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## Binocular disparity and Stereopsis

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**Binocular disparity and Stereopsis**Bruce Cumming Laboratory of Sensorimotor Research, National Eye Institute, National Institutes of Health**Put red lens over left eye, blue lens over right eye**Stereo anaglyph by Prof. Michael Greenhalgh, Australian National University (with permission).**stereopsis**L R**correspondence problem**left eye’s image right eye’s image**random-dot patterns**• a completely unnatural stimulus • image changes every few ms • no recognisable objects e.g. faces • each dot has dozens of identical potential matches • and yet a clear perception of depth!**Neurons and depth perception**• A simple model to generate disparity signals. • How neurons reflect this. • Some psychophysical limits this explains. • Further processing.**head image from Royal Holloway University of London Vision**Research Group (with permission)**Right retina**Receptive Field Left retina Fovea**** * * Disparity-selective neuron Right RF R Left RF L**basic building-block**• inner product of image with receptive field Pos(v)**….**….S= response + 1 + 1 -0.1**=l**=r Left RF + S + Right RF**Output (spike rate)**l1 r1 r2 l2 l2 r1 Input (membrane V)**BS 2**BS 3 BS 4 Circuitry for complex cell left right binocular simple cells RF1 BS 1 complex cell RF2 Cx If RF2 = -RF 1 in both eyes, then half squaring then summing is equivalent to simply squaring.**square the result**sum over many such subunits add together energy model convolution of left eye’s image with jth left receptive field convolution of right eye’s image with jth right receptive field**L**R L R Right Stimulus Position Complex cell Left Stimulus Position Model Ohzawa et al, 1990**Disparity-selective neuron**Right RF R Left RF L**L**R L R L R L R Right Stimulus Position Complex cell Left Stimulus Position Model Ohzawa et al 1990**** * * Disparity-selective neuron Right RF R Left RF L**1**0.5 0 -0.5 -1 Left RF Right RF -d d 0 Correlation -50 0 50 Disparity (pixels)**1**0.5 0 -0.5 -1 Patern 1 Patern 2 Patern 3 Patern 4 Correlation Patern 5 Mean -50 0 50 Disparity (pixels)**d**-d 0 Disparity**1**0.5 0 -0.5 -1 Right RF Left RF Correlation 0 Disparity**DeAngelis, Ohzawa and Freeman, (1991)**Cat simple cell RF maps**For single subunits (simple)**• Odd symmetric disparity tuning implies phase disparity • Even symmetry around non-zero disparity implies position disparity True for complex cells if: • All subunits have same phase disparity • All subunits have same position disparity.**Monkey complex cells**duf043 duf065 60 40 Firing rate (spikes/s) 20 0 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 0.8 -1.4 -0.9 -0.4 0.1 0.6 1.1 1.4 Disparity (degrees)**So far:**• Energy model measures cross-correlation after filtering. • V1 contains a bank of filters measuring these correlations after displacements of both phase and position.**** * * Disparity-selective neuron Right RF R Left RF L**the neuronal response**cf: 0.06 cpd 80 60 response [spikes/sec] 40 20 0 0 0.5 1 1.5 2 time [sec]**the neuronal response**cf: 0.06 cpd 80 60 40 20 0 0 0.5 1 1.5 2 response [spikes/sec] cf: 0.5 cpd 80 60 40 20 0 0 0.5 1 1.5 2 time [sec]**f1**relative modulation corrugation-frequency [cpd] relative modulation cf: 0.06 cpd 80 60 40 f0 20 0 0 0.5 1 1.5 2 response [spikes/sec] cf: 0.5 cpd 80 60 40 20 0 0 0.5 1 1.5 2 time [sec]**SDsf [cpd]**SDsf [cpd] SDsf [cpd] SDsf [cpd] SDsf [cpd] SDsf [cpd] SDsf [cpd] SDsf [cpd] SDsf [cpd] SDsf [cpd] RM (f1/f0) RM (f1/f0) RM (f1/f0) RM (f1/f0) RM (f1/f0) RM (f1/f0) RM (f1/f0) RM (f1/f0) RM (f1/f0) RM (f1/f0) sf [cpd] sf [cpd] sf [cpd] sf [cpd] sf [cpd] sf [cpd] sf [cpd] sf [cpd] sf [cpd] sf [cpd] 1/(2πSDrf) [degree-1] 1/(2πSDrf) [degree-1] 1/(2πSDrf) [degree-1] 1/(2πSDrf) [degree-1] 1/(2πSDrf) [degree-1] 1/(2πSDrf) [degree-1] 1/(2πSDrf) [degree-1] 1/(2πSDrf) [degree-1] 1/(2πSDrf) [degree-1] 1/(2πSDrf) [degree-1] response [spikes/sec] response [spikes/sec] response [spikes/sec] response [spikes/sec] response [spikes/sec] response [spikes/sec] response [spikes/sec] response [spikes/sec] response [spikes/sec] response [spikes/sec] vertical position [°] vertical position [°] vertical position [°] vertical position [°] vertical position [°] vertical position [°] vertical position [°] vertical position [°] vertical position [°] vertical position [°] output exponent: 1 2 4 2 1.5 1 corrugation cutoff [cpd] 0.5 0 n=19 r=0.45 0 0.5 1 1.5 2 1/(2*π*SD of RF height) [degree-1]**Predicted from mean V1 response**(mean ecentricity 3.7º)**Temporal impulse response (LGN)**10ms Reppas, Usrey and Ried (2000)**drifting luminance grating**80 disparity modulation 1.5 40 40 response [spikes/sec] tf cutoff for drifting luminance grating [Hz] 1 20 relative modulation [f1/f0] 0 n=27 0.5 0 0 20 40 0 tf cutoff for disparity modulation [Hz] 1 10 100 temporal frequency [Hz] temporal frequency [Hz] Temporal frequency tuning for contrast and disparity**Summary**• We don’t solve the correspondence problem dot-by-dot. • Is this enough?**1**0.5 0 -0.5 -1 Correlation -50 0 50 RF Disparity (pixels)**1**0.5 0 -0.5 -1 Correlation -50 0 50 RF Disparity (pixels)**P’**P direction of gaze nodal point fovea **Y**Z X **Y**Z X **Y**Z X **probability density function for disparities encountered**during natural viewing -15 -10 -5 vertical disparity (degrees) 0 5 10 15 -10 0 10 20 30 horizontal disparity (degrees)**probability density function for disparities encountered**during natural viewing -1 -0.5 vertical disparity (degrees) 0 0.5 1 -1 -0.5 0 0.5 1 horizontal disparity (degrees)**-6**-4 -2 0 vertical disparity 2 4 6 -15 -10 -5 0 5 10 15 20 25 30 horizontal disparity