Last weekSlide 2TodaySlide 4Recognition problemsHow do human do recognition?Observation 1:Slide 8Slide 9Observation 2:Observation 3:Slide 12Observation 4:The list goes onFace detectionOne simple method: skin detectionSkin detectionSkin classification techniquesProbabilityProbabilistic skin classificationLearning conditional PDF’sSlide 22Bayes ruleBayesian estimationSkin detection resultsGeneral classificationLinear subspacesDimensionality reductionPrincipal component analysisThe space of facesSlide 31EigenfacesProjecting onto the eigenfacesRecognition with eigenfacesChoosing the dimension KIssues: dimensionality reductionIssues: data modelingGenerative vs. DiscriminativeIssues: speedViola/Jones: featuresIntegral Image (aka. summed area table)Viola/Jones: handling scaleCascaded ClassifierViola/Jones results:ApplicationSlide 46The class scheduleLast week•Multi-Frame Structure from Motion: •Multi-View StereoUnknownUnknowncameracameraviewpointsviewpointsLast week•PCAToday•RecognitionToday•RecognitionRecognition 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 candidatesHow do human do recognition? •We don’t completely know yet•But we have some experimental observations.Observation 1:Observation 1:The “Margaret Thatcher Illusion”, by Peter ThompsonObservation 1:The “Margaret Thatcher Illusion”, by Peter Thompson•http://www.wjh.harvard.edu/~lombrozo/home/illusions/thatcher.html#bottom •Human process up-side-down images seperatelyObservation 2:Jim CarreyKevin Costner• High frequency information is not enoughObservation 3:Observation 3:• Negative contrast is difficultObservation 4:• Image Warping is OKThe list goes on•Face Recognition by Humans: Nineteen Results All Computer Vision Researchers Should Know About http://web.mit.edu/bcs/sinha/papers/19results_sinha_etal.pdfFace 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 skinSkin 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 techniquesSkin classifier•Given X = (R,G,B): how to determine if it is skin or not?•Nearest neighbor–find labeled pixel closest to X–choose the label for that pixel•Data modeling–fit a model (curve, surface, or volume) to each class•Probabilistic data modeling–fit a probability model to each classProbability•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 Ycontinuous X discrete Xcalled a PDF-probability distribution/density function-a 2D PDF is a surface, 3D PDF is a volumeProbabilistic 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, eigenvalsLearning 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)domain knowledge(prior)what we want(posterior)normalization termThe 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 setBayesian estimation•Bayesian estimation•Goal is to choose the label (skin or ~skin) that maximizes the posterior–this is called Maximum A Posteriori (MAP) estimationlikelihood posterior (unnormalized)0.5•Suppose the prior is uniform: P(skin) = P(~skin) = = minimize probability of misclassification–in this case ,–maximizing the posterior is equivalent to maximizing the likelihood» if and only if –this is called Maximum Likelihood (ML) estimationSkin detection results•This same procedure applies in more general circumstances•More than two classes•More than one dimensionGeneral classificationH. Schneiderman and T.KanadeExample: face detection•Here, X is an image region–dimension = # pixels –each face can be thoughtof as a point in a highdimensional spaceH. 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.pdfLinear subspaces•Classification can be expensive•Must either search (e.g., nearest neighbors) or store large PDF’sSuppose the data points are arranged as above•Idea—fit a line, classifier measures distance to lineconvert x into v1, v2 coordinatesWhat does the v2 coordinate measure?What does the v1 coordinate measure?- distance to line- use it for classification—near 0 for orange pts- position