1. True/False. [12 pts] (parts a–l; 1 point for each correct answer, 0 points for each
blank/incorrect answer). For each statement, circle T if true and F if false.
(a) [1 pt] T F
Pre-ﬁltering an image with a Gaussian ﬁlter, then downsam-
pling (throwing away every other column and row), is equiva-
lent to downsampling ﬁrst, then ﬁltering the resulting image
with a smaller kernel.
(b) [1 pt] T F Parallel lines are preserved under afﬁne transforms.
(c) [1 pt] T F
A fundamental matrix only describes two-view geometry ex-
actly if the images are free of radial distortion.
(d) [1 pt] T F Photometric stereo requires scenes with constant albedo.
(e) [1 pt] T F
Non-maxima suppression can be implemented with a linear
(f) [1 pt] T F
The Harris operator is invariant under inverting the intensities
of an image (i.e., replacing all intensities I(x; y) with 255
I(x; y), assuming that intensities range from 0 to 255).
(g) [1 pt] T F
For each unique spectrum of light hitting the retina, humans
will perceive a unique color; in other words, there is a one-to-
one mapping between light spectra and perceived colors.
(h) [1 pt] T F
A good local feature descriptor should generally be equivari-
ant with respect to image intensity changes, i.e., as the image
becomes brighter, the values in the descriptors derived for local
features in the image should become proportionally larger.
(i) [1 pt] T F
When selecting good hyperparameters for use in building a
machine learning model, the best practice is to ﬁnd the hyper-
parameters that result in the best accuracy on the test set.
(j) [1 pt] T F
A CNN-based classiﬁcation network will still make correct pre-
dictions even if the object in the image changes its orientation
or position, since convolutional layers are inherently invariant
to translation and rotations.
(k) [1 pt] T F
When building a CNN from various layers, true or false: you
shouldn’t put two fully connected layers one after the other
separated by a ReLU unit, because this setup is mathematically
equivalent to a single fully connected layer.
(l) [1 pt] T F
Assuming the same sized input, a fully connected layer of a
CNN tends to havemore parameters than a convolutional layer.
2. Short answer [8 pts] (parts a–d)
(a) [2 pts] What is the maximum number of vanishing points that can appear in
(b) [2 pts] Which of the following functions would make a good activation
function to use between two layers of a neural network: (a) f(x) = 0, (b) f(x) =
x, (c) f(x) = max(x; 0). Explain.
(c) [2 pts] How many parameters are involved in a convolutional layer consisting
of 16 stride-2 convolutions of size 55? Assume the input to the layer is a
3-channel RGB image.
(d) [2 pts] Suppose you are creating a new dataset of images involving people.
From an ethical standpoint, what is one example of a potential ethical issue that
can arise when creating or using such a dataset?
3. Fundamental matrices [8 pts] (parts a–d) Consider two images I and J. Sup-
pose we are given the fundamental matrix F that relates a pixel in image I to its
corresponding epipolar line in image J. Assume that for each image, the upper-left
image corner is the origin, with the image x-axis pointing right, and the image y-axis
0 1 0
1 0 1
0 1 0
Note that F is a valid fundamental matrix (we checked).
(a) [1 pt] What is the rank of F?
(b) [3 pts] Given a pixel at location p = (2; 1) in image I, compute the corre-
sponding epipolar line in image J. (Please write the line either in homogeneous
coordinates, or as a line equation of the form Ax + By + C = 0.)
(c) [2 pts] Suppose we reverse the order of images I and J. What is the new
fundamental matrix relating points in image J to lines in image I?
(d) [2 pts] Now go back again to the original I and J.What is the epipole in image
J (i.e., the projection of I’s center of projection into J?) [You might ﬁnd this
problem slightly tricky, in which case, we suggest moving on and coming back
to this problem at the end, along with any other problems you found tricky.]
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