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# Computer Vision Problem Set 1 SOLUTION

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ECS 189G: Intro to Computer Vision
Problem Set 1

Instructions
1. Answer sheets must be submitted on SmartSite. Hard copies will not be accepted.
FirstName_LastName_PS1.pdf.
3. Please submit your code and input /output images in a zip file named: FirstName_LastName_PS1.zip.
Please do not create subdirectories within the main directory.
4. You may collaborate with other students. However, you need to write and implement your own
solutions. Please list the names of students you discussed the assignment with.

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## Description

ECS 189G: Intro to Computer Vision
Problem Set 1

Instructions
1. Answer sheets must be submitted on SmartSite. Hard copies will not be accepted.
FirstName_LastName_PS1.pdf.
3. Please submit your code and input /output images in a zip file named: FirstName_LastName_PS1.zip.
Please do not create subdirectories within the main directory.
4. You may collaborate with other students. However, you need to write and implement your own
solutions. Please list the names of students you discussed the assignment with.
5. For the implementation questions, make sure your code is documented, is bug-free, and works out
of the box. Please be sure to submit all main and helper functions. Be sure to not include absolute
paths. Points will be deducted if your code does not run out of the box.
6. If plots are required, you must include them in your answer sheet (pdf) and your code must
display them when run. Points will be deducted for not following this protocol.
I. Short answer problems [30 points]
1. Give an example of how one can exploit the associative property of convolution to more
efficiently filter an image.
2. This is the input image: [0 0 1 1 0 0 1 1]. What is the result of dilation with a structuring
element [1 1 1]?
3. The filter f’ = [0 -1/2 0 1/2 0] gives an estimate of the first derivative of the image in the x
direction. What is the corresponding second derivative filter f”? (Hint: Asymmetric filters must be
flipped prior to convolution.)
4. Describe a possible flaw in the use of additive Gaussian noise to represent image noise.
5. Design a method that takes video data from a camera perched above a conveyor belt at an
automotive equipment manufacturer, and reports any flaws in the assembly of a part. Your
response should be a list of concise, specific steps, and should incorporate several techniques covered
in class thus far. Specify any important assumptions your method makes.
II. Programming problem: content-aware image resizing [70 points]
For this exercise, you will implement a version of the content-aware image resizing technique described in
Shai Avidan and Ariel Shamir’s SIGGRAPH 2007 paper, “Seam Carving for Content-Aware Image Resizing”.
The paper is available off the course website. The goal is to implement the method, and then examine and
explain its performance on different kinds of input images.
First read through the paper, with emphasis on sections 3, 4.1, and 4.3. Note: choosing the next pixel to add
one at a time in a greedy manner will give sub-optimal seams; the dynamic programming solution ensures the
best seam (constrained by 8-connectedness) is computed. Use the dynamic programming solution as given in
the paper and explained in class.
Write Matlab code with functions that can do the following tasks. Save each of the below functions in a file
called <function-name.m and submit all of them.
• energyImage = energy_image(im)- to compute the energy at each pixel using the magnitude of
the x and y gradients (equation 1 in the paper; sqrt(dx^2+dy^2)). The gradients should be computed with
the grayscale converted image. You do not need to smooth the image before computing the gradients.
The input im should be an MxNx3 matrix of datatype uint8. (It can be the output of imread on a color
image.) The output energyImage should be a 2D matrix of datatype double.
• cumulativeEnergyMap =
cumulative_minimum_energy_map(energyImage,seamDirection)- to compute
minimum cumulative energy. The input energyImage should be a 2D matrix of datatype double (the
output of energy_image function defined above). The input seamDirection can be the strings
‘HORIZONTAL’ or ‘VERTICAL’. The output cumulativeEnergyMap must be a 2D matrix of
datatype double.
• verticalSeam = find_optimal_vertical_seam(cumulativeEnergyMap) – to
compute the optimal vertical seam. The input cumulativeEnergyMap should be a 2D matrix of
datatype double (the output of the cumulative_minimum_energy_map function defined above).
The output verticalSeam must be a vector containing the column indices of the pixels which form
the seam for each row.
• horizontalSeam =
find_optimal_horizontal_seam(cumulativeEnergyMap)- to compute the optimal
horizontal seam. The input cumulativeEnergyMap should be a 2D matrix of datatype
double (the output of the cumulative_minimum_energy_map function defined above).
The output horizontalSeam must be a vector containing the row indices of the pixels which
form the seam for each column.
• display_seam(im,seam,seamDirection)- to display the selected type of seam on top of an image.
The input im should be an image of type jpg. seam can be the output of
find_optimal_vertical_seam or find_optimal_horizontal_seam. seamDirection
can be the strings ‘HORIZONTAL’ or ‘VERTICAL’. The function should display the input image and plot
the seam on top of it. Hint: The origin of the plot will be the top left corner of the image.
• Functions with the following interface:
[reducedColorImage,reducedEnergyImage] = reduce_width(im,energyImage)
[reducedColorImage,reducedEnergyImage] = reduce_height(im,energyImage)
These functions should take as inputs (a) an MxNx3 matrix im of datatype uint8 and (b) a 2D matrix
energyImage of datatype double. The input energyImage can be the output of the energy_image
function. The output must return 2 variables: (a) a 3D matrix reducedColorImage same as the input
image but with its width or height reduced by one pixel; (b) a 2D matrix reducedEnergyImage of
datatype double same as the input energyImage, but with its width or height reduced by one pixel.
Answer each of the following, and include image displays where appropriate:
1. [10 points] Write a script called seam_carving_reduce_width.m which does the following by using
the functions defined above:
http://web.cs.ucdavis.edu/~yjlee/teaching/resources/inputSeamCarvingPrague.jpg
b) Reduces the width of the image by 100 pixels using the above functions.
c) Saves the resulting image as outputReduceWidthPrague.png. Submit it. Display this output
d) Repeat the steps for an input image called inputSeamCarvingMall.jpg. Download the image
from http://web.cs.ucdavis.edu/~yjlee/teaching/resources/inputSeamCarvingMall.jpg. Save the output
2. [10 points] Repeat the above steps for both input images, but reduce the height by 100 pixels. Call the
script SeamCarvingReduceHeight.m, and save the output images as
outputReduceHeightPrague.png and outputReduceHeightMall.png, respectively. Display
both outputs in your answer sheet. Submit the script for image inputSeamCarvingPrague.jpg
3. [10 points] Display in your answer sheet: (a) the energy function output for the provided image
inputSeamCarvingPrague.jpg, and (b) the two corresponding cumulative minimum energy maps for
the seams in each direction (use the imagesc function). Explain why these outputs look the way they do
given the original image’s content.
4. [10 points] For the same image inputSeamCarvingPrague.jpg, display the original image together
with (a) the first selected horizontal seam and (b) the first selected vertical seam. Explain why these are
the optimal seams for this image.
5. [10 points] Make some change to the way the energy function is computed (i.e., filter used, its
parameters, or incorporating some other prior knowledge). Display the result and explain the impact on the
results for some example. You need not submit this code.
6. [20 points] Now, for the real results! Use your system with different kinds of images and seam
combinations, and see what kind of interesting results it can produce. The goal is to form some
perceptually pleasing outputs where the resizing better preserves content than a blind resizing would, as
well as some examples where the output looks unrealistic or has artifacts.
Include results for at least three images of your own choosing (be sure to credit any photo sources).
Include an example or two of a “bad” outcome. Be creative in the images you choose, and in the amount of
combined vertical and horizontal carvings you apply. Try to predict types of images where you might see
something interesting happen. It’s ok to fiddle with the parameters (seam sequence, number of seams, etc)
to look for interesting and explainable outcomes.
For each result, include the following things, clearly labeled (see title function):
a) the original input image,
c) the result one would get if instead a simple resampling were used (via Matlab’s imresize),
d) the input and output image dimensions,
e) the sequence of enlargements and removals that were used, and
f) a qualitative explanation of what we’re seeing in the output.
III. [OPTIONAL] Extra credit [up to 10 points each, max possible 20 points
extra credit]
Below are ways to expand on the system you built above. If you choose to do any of these (or design your
own extension) include in your answer sheet an explanation of the extension as well as images displaying the
results and a short explanation of the outcomes. Also include a line or two of instructions telling what needs to
be done to execute that part of your code and submit your code.
1. Allow a user to mark an object to be removed, and then remove seams until all pixels on that object are
gone (as suggested in section 4.6 of the paper). Either hard-code the region specific to the image, or
allow interactive choices (Matlab’s ginput or impoly functions are useful to get mouse clicks or draw
polygons).
how it can influence the results as compared to using the gradient magnitude. Choose an image or two
that illustrates the differences well.
3. To avoid warping regions containing people’s faces, have the system try to detect skin-colored pixels,
and let that affect the energy map. Try using the hue (H) channel of HSV color space (see Matlab’s
rgb2hsv function to map to HSV color space). Think about how to translate those values into energy
function scores.
4. Implement functions to increase the width or height of the input image, blending the neighboring
pixels along a seam. (See the Seam Carving paper for details.) Demonstrate on an image that clearly
shows the impact.
5. Implement the greedy solution, and compare the results to the optimal DP solution.
Matlab hints:
• Useful functions: imfilter, im2double, fspecial, imread, imresize,
rgb2gray, imagesc, imshow, subplot.
• To plot points on top of a displayed image, use imshow(im); followed by hold on; followed by
plot(…);.
• Be careful with double and uint8 conversions as you go between computations with the images and
displaying them.
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