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Recognition The “Margaret Thatcher Illusion”, by Peter Thompson Readings • • C. Bishop, “Neural Networks for Pattern Recognition”, Oxford University Press, 1998, Chapter 1. Szeliski, Chapter 14.2.1 (eigenfaces) Recognition The “Margaret Thatcher Illusion”, by Peter Thompson What do we mean by “recognition”? Next 15 slides adapted from Li, Fergus, & Torralba’s excellent short course on category and object recognition Verification: is that a lamp? Detection: are there people? Identification: is that Potala Palace? Object categorization mountain tree building banner street lamp vendor people Scene and context categorization • outdoor • city •… Applications: Computational photography Applications: Assisted driving Pedestrian and car detection meters Ped Ped Car meters Lane detection • Collision warning systems with adaptive cruise control, • Lane departure warning systems, • Rear object detection systems, Applications: image search Challenges: viewpoint variation Michelangelo 1475-1564 Challenges: illumination variation slide credit: S. Ullman Challenges: occlusion Magritte, 1957 Challenges: scale Challenges: deformation Xu, Beihong 1943 Challenges: background clutter Klimt, 1913 Challenges: intra-class variation Face detection How to tell if a face is present? One simple method: skin detection skin 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 classifier • A pixel X = (R,G,B) is skin if it is in the skin region • But how to find this region? 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 classifier • Given X = (R,G,B): how to determine if it is skin or not? Skin classification techniques Skin classifier: Given X = (R,G,B): how to determine if it is skin or not? • Nearest neighbor – find labeled pixel closest to X • Find plane/curve that separates the two classes – popular approach: Support Vector Machines (SVM) • Data modeling – – fit a model (curve, surface, or volume) to each class probabilistic version: fit a probability density/distribution model to each class Probability Basic probability • X is a random variable • P(X) is the probability that X achieves a certain value called a PDF -probability distribution/density function -a 2D PDF is a surface, 3D PDF is a volume • • or continuous X discrete X • 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 – Skin classifier • Given X = (R,G,B): how to determine if it is skin or not? • Choose interpretation of highest probability – set X to be a skin pixel if and only if Where do we get and ? 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 This doesn’t work as well in higher-dimensional spaces. Why not? Approach: fit parametric PDF functions • common choice is rotated Gaussian – – center covariance » orientation, size defined by eigenvecs, eigenvals 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 But this isn’t quite what we want • Why not? How to determine if a pixel is skin? • We want P(skin | R) not P(R | skin) • How can we get it? Bayes rule In terms of our problem: what we measure (likelihood) what we want (posterior) domain knowledge (prior) normalization term What could we use for the prior P(skin)? • Could use domain knowledge – – P(skin) may be larger if we know the image contains a person for a portrait, P(skin) may be higher for pixels in the center • Could learn the prior from the training set. How? – P(skin) may be proportion of skin pixels in training set Bayesian estimation likelihood Bayesian estimation posterior (unnormalized) = minimize probability of misclassification • Goal is to choose the label (skin or ~skin) that maximizes the posterior – this is called Maximum A Posteriori (MAP) estimation Bayesian estimation likelihood Bayesian estimation posterior (unnormalized) = minimize probability of misclassification • Goal is to choose the label (skin or ~skin) that maximizes the posterior – this is called Maximum A Posteriori (MAP) estimation • Suppose the prior is uniform: P(skin) = P(~skin) = 0.5 – in this case , – maximizing the posterior is equivalent to maximizing the likelihood » if and only if – this is called Maximum Likelihood (ML) estimation Skin detection results General classification This same procedure applies in more general circumstances • More than two classes • More than one dimension Example: face detection • Here, X is an image region – – dimension = # pixels each face can be thought of as a point in a high dimensional space H. Schneiderman, T. Kanade. "A Statistical Method for 3D Object Detection Applied to Faces and Cars". IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2000) http://www-2.cs.cmu.edu/afs/cs.cmu.edu/user/hws/www/CVPR00.pdf H. Schneiderman and T.Kanade Linear subspaces convert x into v1, v2 coordinates What does the v2 coordinate measure? - distance to line - use it for classification—near 0 for orange pts What does the v1 coordinate measure? - position along line - use it to specify which orange point it is Classification can be expensive • Big search prob (e.g., nearest neighbors) or store large PDF’s Suppose the data points are arranged as above • Idea—fit a line, classifier measures distance to line Dimensionality reduction Dimensionality reduction • We can represent the orange points with only their v1 coordinates – since v2 coordinates are all essentially 0 • • This makes it much cheaper to store and compare points A bigger deal for higher dimensional problems Linear subspaces Consider the variation along direction v among all of the orange points: What unit vector v minimizes var? What unit vector v maximizes var? Solution: v1 is eigenvector of A with largest eigenvalue v2 is eigenvector of A with smallest eigenvalue Principal component analysis (PCA) 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” – these eigenvectors are known as the principal components 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 1. Process the image database (set of images with labels) • • Run PCA—compute eigenfaces Calculate the K coefficients for each image 2. Given a new image (to be recognized) x, calculate K coefficients 3. Detect if x is a face 4. If it is a face, who is it? • Find closest labeled face in database • nearest-neighbor in K-dimensional space Choosing the dimension K eigenvalues i= K NM How many eigenfaces to use? Look at the decay of the eigenvalues • the eigenvalue tells you the amount of variance “in the direction” of that eigenface • ignore eigenfaces with low variance Object recognition This is just the tip of the iceberg • Better features: – – – – edges (e.g., SIFT) motion depth/3D info ... • Better classifiers: – e.g., support vector machines (SVN) • Speed (e.g., real-time face detection) • Scale – e.g., Internet image search Recognition is a very active research area right now