Description
Question 1. [50 points]
The responses of a cat LGN cell to two-dimensional visual images are contained in the file
c2p3.mat, data are described in Kara et al., Neuron 30:803-817 (2000). In the file, counts is
a vector containing the number of spikes in each 15.6 ms bin, and stim contains the 32767,
16×16 images that were presented at the corresponding times. Specifically, stim(x,y,t) is
the stimulus presented at the coordinate (x,y) at time step t. Answer the questions below.
(Note that stim is provided in integer format.)
a) Calculate the STA images for each of the 10 time steps before each spike and show them
all. For display, use imagesc with a grayscale colormap and identical display windowing
for all STA images. Based on the STA derived filter, describe what type of spatio-temporal
stimulus this LGN cell is selective for.
b) Describe the changes in STA images across time. Sum the STA images over one of the
spatial dimensions. You should obtain a matrix of 16 pixels by 10 time steps as a result of
this process. Show this matrix (using imagesc). Based on the computed matrix, describe
the temporal selectivity of the LGN cell. Is the matrix space-time separable?
c) Project the stimulus onto the STA image at a single time step prior to the spike. Obtain
the projection for each time sample by computing the Frobenius inner product between the
stimulus image and the STA image. Create a histogram from all stimulus projections, and
another histogram from stimulus projections at time bins where a non-zero spike count was
observed. Use identical binning for the two histograms, and normalize each histogram to
a maximum of 1. Compare the histograms with a bar plot. Comment on whether STA
significantly discriminates spike-eliciting stimuli.
Question 2. [50 points] Answer the questions below. Include plots whenever applicable.
a) Construct an on-center difference-of-gaussians (DOG) center-surround receptive field
centered at 0:
D(x, y) = 1
2πσ2
c
e
−(x
2+y
2
)/2σ
2
c −
1
2πσ2
s
e
−(x
2+y
2
)/2σ
2
s (1)
Sample this receptive field as a 21×21 matrix, with a central Gaussian width of σc = 2 pixels
and a surround Gaussian width of σs = 4 pixels. Display the generated receptive field.
b) Neurons in lateral geniculate nuclei (LGN) have DOG receptive fields. Suppose that
there is a separate LGN neuron with a receptive field centered on each pixel in the image.
Compute the responses of each neuron to the image given in hw2_image.bmp. Place the
neural responses topographically according to the centers of their receptive fields, and display
the neural activity as an image (using imagesc). (Note: Be careful not to introduce artifacts
at the image boundary.)
c) Build an edge detector by thresholding the neural activity image (i.e., setting all values
above a certain threshold to 1 and the remainder to 0.) Tune the parameters of the DOG
receptive fields and the threshold to optimize the edge detector’s performance.
d) Construct a Gabor receptive field on the same 21×21 pixel grid:
D(~x) = exp
−
~k(θ) · ~x2
/2σ
2
l −
~k⊥(θ) · ~x2
/2σ
2
w
cos
2π
~k⊥(θ) · ~x
λ
+ φ
!
(2)
Here, ~k(θ) is a unit vector with the orientation θ,
~k⊥(θ) is a unit vector orthogonal to ~k(θ),
and θ, σl
, σw, λ and φ are parameters the comprise the Gabor filter. Start with assumption
that θ = π/2, σl = σw = 3 pixels, λ = 6 pixels, and φ = 0. Display the generated receptive
field.
e) Simple cells in V1 have Gabor receptive fields. Suppose that there is a separate V1 neuron
with a receptive field centered on each pixel in the image. Compute the responses of each
neuron to the image given in hw2_image.bmp. Place the neural responses topographically
according to the centers of their receptive fields, and display the neural activity as an image
(using imagesc). What is the function of this Gabor filter?
f) Construct 4 Gabors with θ = 0, π/6, π/3, π/2. Compute combined neural responses to
the image hw2_image.bmp, by summing the outputs of the individual receptive fields (for
different θ). Does the edge detection performance look better in this case? What can you
do with these 4 Gabors to further improve the performance?
