What is the function of vision?

What is the function of vision?

What is the function of vision?

What is the function of vision?

Visual illusions

Visual illusions : Pareidolia

Visual illusions : Pareidolia

Visual illusions : Pareidolia

Visual illusions: Context

Ilusions of brightness or lightness Akiyoshi KITAOKA

Visual illusions: Context

Visual illusions: Context

Principles of vision?

Computational neuroscience of vision

Anatomy of the Human Visual system

Human Visual system : the HMAX model

Convolutional Neural Networks : Hierarchy

Convolutional Neural Networks (CNNs)

Primary visual cortex: Hubel & Wiesel

Primary visual cortex: Hubel & Wiesel

[Hubel & Wiesel, 1962] - from @Neuroslicer

Convolutional Neural Networks : hierarchy

Convolutional Neural Networks : Mathematics

• One-dimensional discrete convolution (eg in time) with a kernel $g$ of radius $K$: $$(f \ast g)[n]=\sum_{m=-K}^{K} f[n-m] \cdot g[m]$$

Convolutional Neural Networks : Mathematics

• Convolution of an image (two-dimensional) with a kernel $g$ of radius $K\times K$:

$$(f \ast g)[x, y] = \sum_{i=-K}^{K} \sum_{j=-K}^{K} f[x-i, y-j] \cdot g[i, j]$$

Convolutional Neural Networks : Mathematics

• Cross-correlation of an image (two-dimensional) with a kernel $g$ of radius $K\times K$:

$$(f \ast \tilde{g})[x, y] = \sum_{i=-K}^{K} \sum_{j=-K}^{K} f[x+i, y+j] \cdot g[i, j]$$

Convolutional Neural Networks : Mathematics

Convolutional Neural Networks : Mathematics

• Correlation of an image defined on several channels (note the order of the indices):

$$(f \ast \tilde{g})[x, y] = \sum_{c=1}^{C} \sum_{i,j} f[c, x+i, y+j] \cdot g[c, i, j]$$

Convolutional Neural Networks : Mathematics

• Correlation of a multi-channel image for multiple output channels (note the order of the indices):

$$(f \ast \tilde{g})[k, x, y] = \sum_{c=1}^{C} \sum_{i,j} f[c, x+i, y+j] \cdot g[k, c, i, j]$$

Convolutional Neural Networks : Predictive coding

Convolutional Neural Networks : Predictive coding

Convolutional Neural Networks : Topography

Convolutional Neural Networks : Topography

Dynamics of vision

Dynamics of vision

Dynamics of vision

Dynamics of vision

Dynamics of vision

Dynamics of vision

Dynamics of vision

Dynamics of vision

Flash-lag effect: MBP (Khoei et al, 2017)

Dynamics of vision

Spiking Neural Networks: Leaky Integrate-and-Fire Neuron

Spiking Neural Networks in neurobiology

Spiking Neural Networks in neurobiology

Spiking Neural Networks in neurobiology

Spiking Neural Networks in neurobiology

Spiking Neural Networks: Spiking motifs

Spiking Neural Networks: Spiking motifs

Spiking Neural Networks: Spiking motifs

Spiking Neural Networks in neuromorphic engineering

Spiking Neural Networks in neuromorphic engineering

Spiking Neural Networks in neuromorphic engineering

Spiking Neural Networks in neuromorphic engineering

Spiking Neural Networks in neuromorphic engineering

Interactions between machine learning, artificial neural networks and our understanding of biological vision

Laurent Perrinet

[2023-05-10] NeuroSchool PhD Program in Neuroscience: Computation Neuroscience

Contact me @ laurent.perrinet@univ-amu.fr