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Introduction to Computer Vision (ECSE 415)
Assignment 2: Image Matching and Face
Detection

Please submit your assignment solutions electronically via the myCourses
assignment dropbox. The submission should include a single jupyter notebook.
More details on the format of the submission can be found below. Submissions
that do not follow the format will be penalized 10%. Attempt all parts of this
assignment. The assignment will be graded out of total of 85 points.
You can use OpenCV and Numpy library functions for all parts
of the assignment unless specified otherwise.

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Introduction to Computer Vision (ECSE 415)
Assignment 2: Image Matching and Face
Detection

Please submit your assignment solutions electronically via the myCourses
assignment dropbox. The submission should include a single jupyter notebook.
More details on the format of the submission can be found below. Submissions
that do not follow the format will be penalized 10%. Attempt all parts of this
assignment. The assignment will be graded out of total of 85 points.
You can use OpenCV and Numpy library functions for all parts
of the assignment unless specified otherwise.
Submission Instructions
1. Submit a single jupyter notebook consisting of the solution of the entire
assignment.
2. Comment your code appropriately.
3. Do not forget to run Markdown cells.
4. Do not submit input/output images. Output images should be displayed
in the jupyter notebook itself. Assume input images are kept in the same
directory as the codes.
5. Make sure that the submitted code is running without error. Add a
README file if required.
6. If external libraries were used in your code please specify their name and
version in the README file.
7. Answers to reasoning questions should be comprehensive but concise.
8. Submissions that do not follow the format will be penalized 10%.
1
Figure 1: Reference image of a book.
1 Invariance of SIFT Features (34 Points)
You are given a reference image of a book as shown in Figure 1. Verify the
invariance of SIFT features under changes in image scale and rotation.
1.1 Invariance Under Changes in Scale
1. Compute SIFT keypoints for the reference image. (2 points)
2. Scale reference image using scaling factors of (0.2, 0.5, 0.8, 1.25, 2, 5). (2
points)
3. Compute SIFT keypoints for the transformed images. (2 points)
4. Match all keypoints of the reference image to the transformed images using
a brute-force method. (2 points)
5. Sort matching keypoints according to the matching distance. (2 points)
6. Display top ten matched keypoints for each pair of reference image and a
transformed image. (2 points)
7. Plot the matching distance for top 100 matched keypoints. Plot indices
of keypoints on x-axis and corresponding matching distance on y-axis. (2
points)
8. Discuss the trend in the plotted results. What is the effect of increasing
the scale on the matching distance? Reason the cause. (3 points)
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1.2 Invariance Under Rotation
1. Compute SIFT keypoints for the reference image. (2 points)
2. Rotate reference image at the angle of (10, 30, 90, 150, 170, 180). (2
points)
3. Compute SIFT keypoints for the transformed images. (2 points)
4. Match all keypoints of the reference image to the transformed images using
a brute-force method. (2 points)
5. Sort matching keypoints according to the matching distance. (2 points)
6. Display top ten matched keypoints for each pair of reference image and a
transformed image. (2 points)
7. Plot the matching distance for top 100 matched keypoints. Plot indices
of keypoints on x-axis and corresponding matching distance on y-axis. (2
points)
8. Discuss the trend in the plotted results. What is the effect of increasing
the angle of rotation on the matching distance? Reason the cause. (3
points)
2 Matching using SIFT – Book Reveal (16 Points)
You are given an image of the reference book taken under different acquisition
conditions: (a) under occlusions (Figure 2(a)) and (2) under different lighting
conditions (Figure 2(b)). The task is to transform the image of the book in
Figure 2(a) and align and merge it with the occluded view in (Figure 2(b) to
generate an image with an unoccluded view of the book (See Figure 2(c)). To
achieve this objective, please perform following steps:
1. Find SIFT keypoints in given input images. (2 points)
(a) (b) (c)
Figure 2: Input and desired output for image manipulation task (a) image of an
occluded book (book occlusion.jpg) (b) reference image of a book in different
lighting condition (book crop.jpg) (c) desired output.
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Figure 3: Examples of CelebA dataset images.
2. Match keypoints of reference image to the keypoints of the occluded image
using brute-force method. (2 points)
3. Sort matching keypoints according to the matching distance. (2 points)
4. Display top ten matching keypoints. (2 points)
5. Compute a homography to align the images using RANSAC method and
apply the transformation on the reference image. (6 points)
6. Paste transformed reference image on the occluded view to generate unoccluded view as shown in Figure 2(c). (2 points)
3 Face detection (35 Points)
In this question, you will work on the task of Face detection. For this purpose,
you will explore two different algorithms for this purpose: (1) EigenFaces and
(2) Viola-Jones detector.
We will use a publicly available celebA face dataset (Figure 3). A subset
of 1000 images is given with the assignment. From these images, choose any
random 100 images as your training dataset.
Note: For this section (Face Detection), we will work with grayscale
images. DO NOT forget to convert your images to GrayScale from
RGB images.
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(a) (b)
Figure 4: Face Detection: (a) Group Image and (b) example of detected faces
with bounding boxes around the detected faces.
3.1 Eigenface Representation
Produce eigenface representation for your training data through PCA. Please
note that you are not allowed to use the in-built PCA function in OpenCV/ScikitLearn. You should implement Snapshot method for PCA (covered in class –
Lecture 8 – Slide 55) from scratch using numpy (15 points) 1
. Display first
6 eigenfaces (3 points)
3.2 Face Detection
You will now detect all the faces in a group image (Figure 4 (a)). Use a sliding
window to detect the faces. We will follow PCA base detection algorithm covered in class (Lecture 8 – Slide 63). Set a threshold on the distance in eigenspace
between the window contents and your training data. Try different values of
thresholds and use the one which gives you good results. Display your image
with bounding boxes around detected faces for your best threshold (ex. Figure
4 (b)) 2
(10 points). How well does the method work? How many false positive
face detections do you get? (2 points).
Use an existing implementation of the Viola-Jones face detector, and compare the results with your detector (e.g. how many false positives do you obtain?). Under what conditions would you expect the Viola-Jones detector to
work when PCA does not? (5 points)
1You are allowed to use numpy.linalg for computing eigenvalues and eigenvectors
2You can use any online available code for bounding box generation. Please cite the source
for this in your report.
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