CS 231A Computer Vision Midterm
Tuesday October 30, 2012
Solution Set
1 Multiple Choice (22 points)
Each question is worth 2 points . To discourage random guessing, 1 point will be deducted
for a wrong answer on multiple choice questions! For answers with multiple answers, 2
points will only be awarded if all correct choices are selected, otherwise, it is wrong
and will incur a 1 point penalty . Please draw a circle around the option(s) to indicate your
answer. No credit will be awarded for unclear/ambiguous answers.
1. (Pick one) If all of our data points are in R2, which of the following clustering algorithms
can handle clusters of arbitrary shape?
(a) k-means.
(b) k-means++.
(c) EM with a gaussian mixture model.
(d) mean-shift.
Solution Only d
2. (Pick one) Suppose we are using a Hough transform to do line tting, but we notice that
our system is detecting two lines where there is actually one in some example image.
Which of the following is most likely to alleviate this problem?
(a) Increase the size of the bins in the Hough transform.
(b) Decrease the size of the bins in the Hough transform.
(c) Sharpen the image.
(d) Make the image larger.
Solution a
3. (Pick one) Which of the following processes would help avoid aliasing while downsampling
an image?
1 (a) Image sharpening.
(b) Image blurring.
(c) Median ltering where you replace every pixel by the median of pixels in a window
around the pixel.
(d) Histogram equalization.
Solution b
4. (Circle all that apply) A Sobel lter can be written as
2
41 2 1
0 0 0
1 2 13
5=2
41
0
13
5
1 2 1
(1)
Which of the following statements are true
(a) Separating the lter in the above manner, reduces the number of computations.
(b) It is similar to applying a gaussian lter followed by a derivative.
(c) Separation leads to spurious edge artifacts.
(d) Separation approximates the rst derivative of gaussian.
Solution a and b
5. (Pick one) Which of the following is true for Eigenfaces (PCA)
(a) Can be used to e ectively detect deformable objects.
(b) Invariant to ane transforms.
(c) Can be used for lossy image compression.
(d) Is invariant to shadows.
Solution c
6. (Pick one) Downsampling can lead to aliasing because
(a) Sampling leads to additions of low frequency noise.
(b) Sampled high frequency components result in apparent low frequency components.
(c) Sampling increases the frequency components in an image.
(d) Sampling leads to spurious high frequency noise
Solution b
7. (Pick one) If we replace one lens on a calibrated stereo rig with a bigger one, what can
we say about the essential matrix, E, and the fundamental matrix, F?
2 (a) E can change due to a possible change in the physical length of the lens. F is un-
changed.
(b) F can change due to a possible change in the lens characteristics. E is unchanged.
(c) E can change due to a possible change in the lens characteristics. F is unchanged.
(d) Both are unchanged.
Solution b
8. (Pick one) Which of the following statements describes an ane camera but not a general
perspective camera?
(a) Relative sizes of visible objects in a scene can be determined without prior knowledge.
(b) Can be used to determine the distance from a object of a known height.
(c) Approximates the human visual system.
(d) An in nitely long plane can be viewed as a line from the right angle.
Solution a
9. (Circle all that apply) Which of the following could a ect the intrinsic parameters of a
camera?
(a) A crooked lens system.
(b) Diamond/Rhombus shaped pixels with non right angles.
(c) The aperture con guration and construction.
(d) Any o set of the image sensor from the lens's optical center.
Solution A,B,D
10. (Circle all that apply) For camera calibration, we learned that since there are 11 unknown
parameters, we need at least 6 correspondences to calibrate. Assuming that you couldn't nd a calibration target with the minimum of 6 corners to use as correspondences, you
decide to take multiple pictures from di erent viewpoints of a stationary pattern with N
corners, where N < 6, which of the following statements is true?
(a) The number of images, Kmust satisfy 2 NK > 6, the value of Nisn't important, so
long as it as N > 0.
(b) The problem is unsolvable, since you do not have enough correspondences in a single
image, and changing the view point changes the extrinsics.
(c) The number of unknown parameters scales with the number of unique images taken
when the calibration target is stationary.
(d) The number of unknown parameters is xed, but the Ncorners must not be co-linear.
Solution C
3
Tuesday October 30, 2012
Solution Set
1 Multiple Choice (22 points)
Each question is worth 2 points . To discourage random guessing, 1 point will be deducted
for a wrong answer on multiple choice questions! For answers with multiple answers, 2
points will only be awarded if all correct choices are selected, otherwise, it is wrong
and will incur a 1 point penalty . Please draw a circle around the option(s) to indicate your
answer. No credit will be awarded for unclear/ambiguous answers.
1. (Pick one) If all of our data points are in R2, which of the following clustering algorithms
can handle clusters of arbitrary shape?
(a) k-means.
(b) k-means++.
(c) EM with a gaussian mixture model.
(d) mean-shift.
Solution Only d
2. (Pick one) Suppose we are using a Hough transform to do line tting, but we notice that
our system is detecting two lines where there is actually one in some example image.
Which of the following is most likely to alleviate this problem?
(a) Increase the size of the bins in the Hough transform.
(b) Decrease the size of the bins in the Hough transform.
(c) Sharpen the image.
(d) Make the image larger.
Solution a
3. (Pick one) Which of the following processes would help avoid aliasing while downsampling
an image?
1 (a) Image sharpening.
(b) Image blurring.
(c) Median ltering where you replace every pixel by the median of pixels in a window
around the pixel.
(d) Histogram equalization.
Solution b
4. (Circle all that apply) A Sobel lter can be written as
2
41 2 1
0 0 0
1 2 13
5=2
41
0
13
5
1 2 1
(1)
Which of the following statements are true
(a) Separating the lter in the above manner, reduces the number of computations.
(b) It is similar to applying a gaussian lter followed by a derivative.
(c) Separation leads to spurious edge artifacts.
(d) Separation approximates the rst derivative of gaussian.
Solution a and b
5. (Pick one) Which of the following is true for Eigenfaces (PCA)
(a) Can be used to e ectively detect deformable objects.
(b) Invariant to ane transforms.
(c) Can be used for lossy image compression.
(d) Is invariant to shadows.
Solution c
6. (Pick one) Downsampling can lead to aliasing because
(a) Sampling leads to additions of low frequency noise.
(b) Sampled high frequency components result in apparent low frequency components.
(c) Sampling increases the frequency components in an image.
(d) Sampling leads to spurious high frequency noise
Solution b
7. (Pick one) If we replace one lens on a calibrated stereo rig with a bigger one, what can
we say about the essential matrix, E, and the fundamental matrix, F?
2 (a) E can change due to a possible change in the physical length of the lens. F is un-
changed.
(b) F can change due to a possible change in the lens characteristics. E is unchanged.
(c) E can change due to a possible change in the lens characteristics. F is unchanged.
(d) Both are unchanged.
Solution b
8. (Pick one) Which of the following statements describes an ane camera but not a general
perspective camera?
(a) Relative sizes of visible objects in a scene can be determined without prior knowledge.
(b) Can be used to determine the distance from a object of a known height.
(c) Approximates the human visual system.
(d) An in nitely long plane can be viewed as a line from the right angle.
Solution a
9. (Circle all that apply) Which of the following could a ect the intrinsic parameters of a
camera?
(a) A crooked lens system.
(b) Diamond/Rhombus shaped pixels with non right angles.
(c) The aperture con guration and construction.
(d) Any o set of the image sensor from the lens's optical center.
Solution A,B,D
10. (Circle all that apply) For camera calibration, we learned that since there are 11 unknown
parameters, we need at least 6 correspondences to calibrate. Assuming that you couldn't nd a calibration target with the minimum of 6 corners to use as correspondences, you
decide to take multiple pictures from di erent viewpoints of a stationary pattern with N
corners, where N < 6, which of the following statements is true?
(a) The number of images, Kmust satisfy 2 NK > 6, the value of Nisn't important, so
long as it as N > 0.
(b) The problem is unsolvable, since you do not have enough correspondences in a single
image, and changing the view point changes the extrinsics.
(c) The number of unknown parameters scales with the number of unique images taken
when the calibration target is stationary.
(d) The number of unknown parameters is xed, but the Ncorners must not be co-linear.
Solution C
3
