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Assignment 0 Scipy Practice1

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COMP5421 Computer Vision
Homework Assignment 0
Scipy Practice1
This homework will not be graded. It is meant to provide some Python/Scipy practice exercises
to ensure that coding will not be an obstacle for you during this course. However, it IS REQUIRED
that you submit an attempt. Please follow the submission instructions at the end of the assignment. This and future assignments will assume that you are using Python 3+ and the latest Scipy
libraries (numpy, matplotlib, etc). The recommended approach is to use the Anaconda Python 3
distribution.
1 Color Channel alignment
You have been given the red, green, and blue channels of an image2
that were taken separately
using an old technique that captured each color on a separate piece of glass3 These files are named
red.npy, green.npy, and blue.npy respectively (in the data folder). Because these images were
taken separately, just combining them in a 3-channel matrix may not work. For instance, Figure 1
shows what happens if you simply combine the images without shifting any of the channels.
Your job is to take 3-channel RGB (red-green-blue) image and produce the correct color image
(closest to the original scene) as output. Because in the future you may be hired to do this on
hundreds of images, you cannot hand-align the image; you must write a function that finds the
best possible displacement.
The easiest way to do this is to exhaustively search over a window of possible displacements for
the different channels (you can assume the displacement will be between -30 and 30 pixels). Score
the alignment from each possible displacement with some heuristic and choose the best alignment
using these scores. You can use the following metrics:
1. Sum of Squared Differences (SSD)
This metric tries to compare the distance between two vectors, hence we can use this to
compare image pixel intensity differences. For two vectors u, v of length N, this metric is
defined as
SSD(u, v) = X
N
i=1
(u[i] − v[i])2
(essentially like the Euclidean distance metric).
2. Normalized Cross Correlation (NCC)4
This metric compares normalized unit vectors using a dot product, that is for vectors u, v,
NCC (u, v) = u
||u|| ·
v
||v||
Implement an algorithm which finds the best alignment of the three channels to produce a good
RGB image; it should look something like Figure 2. Try to avoid using for loops when computing
1Credit to CMU Simon Lucey, Nate Chodosh, Ming-Fang Chang, Chengqian Che, Gaurav Mittal, Purna Sowmya
Munukutla
2downloaded from http://www.loc.gov/pictures/collection/prok/
3Credit to Kris Kitani and Alyosha Efros for this problem.
4
https://en.wikipedia.org/wiki/Cross-correlation\#Normalized_cross-correlation
1
Figure 1: Combining the red, green, and blue channels without shifting
Figure 2: Aligned image
the metrics (SSD or NCC) for a specific offset. Some starter code is given in script1.py and
alignChannels.py. Save your result as rgb output.jpg in the results folder.
2 Image warping
We will be writing code that performs affine warping on an image. Code has been provided to get
you started. In the following sections you will be adding your own code.
2.1 Example code
The file script2.py contains example code which demonstrates basic image loading and displaying
as well as the behavior of an image warping function. Try running script2. You should see something
like Figure 3. This script calls the function warp in warpA check.py, which is simply a wrapper
for scipy’s own function scipy.ndimage.affine transform.
2
Figure 3: See script2.py
2.2 Affine warp
You will write your own function in warpA.py, that should give the same output as the function in
warpA check.py. First we’ll walk through what you need to know about affine transformations.
An affine transform relates two sets of points:
p
i
warped =

a b
c d !
| {z }
L
p
i
source + t (1)
where p
i
source and p
i
warped denote the 2D coordinates (e.g., p
i
s = (x
i
s
, yi
s
)
T
) of the i-th point in
the source space and destination (or warped) space respectively, L is a 2×2 matrix representing the
linear component, and t is a 2×1 vector representing the translational component of the transform.
To more conveniently represent this transformation, we will use homogeneous coordinates, i.e.,
p
i
s and p
i
w will now denote the 2D homogeneous coordinates (e.g., p
i
s ≡ (x
i
s
, y
i
s
, 1)T
), where “≡”
denotes equivalence up to scale, and the transform becomes:
p
i
d ≡

L t
0 0 1
!
| {z }
A
p
i
s
(2)
• Implement a function that warps image im using the affine transform A:
warp im = warpA(im, A, output shape)
Inputs: im is a grayscale double typed Numpy matrix of dimensions height × width × 5
, A is
5
Images in Numpy are indexed as im(row, col, channel) where row corresponds to the y coordinate (height),
and col to the x coordinate (width).
3
a 3 × 3 non-singular matrix describing the transform (p
i
warped ≡ Api
source ), and
output size=[out height,out width]; of the warped output image.
Outputs: warp im of size out size(1) × out size(2) is the warped output image.
The coordinates of the sampled output image points p
i
warped should be the rectangular range
(0, 0) to (width − 1, height − 1) of integer values. The points p
i
source must be chosen such that their
image, Api
source , transforms to this rectangle.
Implementation-wise, this means that we will be looking up the value of each of the destination
pixels by sampling the original image at the computed p
i
source . (Note that if you do it the other
way round, i.e., by transforming each pixel in the source image to the destination, you could get
“holes” in the destination because the mapping need not be 1 to 1). In general, the transformed
values pisource will not lie at integer locations and you will therefore need to choose a sampling
scheme; the easiest is nearest-neighbor sampling (something like, round(p
i
source )). You should be
able to implement this without using for loops (one option is to use numpy.meshgrid and Numpy’s
multidimensional indexing), although it might be easier to implement it using loops first. Save the
resulting image in results/transformed.jpg.
You should check your implementation to make sure it produces the same output as the warp
function provided in warpA check.py (for grayscale or RGB images). Obviously the purpose of this
exercise is practicing Python/Scipy by implementing your own function without using anything like
scipy.ndimage.affine transform.
3 Submission and Deliverables
Please submit a zip file to CASS for this homework of the form <ust-login-id>.zip. Running
script1.py and script2.py from within the code/ folder should produce the outputs
transformed.jpg, and rgb output.jpg in the results/ folder. You should not include the data/
folder in your submission. An example submission zip file should be:
sigbovik.zip:
• code/
– script1.py
– script2.py
– warpA.py
– warpA check.py
– any other files your code needs to run
• results/
– rgb output.jpg for Question 1
– transformed.jpg for Question 2
4

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