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2	Recognition Readings C. Bishop, “Neural Networks for Pattern Recognition”, Oxford University Press, 1998, Chapter 1. Forsyth and Ponce, 22.3 (eigenfaces)
3	Recognition Readings C. Bishop, “Neural Networks for Pattern Recognition”, Oxford University Press, 1998, Chapter 1. Forsyth and Ponce, 22.3 (eigenfaces)
4	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
5	Face detection How to tell if a face is present?
6	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
7	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?
8	Skin classification techniques
9	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
10	Probabilistic skin classification Now we can model uncertainty Each pixel has a probability of being skin or not skin
11	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 R_i contains the proportion of skin pixels with color R_i
12	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 R_i contains the proportion of skin pixels with color R_i
13	Bayes rule In terms of our problem:
14	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
15	Skin detection results
16	General classification This same procedure applies in more general circumstances More than two classes More than one dimension
17	Linear subspaces Classification is still expensive Must either search (e.g., nearest neighbors) or store large PDF’s
18	Dimensionality reduction
19	Linear subspaces
20	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”
21	The space of faces An image is a point in a high dimensional space An N x M image is a point in R^NM We can define vectors in this space as we did in the 2D case
22	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, ..., v_K any face
23	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?
24	Projecting onto the eigenfaces The eigenfaces v₁, ..., v_K span the space of faces A face is converted to eigenface coordinates by
25	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?
26	Limits of PCA Attempts to fit a hyperplane to the data can be interpreted as fitting a Gaussian, where A is the covariance matrix this is not a good model for some data If you know the model in advance, don’t use PCA regression techniques to fit parameters of a model Several alternatives/improvements to PCA have been developed LLE: http://www.cs.toronto.edu/~roweis/lle/ isomap: http://isomap.stanford.edu/ kernel PCA: http://www.cs.ucsd.edu/classes/fa01/cse291/kernelPCA_article.pdf For a survey of such methods applied to object recognition Moghaddam, B., "Principal Manifolds and Probabilistic Subspaces for Visual Recognition", IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), June 2002 (Vol 24, Issue 6, pps 780-788) http://www.merl.com/papers/TR2002-13/
27	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 new work (e.g., Linda Shapiro’s group at UW), seeks to recognize 3D objects (meshes) by training on 3D scan data