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Complex cells and the representation of local imagestructure
, 2010
"... Abstract: The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modelled by Gabor functions, or by Gaussian derivatives. Gabor functions can also be combined in an 'energy model' of the complex cell response. This paper propose ..."
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Abstract: The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modelled by Gabor functions, or by Gaussian derivatives. Gabor functions can also be combined in an 'energy model' of the complex cell response. This paper proposes an alternative model of the complex cell, based on Gaussian derivatives. It is most important to account for the insensitivity of the complex response to small shifts of the image. The new model uses a linear combination of the first few derivative filters, at a single position, to approximate the first derivative filter, at a series of adjacent positions. The maximum response, over all positions, gives a signal that is insensitive to small shifts of the image. This model, unlike previous approaches, is based on the scale space theory of visual processing. In particular, the complex cell is built from filters that respond to the 2d differential structure of the image. The computational aspects of the new model are studied in one and two dimensions, using the steerability of the Gaussian derivatives. The response of the model to basic images, such as edges and gratings, is derived formally. The response to natural images is also evaluated, using statistical measures of shift insensitivity. The relevance of the new model to the cortical image representation is discussed.
A Differential Model of the Complex Cell
, 2011
"... The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modeled by Gabor functions or gaussian derivatives. Gabor functions can also be combined in an energy model of the complex cell response. This letter proposes an alternative model of t ..."
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The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modeled by Gabor functions or gaussian derivatives. Gabor functions can also be combined in an energy model of the complex cell response. This letter proposes an alternative model of the complex cell, based on gaussian derivatives. It is most important to account for the insensitivity of the complex response to small shifts of the image. The new model uses a linear combination of the first few derivative filters, at a single position, to approximate the first derivative filter, at a series of adjacent positions. The maximum response, over all positions, gives a signal that is insensitive to small shifts of the image. This model, unlike previous approaches, is based on the scale space theory of visual processing. In particular, the complex cell is built from filters that respond to the 2D differential structure of the image. The computational aspects of the new model are studied in one and two dimensions, using the steerability of the gaussian derivatives. The response of the model to basic images, such as edges and gratings, is derived formally. The response to natural images is also evaluated, using statistical measures of shift insensitivity. The neural implementation and predictions of the model are discussed.
The Number of Cortical Neurons Used
"... A neuron’s receptive field is the area in the visual field in which it responds to light. A neuron has one cell body and many dendrites. Physiologically, the integration occurs as the signals from the many dendrites converge on the cell body. The integrated input signals cause the cell to fire, i.e. ..."
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A neuron’s receptive field is the area in the visual field in which it responds to light. A neuron has one cell body and many dendrites. Physiologically, the integration occurs as the signals from the many dendrites converge on the cell body. The integrated input signals cause the cell to fire, i.e. produce an action potential. The cell firing stimulates the dendrites of other neurons. The integration is linear (weighted averaging) even though the cell firing depends nonlinearly on that weighted average. The main nonlinearity is a threshold. The cell does not fire if the weighted average is less than the neuron’s threshold. Thus, although a complete mathematical model of the neuron would include the nonlinearity of the cell’s response, the spatial integration by the cell’s receptive field (or dendrites) is a simple sum, a linear weighted average. That weighted average is a sample of the image in the visual field of the observer. The weighting functions that produce these samples have been extensively studied in individual neurons in fish, cats, and monkeys, but very little is known about how these animals and people use multiple neurons to see. There are hundreds of millions of neurons in the visual cortex, but so little is known that previously studied performance of human observers might be accounted for by using a single cortical neuron. Here a new technique, based on a new mathematical theorem, allows noninvasive visual tests to demonstrate that people use a large number of neurons. More specifically, I find that people take 100 samples to perform my tasks. Each neuron takes one or two samples, so the observers must be using at least fifty neurons to do my visual tasks. Saying how many neurons are used is a significant step towards the ultimate goal of explaining how these neurons do the visual computation that is seeing.
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"... nce de d of or w oss pec Th me wid an om y o th lib re a we cr ho n ng eels 1. INTR In this experim there a orienta ered t selectiv visual s neuron tation, conten and wi vering primar that th and co and wo cated t cells h have m in a lin excitato [3,4]. I as tune tivities that th recepti of the ima ..."
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nce de d of or w oss pec Th me wid an om y o th lib re a we cr ho n ng eels 1. INTR In this experim there a orienta ered t selectiv visual s neuron tation, conten and wi vering primar that th and co and wo cated t cells h have m in a lin excitato [3,4]. I as tune tivities that th recepti of the image that overlie each receptive field. s and em in ctionay be ssibly n just scribe d the es was transe cell/ d that f such plete. added 12] is nnecctions e task bel & hieve? gy and been ch as ormase are annot embark on a fair, critical, review, but our approach is largely motivated by the failure of the above models to provide insight into early vision at the level of computational theory. David Marr [16] suggested this was the