Notes

Outline

Announcements Project 2 artifacts Project 3 due Thursday night Project 3 artifacts due Friday night Don’t miss Thursday’s lecture Jiwon & David will give it Need this material for project 4 Picture taking at the end of today’s lecture Midterms returned today (end of lecture)

Recognition Readings C. Bishop, “Neural Networks for Pattern Recognition”, Oxford University Press, 1998, Chapter 1. Forsyth and Ponce, pp. 723-729 (eigenfaces)

Recognition Readings C. Bishop, “Neural Networks for Pattern Recognition”, Oxford University Press, 1998, Chapter 1. (handout) Forsyth and Ponce, pp. 723-729 (eigenfaces)

Recognition problems What is it? Object detection Who is it? Recognizing identity What are they doing? Activities All of these are classification problems Choose one class from a list of possible candidates

Face detection How to tell if a face is present?

One simple method:  skin detection Skin pixels have a distinctive range of colors Corresponds to region(s) in RGB color space for visualization, only R and G components are shown above

Skin detection Learn the skin region from examples Manually label pixels in one or more “training images” as skin or not skin Plot the training data in RGB space skin pixels shown in orange, non-skin pixels shown in blue some skin pixels may be outside the region, non-skin pixels inside.  Why?

Skin classification techniques

Probability Basic probability X is a random variable P(X) is the probability that X achieves a certain value                                     or Conditional probability:   P(X | Y) probability of X given that we already know Y

Probabilistic skin classification Now we can model uncertainty Each pixel has a probability of being skin or not skin

Learning conditional PDF’s We can calculate P(R | skin) from a set of training images It is simply a histogram over the pixels in the training images each bin Ri contains the proportion of skin pixels with color Ri

Bayes rule In terms of our problem:

Bayesian estimation Bayesian estimation Goal is to choose the label (skin or ~skin) that maximizes the posterior this is called Maximum A Posteriori (MAP) estimation

Skin detection results

General classification This same procedure applies in more general circumstances More than two classes More than one dimension

Linear subspaces Classification is still expensive Must either search (e.g., nearest neighbors) or store large PDF’s

Dimensionality reduction

Linear subspaces

Principle component analysis Suppose each data point is N-dimensional Same procedure applies: The eigenvectors of A define a new coordinate system eigenvector with largest eigenvalue captures the most variation among training vectors x eigenvector with smallest eigenvalue has least variation We can compress the data by only using the top few eigenvectors corresponds to choosing a “linear subspace” represent points on a line, plane, or “hyper-plane”

The space of faces An image is a point in a high dimensional space An N x M image is a point in RNM We can define vectors in this space as we did in the 2D case

Dimensionality reduction The set of faces is a “subspace” of the set of images Suppose it is K dimensional We can find the best subspace using PCA This is like fitting a “hyper-plane” to the set of faces spanned by vectors v1, v2, ..., vK any face

Eigenfaces PCA extracts the eigenvectors of A Gives a set of vectors v1, v2, v3, ... Each one of these vectors is a direction in face space what do these look like?

Projecting onto the eigenfaces The eigenfaces v1, ..., vK span the space of faces A face is converted to eigenface coordinates by

Recognition with eigenfaces Algorithm Process the image database (set of images with labels) Run PCA—compute eigenfaces Calculate the K coefficients for each image Given a new image (to be recognized) x, calculate K coefficients Detect if x is a face If it is a face, who is it?

Object recognition This is just the tip of the iceberg We’ve talked about using pixel color as a feature Many other features can be used: edges motion (e.g., optical flow) object size ... Classical object recognition techniques recover 3D information as well given an image and a database of 3D models, determine which model(s) appears in that image often recover 3D pose of the object as well

Summary Things to take away from this lecture Classifiers Probabilistic classification decision boundaries learning PDF’s from training images Bayesian estimation Principle component analysis Eigenfaces algorithm