A short quiz on humans (mostly faces)

Adrian F. Clark

1. Faces are allegedly more attractive if:

   • facial features are slightly asymmetrical
   • the lips are oval in shape
   • the hair and skin are in the same region in HSV space

   • the shape matches the golden ratio

   People are supposed to have more beautiful faces if the shape is closer to the golden ratio. No, I don't believe it either.

2. What is Adaptive Boosting?

   • a method for combining multiple weak classifiers into one strong classifier

   • an adaptive way of choosing the best single classifier for a task
   • a way of improving the contrast of an image based on the local grey levels
   • a method for improving the performance of a single weak classifier

   Adaptive booting is the way that the Viola-Jones algorithm combines multiple Haar features, each of which is a weak classifier individually, into a strong classifier

3. Which of the following techniques is "eigenfaces" built on?

   • Linear Discriminant Analysis
   • Support Vector Machine
   • Convolutional Neural Network

   • Principal Component Analysis

   Eigenfaces is based on a Principal Component Analysis or Eigen decomposition of the training data. The other methods listed are also machine learning techniques and some of them may be used in conjunction with PCA to recognise faces, but the resulting technique is not eigenfaces.

4. What is covariance?

   • a pair of images having similar variances

   • a measure of the similarity of variations in the images

   • another name for cross-correlation
   • a pair of images having dissimilar variances

   The covariance measures whether variations in images happen "in step". For two images $P$ and $Q$ with means $\bar P$ and $\bar Q$, it is $\sum (P_{ij} - \bar P) (Q_{ij} - \bar Q)$.

5. What does Principal Component Analysis (PCA), as used in eigenfaces, do?

   • splits up features into components
   • finds the most similar set of features in a database

   • finds the directions in feature space with the largest variations

   • finds the most important direction in an image

   PCA finds the direction in feature space with the largest variance, then the next-largest direction that is perpendicular to the first -- and so on. For the mathematically-inclined, this forms a set of basis vectors to the feature space using the criterion of maximising variance.

6. How is Principal Component Analysis performed?

   • by Linear Discriminant Analysis of the variance of an image

   • by Eigen decomposition of the covariance matrix

   • by Eigen decomposition of the variance of an image
   • by Linear Discriminant Analysis of the covariance matrix

   PCA is performed by calculating the covatiance matrix and then performing an eigen decomposition of it. The resulting eigenvectors or Principal Components describe the different ways in which the images vary and can be used for "transforming" an image. When that is done, the eigenvalues are a set of weights that describe how the principal components are combined to give that image. These weights can be used for recognition: the closer they are to something in the training image set, the more similar they are.

7. What is the basis of the HOG feature detector?

   • a histogram of pixel values
   • a histogram of colour differences

   • a histogram of edge orientations

   • a histogram of edge gradients

   HOG stands for "histogram of oriented gradients", so the histogram is of edge orientations, also known as edge directions.

8. The Viola-Jones face detection algorithm is based around the use of which type of features?

   • SIFT features

   • Haar features

   • ORB features
   • Edges detected using Canny's edge detector

   Viola-Jones is based around Haar features, which can be calculated very quickly. They provide "weak classifiers" of faces, and carefully-chosen ones can be assembled into a "cascade" that works well. The algorithm is probably implemented on your mobile phone.

9. Why is the integral image representation used in Viola-Jones?

   • it stores where faces lie in an image
   • it allows features to be concatenated into a feature vector

   • it allows Haar features to be calculated in constant time

   • it stores the sum of all the pixels in an image

   The main attraction the integral image representation is that it allows Haar features of any size to be calculated in constant time, using the same underlying mathematics as the anti-aliased texture mapping on a typical graphics card.

10. What are Haar features?

    • differences between the sums of pixels in rectangular regions

    • the sum of differences between a pair of images
    • the number of corners in a region
    • measures of the number of edges in a region

    Haar features are simple, which makes them quick to calculate.