Limits...
Properties of artificial neurons that report lightness based on accumulated experience with luminance.

Morgenstern Y, Rukmini DV, Monson BB, Purves D - Front Comput Neurosci (2014)

Bottom Line: To ask whether these responses are consistent with a wholly empirical concept of visual perception, we optimized simple neural networks that responded according to the cumulative frequency of occurrence of local luminance patterns in retinal images.Based on this estimation of accumulated experience, the neuron responses showed classical center-surround receptive fields, luminance gain control and contrast gain control, the key properties of early level visual neurons determined in animal experiments.These results imply that a major purpose of pre-cortical neuronal circuitry is to contend with the inherently uncertain significance of luminance values in natural stimuli.

View Article: PubMed Central - PubMed

Affiliation: Neuroscience and Behavioral Disorders Program, Duke-NUS Graduate Medical School Singapore, Singapore.

ABSTRACT
The responses of visual neurons in experimental animals have been extensively characterized. To ask whether these responses are consistent with a wholly empirical concept of visual perception, we optimized simple neural networks that responded according to the cumulative frequency of occurrence of local luminance patterns in retinal images. Based on this estimation of accumulated experience, the neuron responses showed classical center-surround receptive fields, luminance gain control and contrast gain control, the key properties of early level visual neurons determined in animal experiments. These results imply that a major purpose of pre-cortical neuronal circuitry is to contend with the inherently uncertain significance of luminance values in natural stimuli.

No MeSH data available.


Determination of cumulative conditional probabilities of the central luminance values in natural stimulus patterns used for training the network. Luminance patterns (A) like the example in Figure 7B were divided into nine regions (B) (eight regions tiling around a polar axis plus the central grid square) whose luminance values were further averaged and segregated into 15 bins. The conditional CDFs of the central grid square luminance in these simplified context patterns (green triangles in C) were fit with a cumulative Gaussian probability function (red curve). The fit was used to estimate 14 scaled luminance values at the center with cumulative probabilities that spanned a 0 to 1 range (red circles in C). During training, the stimuli presented to the networks (D) were one of 14 possible luminance values of the central grid square (red circles in C) embedded in the context pattern of one of the original (37-grid squares) samples (in this case, the exemplar pattern highlighted in blue in A). The ideal response that each network was trained to approximate was the rank on the conditional CDF of the central grid square (T) (see graph).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4217489&req=5

Figure 8: Determination of cumulative conditional probabilities of the central luminance values in natural stimulus patterns used for training the network. Luminance patterns (A) like the example in Figure 7B were divided into nine regions (B) (eight regions tiling around a polar axis plus the central grid square) whose luminance values were further averaged and segregated into 15 bins. The conditional CDFs of the central grid square luminance in these simplified context patterns (green triangles in C) were fit with a cumulative Gaussian probability function (red curve). The fit was used to estimate 14 scaled luminance values at the center with cumulative probabilities that spanned a 0 to 1 range (red circles in C). During training, the stimuli presented to the networks (D) were one of 14 possible luminance values of the central grid square (red circles in C) embedded in the context pattern of one of the original (37-grid squares) samples (in this case, the exemplar pattern highlighted in blue in A). The ideal response that each network was trained to approximate was the rank on the conditional CDF of the central grid square (T) (see graph).

Mentions: Given the enormous number of possible patterns of 37 grid squares with many luminance levels (see Figure 7B), we averaged the luminance intensities falling within eight regions tiling a polar coordinate frame around the central target grid square (Figures 8A,B). Binning the (averaged) luminance intensities of these regions into 15 bins reduced the number of unique context pattern surrounding the target from the initial sample size of 3-million (36 grid square patterns with a continuous range of intensities) to 172,547 total patterns (8 averaged regions with 15 discrete intensities), with sufficient recurring patterns to calculate an estimate of the frequency of occurrence of the central grid square luminance values. The rank on the conditional CDF scale of the central grid square luminance in these stimulus patterns thus approximated the rank of central grid square luminance values in generally similar natural scene contexts. In supplementary tests we verified that the optimized neuron's center-surround receptive field is independent of spatial averaging over eight regions (Supplementary Figure 6). For this purpose we trained networks on the basis of the frequency of occurrence 1-D patterns of nine regions (Supplementary Figure 6A). By sampling nine regions rather than 37 and putting the luminance values of each region into 1 of 15 bins, we were able to compute the frequency of occurrence of a target given the eight surrounding grid squares without employing the spatial averaging.


Properties of artificial neurons that report lightness based on accumulated experience with luminance.

Morgenstern Y, Rukmini DV, Monson BB, Purves D - Front Comput Neurosci (2014)

Determination of cumulative conditional probabilities of the central luminance values in natural stimulus patterns used for training the network. Luminance patterns (A) like the example in Figure 7B were divided into nine regions (B) (eight regions tiling around a polar axis plus the central grid square) whose luminance values were further averaged and segregated into 15 bins. The conditional CDFs of the central grid square luminance in these simplified context patterns (green triangles in C) were fit with a cumulative Gaussian probability function (red curve). The fit was used to estimate 14 scaled luminance values at the center with cumulative probabilities that spanned a 0 to 1 range (red circles in C). During training, the stimuli presented to the networks (D) were one of 14 possible luminance values of the central grid square (red circles in C) embedded in the context pattern of one of the original (37-grid squares) samples (in this case, the exemplar pattern highlighted in blue in A). The ideal response that each network was trained to approximate was the rank on the conditional CDF of the central grid square (T) (see graph).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4217489&req=5

Figure 8: Determination of cumulative conditional probabilities of the central luminance values in natural stimulus patterns used for training the network. Luminance patterns (A) like the example in Figure 7B were divided into nine regions (B) (eight regions tiling around a polar axis plus the central grid square) whose luminance values were further averaged and segregated into 15 bins. The conditional CDFs of the central grid square luminance in these simplified context patterns (green triangles in C) were fit with a cumulative Gaussian probability function (red curve). The fit was used to estimate 14 scaled luminance values at the center with cumulative probabilities that spanned a 0 to 1 range (red circles in C). During training, the stimuli presented to the networks (D) were one of 14 possible luminance values of the central grid square (red circles in C) embedded in the context pattern of one of the original (37-grid squares) samples (in this case, the exemplar pattern highlighted in blue in A). The ideal response that each network was trained to approximate was the rank on the conditional CDF of the central grid square (T) (see graph).
Mentions: Given the enormous number of possible patterns of 37 grid squares with many luminance levels (see Figure 7B), we averaged the luminance intensities falling within eight regions tiling a polar coordinate frame around the central target grid square (Figures 8A,B). Binning the (averaged) luminance intensities of these regions into 15 bins reduced the number of unique context pattern surrounding the target from the initial sample size of 3-million (36 grid square patterns with a continuous range of intensities) to 172,547 total patterns (8 averaged regions with 15 discrete intensities), with sufficient recurring patterns to calculate an estimate of the frequency of occurrence of the central grid square luminance values. The rank on the conditional CDF scale of the central grid square luminance in these stimulus patterns thus approximated the rank of central grid square luminance values in generally similar natural scene contexts. In supplementary tests we verified that the optimized neuron's center-surround receptive field is independent of spatial averaging over eight regions (Supplementary Figure 6). For this purpose we trained networks on the basis of the frequency of occurrence 1-D patterns of nine regions (Supplementary Figure 6A). By sampling nine regions rather than 37 and putting the luminance values of each region into 1 of 15 bins, we were able to compute the frequency of occurrence of a target given the eight surrounding grid squares without employing the spatial averaging.

Bottom Line: To ask whether these responses are consistent with a wholly empirical concept of visual perception, we optimized simple neural networks that responded according to the cumulative frequency of occurrence of local luminance patterns in retinal images.Based on this estimation of accumulated experience, the neuron responses showed classical center-surround receptive fields, luminance gain control and contrast gain control, the key properties of early level visual neurons determined in animal experiments.These results imply that a major purpose of pre-cortical neuronal circuitry is to contend with the inherently uncertain significance of luminance values in natural stimuli.

View Article: PubMed Central - PubMed

Affiliation: Neuroscience and Behavioral Disorders Program, Duke-NUS Graduate Medical School Singapore, Singapore.

ABSTRACT
The responses of visual neurons in experimental animals have been extensively characterized. To ask whether these responses are consistent with a wholly empirical concept of visual perception, we optimized simple neural networks that responded according to the cumulative frequency of occurrence of local luminance patterns in retinal images. Based on this estimation of accumulated experience, the neuron responses showed classical center-surround receptive fields, luminance gain control and contrast gain control, the key properties of early level visual neurons determined in animal experiments. These results imply that a major purpose of pre-cortical neuronal circuitry is to contend with the inherently uncertain significance of luminance values in natural stimuli.

No MeSH data available.