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A Biologically-Inspired Model for a Spiking Retina Adrien Wohrer, Pierre Kornprobst, Thierry Vi´ eville To cite this version: Adrien Wohrer, Pierre Kornprobst, Thierry Vi´ eville. A Biologically-Inspired Model for a Spik- ing Retina. [Research Report] RR-5848, INRIA. 2006, pp.78. <inria-00070178> HAL Id: inria-00070178 https://hal.inria.fr/inria-00070178 Submitted on 19 May 2006 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destin´ ee au d´ epˆ ot et ` a la diffusion de documents scientifiques de niveau recherche, publi´ es ou non, ´ emanant des ´ etablissements d’enseignement et de recherche fran¸cais ou ´ etrangers, des laboratoires publics ou priv´ es.

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Page 1: A Biologically-Inspired Model for a Spiking Retina

A Biologically-Inspired Model for a Spiking Retina

Adrien Wohrer, Pierre Kornprobst, Thierry Vieville

To cite this version:

Adrien Wohrer, Pierre Kornprobst, Thierry Vieville. A Biologically-Inspired Model for a Spik-ing Retina. [Research Report] RR-5848, INRIA. 2006, pp.78. <inria-00070178>

HAL Id: inria-00070178

https://hal.inria.fr/inria-00070178

Submitted on 19 May 2006

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

Page 2: A Biologically-Inspired Model for a Spiking Retina

ISS

N 0

249-

6399

ap por t de r ech er ch e

Thème BIO

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

A Biologically-Inspired Model for a Spiking Retina

Adrien Wohrer — Pierre Kornprobst — Thierry Viéville

N° 5848

Février 2006

Page 3: A Biologically-Inspired Model for a Spiking Retina
Page 4: A Biologically-Inspired Model for a Spiking Retina

Unité de recherche INRIA Sophia Antipolis2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France)

Téléphone : +33 4 92 38 77 77 — Télécopie : +33 4 92 38 77 65

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Page 22: A Biologically-Inspired Model for a Spiking Retina

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Page 23: A Biologically-Inspired Model for a Spiking Retina

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Page 26: A Biologically-Inspired Model for a Spiking Retina

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dP (t)

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α(t) = κNA→B(t).

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P (t) = P∞(t) ∗ Kt(t),¤�j¥fvT

γ(t) = α(t) + β

P∞(t) =α(t)γ(t)

Kt(ξ) = γ(t − ξ) exp(−∫ ξ

0γ(t − u)du

) ªe�®k@tξ > 0

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P∞(t) =α(t)

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N��nrWdvdgjq�x�¡«@Y*tv��Y*mPªKkx�µdgfv�n�W{��ntv{ {�Y*�cjl�xf]jlkn�σR + σh

­ ·µd�®k@t�fvT�Y�d]YC�*kn�W{ ��knX(�?kn��YC�9fCªuj�fhjqd£f]T�YX£r�m�f]jl��m�Y���k@�c�nknmlrefvj�k@� kx�´Y�¸e�?kn��YC�9f]jq�xm�{eYC�C�²bcdC­K`crW��T��¨Wm¥fvY*tUjqd¯{eY5d]�*t]jli?YC{ jl��·z����Y�¸�·�­3[¬fU�nm�¤U�²bed�*kntvt]Y5dg�?kn��{�d�f]k���m�k#¤U¢¬�W�ndvdU�?k@d]j¥fvj��@Y«nYCt]��YCm7ª�¤�j¥fvTE� � i�mlkni�icb ��d]TW�x�?Y$fvTW�#fµ�C�x�§i?Y£�n����tvk²¸cjlX �#fvYC{icb��®r��W�°fvj�k@�

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VH (x, y, t) = V 0H + AH ∆G

x,y,t∗ HH (x, y, t).*!9� �

¤�TWY*tvYHH

jqdUf]TWY�²�nY*t��xo@j��Wo$¨Wm�f]Y*t5³

HH(x, y, t) = GσH(x, y)TαH ,τH

(t).

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jqd {eY�¨���YC{;�@dσR + σh

­ ·µd(�®knt �W�ntv�nX(Y�f]YCtvdαH

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TαH ,τH

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V (t) = E∞ ∗ Kt (t),¤�j�f]T

g∞(t) = Gexc(t) + Ginh(t) + gL,

E∞(t) =Gexc(t)Eexc + Ginh(t)Einh

g∞(t),

Kt(ξ) = g∞(t − ξ) exp(−∫ ξ

0

g∞(t − u)du) ªe�®k@t

ξ > 0.

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VBip(x, y, t) = V 0Bip + AC ∆G

x,y,t∗ HBip (x, y, t),

with :

HBip = HC − wHS ,

HC(x, y, t) = GσC(x, y)TαC ,τC

(t),

HS(x, y, t) = GσS(x, y)TαS ,τS

(t).

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V 0Bip

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AC³w = AS/AC

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0 < w < 1­

I �:@ � 0 �©� �/Á ½ À -�� & ¼ 3 ' )®� ¼ �$ À �C� ) ) ½ ���G)�Á ¾ �3���C� � )Ï� ¼ � � ��knt

w = 1ªWf]T�YiWj��?knmq�xtz¨Wm¥fvY*t

HBipjld � �.�(�.��� � ���.� � �:� � �<�°ª�jl�§f]TWjld

d]Y*��dgY�f]T��#f¯��d]�W�#fvjl�nm�mlb£�n�W{£f]Y*X(�?knt��xmlm�b£��kn��dyf��x�9f 9*kn�WY�kx�?f]T�Y�jlX �xo@Y�¤�jlmlm���kxfuYC�nk@«nY��x�cbtvYCd]��k@�Wd]Ykn�3f]T�Y£i�j��?knmq�xt|��YCm�m fvTW�#f|jldCª

VBip = V 0Bip

�°ª©�ndzkn��Y£�*�x�¦��TWYC��«�YC�nd]jlm�b±dgjl�W�*Yi�knf]T§¨�m¥fvY*t�dHC

�x��{HS

�nt]Y|��k@t]X �xmlj:9*YC{´­[Þ�Ef]T�jqd$�*�@dgY@ªWfvT�Y dg�W�xf]jlkx¢Pf]YCXh�?knt��xm/��tvkn�?Y*t]f]jlYCdµkx�

HBip = HC − HS�nt]Y£i�Y5dyf$dgYCY*�Ef]T�tvknr�o@T

fvT�Y��®knmlmlk#¤�j���o({eY5��knX(�?k@d]j¥fvj�k@�´ª�{ejlt]Y5�°fvm�b�k@iefv�nj��WYC{��®t]k@X *!@� �°³

HBip(x, y, t) = [GσC − GσS ] (x, y)TαC , τC (t) + GσS (x, y)[TαC , τC − TαS , τS

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Ï�C�nd]Y 7Z � �°ªcfvT�Y|{�Y*tvj��#�#fvj��@Yzkn�fvT�Y«@Y*tv��Y*m©jl�

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Tα,τ (t)­�Lzk#¤¯YC�nYCtCª´k@��Y�mq�ndgf£p9r�YCdgf]jlkn�¡d]T�knrWml{"i?Y��n{W{et]Y5d]d]YC{´­ 2;TW�xf�mlj���«ed£�xtvY(f]T�YCt]Y

i?Y�fy¤�Y*YC��fvT�Y��²�nm�rWYCd¯�®knt(α, τ)

�®k@r��W{�Y*X(��jlt]jq�*�nm�mlbnªe�n�W{ fvT�Y|f]jlXhY5d(τ1, τ2, . . . , τn)

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(α, τ)ªWf]T�Yd]r�X kn��fvj�X(Y�¢Pf]kn¢P�?YC�n«

τmax = ατ�x��{�kn�

{�YC�*�²b(fvj�X(Yτdec = τ

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. À �.' 0 À )��5� ) 3 ' )®� ¼ ���Y�f

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−jξtVR(ξx, ξy, ξt) =(− GR(ξ2

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H

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Page 82: A Biologically-Inspired Model for a Spiking Retina

Unité de recherche INRIA Sophia Antipolis2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)

Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes4, rue Jacques Monod - 91893 ORSAY Cedex (France)

Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France)Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France)

Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)

ÉditeurINRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)��������� ���� ���������� ��� ���

ISSN 0249-6399