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Invariance of visual operations at the level of receptive fields.

Lindeberg T - PLoS ONE (2013)

Bottom Line: This paper presents a theory for achieving basic invariance properties already at the level of receptive fields.Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination.The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.

View Article: PubMed Central - PubMed

Affiliation: Department of Computational Biology, School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm, Sweden. tony@csc.kth.se

ABSTRACT
The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due to geometric transformations and lighting variations in the environment. This paper presents a theory for achieving basic invariance properties already at the level of receptive fields. Specifically, the presented framework comprises (i) local scaling transformations caused by objects of different size and at different distances to the observer, (ii) locally linearized image deformations caused by variations in the viewing direction in relation to the object, (iii) locally linearized relative motions between the object and the observer and (iv) local multiplicative intensity transformations caused by illumination variations. The receptive field model can be derived by necessity from symmetry properties of the environment and leads to predictions about receptive field profiles in good agreement with receptive field profiles measured by cell recordings in mammalian vision. Indeed, the receptive field profiles in the retina, LGN and V1 are close to ideal to what is motivated by the idealized requirements. By complementing receptive field measurements with selection mechanisms over the parameters in the receptive field families, it is shown how true invariance of receptive field responses can be obtained under scaling transformations, affine transformations and Galilean transformations. Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination. The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.

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Illustration of how scale selection can be performed from receptive field responses by computing scale-normalized Gaussian derivative operators at different scales and then detecting local extrema over scale.Here, so-called scale-space signatures have been computed at the centers of two different lamps at different distances to the observer. Notice how the local extrema over scale are assumed at coarser scales for the nearby lamp than for the distant lamp. When measured in units of dimension length, the ratio between these scale estimates agrees with the ratio between the sizes of the projected lamps in the image domain.
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pone-0066990-g012: Illustration of how scale selection can be performed from receptive field responses by computing scale-normalized Gaussian derivative operators at different scales and then detecting local extrema over scale.Here, so-called scale-space signatures have been computed at the centers of two different lamps at different distances to the observer. Notice how the local extrema over scale are assumed at coarser scales for the nearby lamp than for the distant lamp. When measured in units of dimension length, the ratio between these scale estimates agrees with the ratio between the sizes of the projected lamps in the image domain.

Mentions: Figure 12 illustrates this idea by performing local scale selection at two different points in a spatial image from local extrema over scale of the scale-normalized Laplacian and the scale-normalized determinant of the Hessian computed from Gaussian-derivative receptive fields at different spatial scales(77)(78)


Invariance of visual operations at the level of receptive fields.

Lindeberg T - PLoS ONE (2013)

Illustration of how scale selection can be performed from receptive field responses by computing scale-normalized Gaussian derivative operators at different scales and then detecting local extrema over scale.Here, so-called scale-space signatures have been computed at the centers of two different lamps at different distances to the observer. Notice how the local extrema over scale are assumed at coarser scales for the nearby lamp than for the distant lamp. When measured in units of dimension length, the ratio between these scale estimates agrees with the ratio between the sizes of the projected lamps in the image domain.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3716821&req=5

pone-0066990-g012: Illustration of how scale selection can be performed from receptive field responses by computing scale-normalized Gaussian derivative operators at different scales and then detecting local extrema over scale.Here, so-called scale-space signatures have been computed at the centers of two different lamps at different distances to the observer. Notice how the local extrema over scale are assumed at coarser scales for the nearby lamp than for the distant lamp. When measured in units of dimension length, the ratio between these scale estimates agrees with the ratio between the sizes of the projected lamps in the image domain.
Mentions: Figure 12 illustrates this idea by performing local scale selection at two different points in a spatial image from local extrema over scale of the scale-normalized Laplacian and the scale-normalized determinant of the Hessian computed from Gaussian-derivative receptive fields at different spatial scales(77)(78)

Bottom Line: This paper presents a theory for achieving basic invariance properties already at the level of receptive fields.Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination.The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.

View Article: PubMed Central - PubMed

Affiliation: Department of Computational Biology, School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm, Sweden. tony@csc.kth.se

ABSTRACT
The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due to geometric transformations and lighting variations in the environment. This paper presents a theory for achieving basic invariance properties already at the level of receptive fields. Specifically, the presented framework comprises (i) local scaling transformations caused by objects of different size and at different distances to the observer, (ii) locally linearized image deformations caused by variations in the viewing direction in relation to the object, (iii) locally linearized relative motions between the object and the observer and (iv) local multiplicative intensity transformations caused by illumination variations. The receptive field model can be derived by necessity from symmetry properties of the environment and leads to predictions about receptive field profiles in good agreement with receptive field profiles measured by cell recordings in mammalian vision. Indeed, the receptive field profiles in the retina, LGN and V1 are close to ideal to what is motivated by the idealized requirements. By complementing receptive field measurements with selection mechanisms over the parameters in the receptive field families, it is shown how true invariance of receptive field responses can be obtained under scaling transformations, affine transformations and Galilean transformations. Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination. The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.

Show MeSH
Related in: MedlinePlus