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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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Spatial component of receptive fields in V1.(left) Simple cells in the striate cortex do usually have strong directional preference in the spatial domain, as reported by DeAngelis et al.[26]. (right) In terms of Gaussian derivatives, first-order directional derivatives of anisotropic affine Gaussian kernels, here aligned to the coordinate directions  and here with  and , can be used as a model for simple cells with a strong directional preference.
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pone-0066990-g009: Spatial component of receptive fields in V1.(left) Simple cells in the striate cortex do usually have strong directional preference in the spatial domain, as reported by DeAngelis et al.[26]. (right) In terms of Gaussian derivatives, first-order directional derivatives of anisotropic affine Gaussian kernels, here aligned to the coordinate directions and here with and , can be used as a model for simple cells with a strong directional preference.

Mentions: where the direction of the directional derivative operator should preferably be aligned to the orientation of one of the eigenvectors of . Figure 9 shows a comparison between this idealized receptive field model over the spatial domain and the spatial response properties of a simple cell in V1.


Invariance of visual operations at the level of receptive fields.

Lindeberg T - PLoS ONE (2013)

Spatial component of receptive fields in V1.(left) Simple cells in the striate cortex do usually have strong directional preference in the spatial domain, as reported by DeAngelis et al.[26]. (right) In terms of Gaussian derivatives, first-order directional derivatives of anisotropic affine Gaussian kernels, here aligned to the coordinate directions  and here with  and , can be used as a model for simple cells with a strong directional preference.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0066990-g009: Spatial component of receptive fields in V1.(left) Simple cells in the striate cortex do usually have strong directional preference in the spatial domain, as reported by DeAngelis et al.[26]. (right) In terms of Gaussian derivatives, first-order directional derivatives of anisotropic affine Gaussian kernels, here aligned to the coordinate directions and here with and , can be used as a model for simple cells with a strong directional preference.
Mentions: where the direction of the directional derivative operator should preferably be aligned to the orientation of one of the eigenvectors of . Figure 9 shows a comparison between this idealized receptive field model over the spatial domain and the spatial response properties of a simple cell in V1.

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