to find the most active neurons for motion detection. All steps employed are physiologically inspired processing schemes and need some degree of simplification and abstraction. The results suggest that our proposed algorithm can achieve better performance than recent state-of-the-art bio-inspired approaches for real world images.

Reduced Representation by Neural Networks with Restricted Receptive Fields

1995 ◽  
Vol 7 (3) ◽  
pp. 507-517 ◽  
Author(s):  
Marco Idiart ◽  
Barry Berk ◽  
L. F. Abbott
Keyword(s):  
Neural Networks ◽  
Biological Networks ◽  
Input Data ◽  
Hebbian Learning ◽  
Receptive Fields ◽  
Principal Component ◽  
Data Sets ◽  
Reduced Representation ◽  
Learning Rules ◽  
Reduced Representations

Model neural networks can perform dimensional reductions of input data sets using correlation-based learning rules to adjust their weights. Simple Hebbian learning rules lead to an optimal reduction at the single unit level but result in highly redundant network representations. More complex rules designed to reduce or remove this redundancy can develop optimal principal component representations, but they are not very compelling from a biological perspective. Neurons in biological networks have restricted receptive fields limiting their access to the input data space. We find that, within this restricted receptive field architecture, simple correlation-based learning rules can produce surprisingly efficient reduced representations. When noise is present, the size of the receptive fields can be optimally tuned to maximize the accuracy of reconstructions of input data from a reduced representation.

Receptive-field characteristics of neurons in cat striate cortex: Changes with visual field eccentricity

1976 ◽  
Vol 39 (3) ◽  
pp. 512-533 ◽  
Author(s):  
J. R. Wilson ◽  
S. M. Sherman
Keyword(s):  
Visual Field ◽  
Receptive Field ◽  
Striate Cortex ◽  
Ocular Dominance ◽  
Receptive Fields ◽  
Direction Selectivity ◽  
Orientation Selectivity ◽  
Simple Cells ◽  
Complex Cells ◽  
Cat Striate Cortex

1. Receptive-field properties of 214 neurons from cat striate cortex were studied with particular emphasis on: a) classification, b) field size, c) orientation selectivity, d) direction selectivity, e) speed selectivity, and f) ocular dominance. We studied receptive fields located throughtout the visual field, including the monocular segment, to determine how receptivefield properties changed with eccentricity in the visual field.2. We classified 98 cells as "simple," 80 as "complex," 21 as "hypercomplex," and 15 in other categories. The proportion of complex cells relative to simple cells increased monotonically with receptive-field eccenticity.3. Direction selectivity and preferred orientation did not measurably change with eccentricity. Through most of the binocular segment, this was also true for ocular dominance; however, at the edge of the binocular segment, there were more fields dominated by the contralateral eye.4. Cells had larger receptive fields, less orientation selectivity, and higher preferred speeds with increasing eccentricity. However, these changes were considerably more pronounced for complex than for simple cells.5. These data suggest that simple and complex cells analyze different aspects of a visual stimulus, and we provide a hypothesis which suggests that simple cells analyze input typically from one (or a few) geniculate neurons, while complex cells receive input from a larger region of geniculate neurons. On average, this region is invariant with eccentricity and, due to a changing magnification factor, complex fields increase in size with eccentricity much more than do simple cells. For complex cells, computations of this geniculate region transformed to cortical space provide a cortical extent equal to the spread of pyramidal cell basal dendrites.

Binocular Combination of Contrast Signals by Striate Cortical Neurons in the Monkey

1997 ◽  
Vol 78 (1) ◽  
pp. 366-382 ◽  
Author(s):  
Earl L. Smith ◽  
Yuzo Chino ◽  
Jinren Ni ◽  
Han Cheng
Keyword(s):  
Cortical Neurons ◽  
Striate Cortex ◽  
Receptive Fields ◽  
Spatial Summation ◽  
Simple Cells ◽  
Complex Cells ◽  
Threshold Response ◽  
Binocular Interactions ◽  
Specific Complex ◽  
Left And Right

Smith, Earl L., III, Yuzo Chino, Jinren Ni, and Han Cheng. Binocular combination of contrast signals by striate cortical neurons in the monkey. J. Neurophysiol. 78: 366–382, 1997. With the use of microelectrode recording techniques, we investigated how the contrast signals from the two eyes are combined in individual cortical neurons in the striate cortex of anesthetized and paralyzed macaque monkeys. For a given neuron, the optimal spatial frequency, orientation, and direction of drift for sine wave grating stimuli were determined for each eye. The cell's disparity tuning characteristics were determined by measuring responses as a function of the relative interocular spatial phase of dichoptic stimuli that consisted of the optimal monocular gratings. Binocular contrast summation was then investigated by measuring contrast response functions for optimal dichoptic grating pairs that had left- to right-eye interocular contrast ratios that varied from 0.1 to 10. The goal was to determine the left- and right-eye contrast components required to produce a criterion threshold response. For all functional classes of cortical neurons and for both cooperative and antagonistic binocular interactions, there was a linear relationship between the left- and right-eye contrast components required to produce a threshold response. Thus, for example for cooperative binocular interactions, a reduction in contrast to one eye was counterbalanced by an equivalent increase in contrast to the other eye. These results showed that in simple cells and phase-specific complex cells, the contrast signals from the two eyes were linearly combined at the subunit level before nonlinear rectification. In non-phase-specific complex cells, the linear binocular convergence of contrast signals could have taken place either before or after the rectification process, but before spike generation. In addition, for simple cells, vector analysis of spatial summation showed that the inputs from the two eyes were also combined in a linear manner before nonlinear spike-generating mechanisms. Thus simple cells showed linear spatial summation not only within and between subregions in a given receptive field, but also between the left- and right-eye receptive fields. Overall, the results show that the effectiveness of a stimulus in producing a response reflects interocular differences in the relative balance of inputs to a given cell, however, the eye of origin of a light-evoked signal has no specific consequence.

scholarly journals Systems-based analysis of dendritic nonlinearities reveals temporal feature extraction in mouse L5 cortical neurons

2017 ◽  
Vol 117 (6) ◽  
pp. 2188-2208 ◽  
Author(s):  
Brian E. Kalmbach ◽  
Richard Gray ◽  
Daniel Johnston ◽  
Erik P. Cook
Keyword(s):  
High Frequency ◽  
Cortical Neurons ◽  
Action Potentials ◽  
Nonlinear Response ◽  
Functional Model ◽  
Low Frequency ◽  
Fast Variable ◽  
Nonlinear Component ◽  
Dendritic Spikes ◽  
Linear And Nonlinear

What do dendritic nonlinearities tell a neuron about signals injected into the dendrite? Linear and nonlinear dendritic components affect how time-varying inputs are transformed into action potentials (APs), but the relative contribution of each component is unclear. We developed a novel systems-identification approach to isolate the nonlinear response of layer 5 pyramidal neuron dendrites in mouse prefrontal cortex in response to dendritic current injections. We then quantified the nonlinear component and its effect on the soma, using functional models composed of linear filters and static nonlinearities. Both noise and waveform current injections revealed linear and nonlinear components in the dendritic response. The nonlinear component consisted of fast Na+ spikes that varied in amplitude 10-fold in a single neuron. A functional model reproduced the timing and amplitude of the dendritic spikes and revealed that they were selective to a preferred input dynamic (~4.5 ms rise time). The selectivity of the dendritic spikes became wider in the presence of additive noise, which was also predicted by the functional model. A second functional model revealed that the dendritic spikes were weakly boosted before being linearly integrated at the soma. For both our noise and waveform dendritic input, somatic APs were dependent on the somatic integration of the stimulus, followed a subset of large dendritic spikes, and were selective to the same input dynamics preferred by the dendrites. Our results suggest that the amplitude of fast dendritic spikes conveys information about high-frequency features in the dendritic input, which is then combined with low-frequency somatic integration. NEW & NOTEWORTHY The nonlinear response of layer 5 mouse pyramidal dendrites was isolated with a novel systems-based approach. In response to dendritic current injections, the nonlinear component contained mostly fast, variable-amplitude, Na+ spikes. A functional model accounted for the timing and amplitude of the dendritic spikes and revealed that dendritic spikes are selective to a preferred input dynamic, which was verified experimentally. Thus, fast dendritic nonlinearities behave as high-frequency feature detectors that influence somatic action potentials.

A biologically inspired scale-space for illumination invariant feature detection

2013 ◽  
Vol 24 (7) ◽  
pp. 074024 ◽  
Author(s):  
Vasillios Vonikakis ◽  
Dimitrios Chrysostomou ◽  
Rigas Kouskouridas ◽  
Antonios Gasteratos
Keyword(s):  
Feature Detection ◽  
Scale Space ◽  
Biologically Inspired ◽  
Illumination Invariant ◽  
Invariant Feature

scholarly journals Spatial and Temporal Features of Synaptic to Discharge Receptive Field Transformation in Cat Area 17

2010 ◽  
Vol 103 (2) ◽  
pp. 677-697 ◽  
Author(s):  
Lionel G. Nowak ◽  
Maria V. Sanchez-Vives ◽  
David A. McCormick
Keyword(s):  
Spatial Frequency ◽  
Response Latency ◽  
Frequency Tuning ◽  
Receptive Fields ◽  
Width Ratio ◽  
Area 17 ◽  
Simple Cells ◽  
Complex Cells ◽  
Temporal Features ◽  
Simple And Complex Cells

The aim of the present study was to characterize the spatial and temporal features of synaptic and discharge receptive fields (RFs), and to quantify their relationships, in cat area 17. For this purpose, neurons were recorded intracellularly while high-frequency flashing bars were used to generate RFs maps for synaptic and spiking responses. Comparison of the maps shows that some features of the discharge RFs depended strongly on those of the synaptic RFs, whereas others were less dependent. Spiking RF duration depended poorly and spiking RF amplitude depended moderately on those of the underlying synaptic RFs. At the other extreme, the optimal spatial frequency and phase of the discharge RFs in simple cells were almost entirely inherited from those of the synaptic RFs. Subfield width, in both simple and complex cells, was less for spiking responses compared with synaptic responses, but synaptic to discharge width ratio was relatively variable from cell to cell. When considering the whole RF of simple cells, additional variability in width ratio resulted from the presence of additional synaptic subfields that remained subthreshold. Due to these additional, subthreshold subfields, spatial frequency tuning predicted from synaptic RFs appears sharper than that predicted from spiking RFs. Excitatory subfield overlap in spiking RFs was well predicted by subfield overlap at the synaptic level. When examined in different regions of the RF, latencies appeared to be quite variable, but this variability showed negligible dependence on distance from the RF center. Nevertheless, spiking response latency faithfully reflected synaptic response latency.

Interactive effects among several stimulus parameters on the responses of striate cortical complex cells

1991 ◽  
Vol 66 (2) ◽  
pp. 379-389 ◽  
Author(s):  
T. J. Gawne ◽  
B. J. Richmond ◽  
L. M. Optican
Keyword(s):  
Striate Cortex ◽  
Neuronal Response ◽  
Receptive Fields ◽  
Response Strength ◽  
Interactive Effects ◽  
Temporal Modulation ◽  
Complex Cells ◽  
Black And White ◽  
Interaction Terms ◽  
Stimulus Parameters

1. Although neurons within the visual system are often described in terms of their responses to particular patterns such as bars and edges, they are actually sensitive to many different stimulus features, such as the luminances making up the patterns and the duration of presentation. Many different combinations of stimulus parameters can result in the same neuronal response, raising the problem of how the nervous system can extract information about visual stimuli from such inherently ambiguous responses. It has been shown that complex cells transmit significant amounts of information in the temporal modulation of their responses, raising the possibility that different stimulus parameters are encoded in different aspects of the response. To find out how much information is actually available about individual stimulus parameters, we examined the interactions among three stimulus parameters in the temporally modulated responses of striate cortical complex cells. 2. Sixteen black and white patterns were presented to two awake monkeys at each of four luminance-combinations and five durations, giving a total of 320 unique stimuli. Complex cells were recorded in layers 2 and 3 of striate cortex, with the stimuli centered on the receptive fields as determined by mapping with black and white bars. 3. An analysis of variance (ANOVA) was applied to these data with the three stimulus parameters of pattern, the luminance-combinations, and duration as the independent variables. The ANOVA was repeated with the magnitude and three different aspects of the temporal modulation of the response as the dependent variables. For the 19 neurons studied, many of the interactions between the different stimulus parameters were statistically significant. For some response measures the interactions accounted for more than one-half of the total response variance. 4. We also analyzed the stimulus-response relationships with the use of information theoretical techniques. We defined input codes on the basis of each stimulus parameter alone, as well as their combinations, and output codes on the basis of response strength, and on three measures of temporal modulation, also taken individually and together. Transmitted information was greatest when the response of a neuron was interpreted as a temporally modulated message about combinations of all three stimulus parameters. The interaction terms of the ANOVA suggest that the response of a complex cell can only be interpreted as a message about combinations of all three stimulus parameters.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Substructure of Direction-Selective Receptive Fields in Macaque V1

2003 ◽  
Vol 89 (5) ◽  
pp. 2743-2759 ◽  
Author(s):  
Margaret S. Livingstone ◽  
Bevil R. Conway
Keyword(s):  
Receptive Fields ◽  
Direction Selectivity ◽  
Positive Interactions ◽  
Null Direction ◽  
Simple Cells ◽  
Complex Cells ◽  
Preferred Direction ◽  
Orientation Axis ◽  
Interaction Regions ◽  
Simple And Complex Cells

We used two-dimensional (2-D) sparse noise to map simultaneous and sequential two-spot interactions in simple and complex direction-selective cells in macaque V1. Sequential-interaction maps for both simple and complex cells showed preferred-direction facilitation and null-direction suppression for same-contrast stimulus sequences and the reverse for inverting-contrast sequences, although the magnitudes of the interactions were weaker for the simple cells. Contrast-sign selectivity in complex cells indicates that direction-selective interactions in these cells must occur in antecedent simple cells or in simple-cell-like dendritic compartments. Our maps suggest that direction selectivity, and on andoff segregation perpendicular to the orientation axis, can occur prior to receptive-field elongation along the orientation axis. 2-D interaction maps for some complex cells showed elongated alternating facilitatory and suppressive interactions as predicted if their inputs were orientation-selective simple cells. The negative interactions, however, were less elongated than the positive interactions, and there was an inflection at the origin in the positive interactions, so the interactions were chevron-shaped rather than band-like. Other complex cells showed only two round interaction regions, one negative and one positive. Several explanations for the map shapes are considered, including the possibility that directional interactions are generated directly from unoriented inputs.

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