La visione spaziale: cellule gangliari e modelli computazionali

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1 La visione spaziale: cellule gangliari e modelli computazionali Corso di Principi e Modelli della Percezione Prof. Giuseppe Boccignone Dipartimento di Informatica Università di Milano boccignone@di.unimi.it Visione spaziale: //le cellule gangliari occhio chiasma ottico nervo ottico collicolo superiore nucleo genicolato laterale corteccia striata

2 Cellule gangliari retiniche e strisce Cellule gangliari: marcatori di luce Ogni cellula è sintonizzata su una certa frequenza spaziale Frequenze basse Risposta debole Frequenze medie Risposta forte Frequenze alte Risposta debole Cellule gangliari retiniche e strisce //selettivita` alle frequenze spaziali Una cellula gangliare può essere rappresentata come un filtro bassa banda Risposta forte Risposta debole Risposta debole mpiezza risposta Frequenza spaziale (cicli x grado)

3 Cellule gangliari retiniche e strisce //selettivita` alle frequenze spaziali mpiezza della risposta Cellule gangliari della retina Frequenza spaziale (cicli x grado) Cellule gangliari retiniche e strisce //l importanza della fase Ogni cellula è sintonizzata su una certa frequenza spaziale Cougell e Robson: la risposta dipende dalla fase del reticolo Il risultato: si comportano come dei rivelatori (detectors) di differenze locali di luminanza

4 Cellule gangliari retiniche e strisce //L illusione ottica delle bande di Mach Dovuto al comportamento di filtro passa alto dei neuroni retinici Invariante per rotazione Cellule gangliari retiniche e strisce //L illusione ottica delle bande di Mach Dovuto al comportamento di filtro passa alto dei neuroni retinici Invariante per rotazione

5 ght Notice that tire distance wer level and ensity distrirs. If percepngle on one th no Mach e an illusion represented ightness we D. The lights lighter ess becomes Cellule gangliari retiniche e strisce //L illusione ottica delle bande di Mach High Low B C D Y Receptors Receptor response LightLight Low (b) High Low Lateral inhibition (c) B C B C Low D D B B C Low (b) Bipolar cells 2 2 High D Distance C D Distance B B High X High Perception Perception of lightness of lightness dark. d can can be ht, as ptual effect e light Mach ach band. The t present in even higher. The upward bump at B represents this slight increase in lightness we see just to left of border. Once across border, we encounter dark Mach band, indicated by downward bump at C that represents slight decrease in lightness we see just to right of border. VL By using circuit in Figure 3.11 and doing a calculation like one we did for Hermann grid, we can show that(a) Mach bands can be explained by lateral inhibition. Each of(a) six receptors in this circuit sends signals to bipolar cells, and each bipolar cell sends lateral inhibition to its neighbors on both sides. Receptors and B correspond to and B in Figure 3.9, which are on light side of border and so receive intense illumination; receptors C and D are on darker side and receive dim illumination. Receptors X and Y D C DistanceD C Distance Bipolar cell response Figure 3.9 Mach bands at a contour between light and dark. (c) (a) Just to left of contour, near B, a faint light band can Figure 3.11 Circuit to explain Mach band effect based on be perceived, and just to right at C, a faint dark band can be Figure 3.9 bands at a contour between and as dark. lateral inhibition. The circuit works like one for Hermann grid in perceived. (b)mach The physical distribution of light light, (a) Just to left of contour, near B, a faint light band Figure 3.5, with each bipolar cell sending inhibition to its neighbors. If measured with a light meter. (c) plot showing perceptualcan effect be perceived, and just to right at C,ataBfaint dark band canmach be we know initial output of each receptor and amount of lateral described in (a). The bump in curve indicates light perceived. (b) The physical distribution of light, as inhibition, we can calculate final output of each bipolar cell. band, and dip in curve at C indicates dark Mach band. The measured a lightour meter. (c) plot bumps thatwith represent perception of showing bands areperceptual not presenteffect in Cengage Learning described in (a). The bump in curve at B indicates light Mach physical distribution. Cengage Learning band, and dip in curve at C indicates dark Mach band. The bumps that represent our perception of bands are not present in Lateral Inhibition and Perception 57 indistribution. This is illustrated Figure 3.9b, which shows light physical Cengage Learning Livelli di spiegazione secondo Marr Come realizzarla fisicamente? measured as we move along line from to D. Notice that light remains same across entire distance Modello This is illustrated in Figure 3.9b, which shows light between and B, n at border drops to a lower level and measured assame we move along D. linethus, from to D. Notice that remains between C and distribution no hint of Mach borders. If percep lightgives remains bands sameatacross entire distance tion followed we would see adrops light to rectangle one between and, B, n at border a loweron level and side and a darker rectangle on or side, with no Mach remains same between C and D. Thus, distribands. But dohint see se bands, so y must be an illusion bution givesweno of Mach bands at borders. If percepcreated by our visual system. tion followed, we would see a light rectangle on one of seonillusory bands is with represented side Our and aperception darker rectangle or side, no Mach graphically in Figure 3.9c, which indicates lightness we bands. But we do see se bands, so y must be an illusion perceiveby asour we visual move system. along line from to D. The lightcreated nessour is high as we begin right across lighter perception ofmoving se to illusory bands is represented stripe, but n, near border at B, lightness becomes graphically in Figure 3.9c, which indicates lightness we perceive as we move along line from to D. The lightness is high as we begin moving to right across lighter stripe, but n, near border at B, lightness becomes

6 Modello Definizione teorica Caratterizzazione del sistema nel dominio delle frequenze spaziali MTF Modello Dalla MTF ricavo la risposta impulsiva del sistema (PSF) input output input output

7 Modello Dalla MTF ricavo la risposta impulsiva del sistema (PSF) Laplaciano di una Gaussiana Laplaciano di una Gaussiana derivo due volte una funzione Gaussiana

8 Livelli di spiegazione secondo Marr Come realizzarla fisicamente?

9 Kernel (PSF) * Convoluzione Immagine input Immagine output Kernel (PSF)

10 Immagine input * Immagine output LoG Kernel (PSF)

11 *

12 Livelli di spiegazione secondo Marr * Come realizzarla fisicamente? Come realizzarla fisicamente? implementazione neurale Log Kernel discreto (PSF) Rappresentazione 3D (PSF) Profilo della Rappresentazione 3D (PSF) Cellula gangliare

13 Livelli di spiegazione secondo Marr * Come realizzarla fisicamente?