SOLVED:Assignment 3: Face Detection and Classification

Description

This assignment will give you the opportunity to practice using eigenvec-tors to perform face detection and identi cation. You will work with a set of images containing faces, use principal components analysis (PCA) to represent them, then use that information to automatically detect those same faces in un-seen data. You will then compare your implementation’s performance to that of the Viola-Jones face detector (use publicly-available code; cite appropriately).

Please submit your assignment solutions electronically via the myCourses as-signment 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 65 points. Note that you can use any of the OpenCV and scikit-learn functions shown during tutorial sessions for this assignment, unless stated otherwise.

• Data (5 Points)

For this assignment, you will have access to face images from a subset of the publicly available Color FERET Database [1] . You can download this dataset from google drive using this link This dataset is provided along with the as-signment. Whereas the complete database contains images from approximately 1000 di erent subjects, the subset of the dataset that you are provided with contains images from only 52 subjects. The subset is arranged into several fold-ers each containing images of a speci c subject in di erent poses. The number of images per subject varies from 32 to 96. Each image is 768×512 pixels and the les are in PPM format. Convert images to gray-scale and down-sample images by the scale of 4. (1 Point)

You now need to prepare your dataset for a face recognition and detection system. Randomly separate the images into training and test sets as described below. A new random selection should be made by your program every time the system is retrained ².

• Train set: For each subject, randomly select 80% of the total images given for that subject. This will be used as the training set. (1 point)

• Test set: All the remaining images from the given subset which are not used in the training set will be used as test images. (1 point)

Display total 10 random images. Plot histogram of the frequency of each image class (in this case the subject) distribution. (2 Points)

• Eigenface Representation (25 Points)

You are now ready to create an eigenface representation for your training dataset through PCA. Please note that you are not allowed to use the in-built PCA

• For debugging purposes, you can x your random seed. This should allow you get same split during di erent runs.

Figure 1: Face Detection: Example image with bounding boxes around the detected faces.

function in OpenCV/Scikit-Learn. You should implement the e cient Snap-shot method for PCA (covered in class, Lecture 9, Slide 55) from scratch using numpy. (15 points)

Plot the fraction of total variance against the number of eigenvectors ³ (2 points). Plot the normalized variance (eigenvalues) against the eigenvector in-dex used for computation. (2 points). Do you need all the vectors to represent the data? Discuss (3 points). Display the rst 5 eigenfaces (5 points).

• Classi cation (15 Points)

For every testing image, nd the nearest neighbour (L2 distance), and check whether both images belong to the same person. To estimate the accuracy of this approach, determine what fraction of your test images has a neighbour that is actually of the same person? Compute the accuracy both in the original high dimensional pixel space and then in the eigenspace, and compare the accuracy values. Would you expect there to be a signi cant di erence? (10 points)

You will now use a linear SVM classi er in the eigenspace. Use the training dataset to t the classi er and the testing dataset to test the classi er. Com-pare the accuracy of this classi er with the nearest neighbour classi er used previously (5 Points).

• Face Detection (20 Points)

You will now detect all the faces in the given group image (Schitts Creek group.jpg)

using PCA. Use a sliding window to detect the faces. Set a threshold on the dis-

• Refer to Tutorial 5 for more details.

tance in eigenspace between the window contents and your training data (Refer to slide 63 of Lecture 9). Try di erent values of thresholds and use the one which gives you good results. Display your image with bounding boxes around the detected faces for the best threshold. (ex. Figure 1) ⁴ (15 points).

Use an existing implementation of the Viola-Jones face detector, and com-pare the results with your detector. Comparisons should be made in terms of the number of true positives, false positives and false negatives (See Appendix). Display the image with bounding boxes around the detected faces. Under what conditions would you expect the Viola-Jones detector to work when PCA does not? (5 points).

Appendix

A bounding box is considered as a true positive if it contains a face image otherwise, it is regarded as a false positive. A missed face (no detected bounding box around) is considered a false negative.

• You can use any online available code for bounding box generation. Please cite the source for this in your report.

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