Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Problem Set 5 for CMSC 426: Image Matching and Transformation - Prof. David Jacobs, Assignments of Computer Science

University of MarylandComputer Science
Prof. David Jacobs

A problem set for cmsc 426 students, focusing on image matching and transformation. The tasks include writing code to find the sum of square differences between rectangular portions of images (sum of squared differences, ssd), comparing a small template to an image in all possible translations using ssd, and finding the best instances of the template in the image. Additionally, there are challenge problems to make the code faster by building a gaussian pyramid and starting the matching at a small scale, and to find the 3d coordinates of points in an image and align them with given coordinates.

Typology: Assignments

Pre 2010

Uploaded on 02/13/2009

koofers-user-87t
koofers-user-87t 🇺🇸

10 documents

1 / 3

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Problem Set 5 CMSC 426
Due: Thursday, May 8
1)
Brute
-
Force, SSD matching.
The class web page contains an image and a template that you can download. Your goal
is to find the regions in the image that best match the template.
a)
Write code to find the sum of square differences between two rectangular
portions of images that are of equal size. d = SSD(R1, R2) should take
two matrices representing portions of images and return the SSD between
them. Test your function on:
R1 = [1, 0, 0, 2; 2, 1, 0, 1]; R2 =
[0, 2, 1, 1; 1, 0, 0, 1];
Turn in your result and code. Hint: You should do this without using any
loops, just with matrix operations. If you use loops, you may find that
your subsequent code is very slow.
40 pts
b)
Write code to compare a small templa
te to an image in all possible
translations of the template, computing the SSD. Only consider
translations that place the template completely inside the image.
A=brute_force_ssd(T,I) should return a matrix, A, that gives the SSD
between T and a subset of I, for every possible shift of T. You only need
to shift T by integer values, don’t worry about interpolation. Test your
code using the template and image from the web page. Display and print
the result A with the command imagesc(A). Turn in this disp
lay and your
code.
30 pts.
c)
Now write code to find the best instances of the template in the image.
The best instance is the one that positions the template in the image to
minimize the SSD. The second best one has minimal SSD of all templates
that don’t
overlap the best one (if you don’t watch this condition, your
second best template will probably be shifted one pixel from your best
template; not a useful result). Display the position of the six best, non
-
overlapping instances of the template in the im
age. You can visualize the
position of the templates as you like. For example, you might use a
matlab command to draw six red rectangles on top of the image, each the
size and position of the template. Turn in a plot of your results and your
code.
30 p
ts.
2)
Challenge Problem: Make the code to Problem 1 faster by building a Gaussian
pyramid, and starting the matching at a small scale. Then move to a larger scale,
restricting your matching to be near the best match at the smaller scale.
pf3

Partial preview of the text

Download Problem Set 5 for CMSC 426: Image Matching and Transformation - Prof. David Jacobs and more Assignments Computer Science in PDF only on Docsity!

Problem Set 5 CMSC 426

Due: Thursday, May 8

  1. Brute-Force, SSD matching.

The class web page contains an image and a template that you can download. Your goal is to find the regions in the image that best match the template.

a) Write code to find the sum of square differences between two rectangular portions of images that are of equal size. d = SSD(R1, R2) should take two matrices representing portions of images and return the SSD between them. Test your function on:

R1 = [1, 0, 0, 2; 2, 1, 0, 1]; R2 = [0, 2, 1, 1; 1, 0, 0, 1];

Turn in your result and code. Hint: You should do this without using any loops, just with matrix operations. If you use loops, you may find that your subsequent code is very slow. 40 pts

b) Write code to compare a small template to an image in all possible translations of the template, computing the SSD. Only consider translations that place the template completely inside the image. A=brute_force_ssd(T,I) should return a matrix, A, that gives the SSD between T and a subset of I, for every possible shift of T. You only need to shift T by integer values, don’t worry about interpolation. Test your code using the template and image from the web page. Display and print the result A with the command imagesc(A). Turn in this display and your code. 30 pts.

c) Now write code to find the best instances of the template in the image. The best instance is the one that positions the template in the image to minimize the SSD. The second best one has minimal SSD of all templates that don’t overlap the best one (if you don’t watch this condition, your second best template will probably be shifted one pixel from your best template; not a useful result). Display the position of the six best, non- overlapping instances of the template in the image. You can visualize the position of the templates as you like. For example, you might use a matlab command to draw six red rectangles on top of the image, each the size and position of the template. Turn in a plot of your results and your code. 30 pts.

  1. Challenge Problem: Make the code to Problem 1 faster by building a Gaussian pyramid, and starting the matching at a small scale. Then move to a larger scale, restricting your matching to be near the best match at the smaller scale.

Experiment with starting the matching at different scales. How small a scale can you start with and still get good results?

Turn in pictures showing the Gaussian pyramid for the template and the image. Turn in pictures showing the six best templates you found, at the largest scale. Turn in several of these pictures, illustrating how the results vary depending on the scale you begin matching. Use the functions tic and toc to measure the speedup you gained with multiscale matching, and report the results. Also turn in your code. 20 pts.

  1. Challenge Problem: The file on the web page called: ‘Problem Set 5 Image.mat’ contains the positions of 24 points in 4 images, and the 3D locations of the first four of these points. Execute the command load(‘Problem Set 5 Image.mat’) and the variable I will contain the 8x24 image matrix, and the variable P4 will contain a 3x4 matrix containing the x,y,z world coordinates of the first four points. Use the factorization algorithm discussed in class and in the text to find the 3D coordinates of all 24 points, up to a linear transformation. Then find a linear transformation (with translation) that will align the first four points with the four points described in P4. This will give you the world coordinates of all 24 points. Plot the x and y coordinates of these points with a command such as plot(pts(1,:), pts(2,:), ‘ko’); (you will know if you’ve got the right answer). Turn in the plot and your code. 20 pts.