Address 15: Eigenfaces .


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Declarations. Last venture page up, athttp://www.cs.cornell.edu/courses/cs6670/2009fa/ventures/p4/One individual from every group ought to present a proposition (to CMS) by tomorrow at 11:59pmProject 3: Eigenfaces. Skin identification results. This same method applies in more broad circumstancesMore than two classesMore than one measurement.
Transcripts
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CS6670: Computer Vision Noah Snavely Lecture 15: Eigenfaces

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Announcements Final venture page up, at http://www.cs.cornell.edu/courses/cs6670/2009fa/ventures/p4/One individual from each group ought to present a proposition (to CMS) by tomorrow at 11:59pm Project 3: Eigenfaces

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Skin identification comes about

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H. Schneiderman and T.Kanade General characterization This same method applies in more broad conditions More than two classes More than one measurement Example: confront identification Here, X is a picture district measurement = # pixels each face can be considered 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/client/hws/www/CVPR00.pdf

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change over x into v 1 , v 2 facilitates What does the v 2 arrange measure? separation to line utilize it for grouping—almost 0 for orange pts What does the v 1 facilitate measure? position along line utilize it to indicate which orange point it is Linear subspaces Classification can be costly Must either seek (e.g., closest neighbors) or store huge PDF\'s Suppose the information focuses are organized as above Idea—fit a line, classifier measures separation to line

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Dimensionality decrease How to discover v 1 and v 2 ? Dimensionality decrease We can speak to the orange focuses with just their v 1 organizes since v 2 directions are all basically 0 This makes it much less expensive to store and think about focuses A greater arrangement for higher dimensional issues

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Linear subspaces Consider the variety along heading v among the greater part of the orange focuses: What unit vector v limits var ? What unit vector v expands var ? 2 Solution: v 1 is eigenvector of A with biggest eigenvalue v 2 is eigenvector of A with littlest eigenvalue

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Principal part examination Suppose every information point is N-dimensional Same methodology applies: The eigenvectors of A characterize another organize framework eigenvector with biggest eigenvalue catches the most variety among preparing vectors x eigenvector with littlest eigenvalue has slightest variety We can pack the information by just utilizing the main few eigenvectors compares to picking a "direct subspace" speak to focuses on a line, plane, or "hyper-plane" these eigenvectors are known as the foremost segments

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= + The space of appearances A picture is a point in a high dimensional space A N x M force picture is a point in R NM We can characterize vectors in this space as we did in the 2D case

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Dimensionality diminishment The arrangement of countenances is a "subspace" of the arrangement of pictures Suppose it is K dimensional We can locate the best subspace utilizing PCA This resembles fitting a "hyper-plane" to the arrangement of confronts spread over by vectors v 1 , v 2 , ..., v K any face

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Eigenfaces PCA separates the eigenvectors of A Gives an arrangement of vectors v 1 , v 2 , v 3 , ... Every one of these vectors is a course in face space what do these resemble?

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Projecting onto the eigenfaces The eigenfaces v 1 , ..., v K traverse the space of countenances A face is changed over to eigenface organizes by

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Detection and acknowledgment with eigenfaces Algorithm Process the picture database (set of pictures with names) Run PCA—register eigenfaces Calculate the K coefficients for each picture Given another picture (to be perceived) x , figure K coefficients Detect if x is a face If it is a face, who is it? Find nearest marked face in database closest neighbor in K-dimensional space

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i = K NM Choosing the measurement K what number eigenfaces to utilize? Take a gander at the rot of the eigenvalues the eigenvalue reveals to you the measure of change "in the course" of that eigenface overlook eigenfaces with low fluctuation eigenvalues

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Issues: measurements What\'s the most ideal approach to think about pictures? need to characterize suitable components relies on upon objective of acknowledgment errand arrangement/identification basic elements function admirably (Viola/Jones, and so on.) correct coordinating complex elements function admirably (SIFT, MOPS, and so forth.)

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Metrics Lots more element sorts that we haven\'t specified minutes, measurements: Earth mover\'s separation, ... edges, bends measurements: Hausdorff, shape setting, ... 3D: surfaces, turn pictures measurements: chamfer (ICP) ...

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If you have a preparation set of pictures: AdaBoost, and so on. Issues: highlight choice If the sum total of what you have is one picture: non-most extreme concealment, and so forth

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Issues: information demonstrating Generative strategies show the "shape" of each class histograms, PCA, blends of Gaussians graphical models (HMM\'s, conviction systems, and so on.) ... Discriminative techniques display limits between classes perceptrons, neural systems bolster vector machines (SVM\'s)

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Generative versus Discriminative Generative Approach show singular classes, priors Discriminative Approach display back straightforwardly from Chris Bishop

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Issues: dimensionality What if your space isn\'t level ? PCA may not help Nonlinear techniques LLE, MDS, and so forth

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Issues: speed Case contemplate: Viola Jones confront locator Exploits two key methodologies: straightforward, super-productive components pruning (fell classifiers) Next few slides adjusted Grauman & Liebe\'s instructional exercise http://www.vision.ee.ethz.ch/~bleibe/educating/instructional exercise aaai08/Also observe Paul Viola\'s discussion (video) http://www.cs.washington.edu/training/courses/577/04sp/contents.html#DM

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Feature extraction "Rectangular" channels Feature yield is contrast between neighboring locales Value at (x,y) is entirety of pixels above and to one side of (x,y) Efficiently calculable with vital picture: any aggregate can be figured in consistent time Avoid scaling pictures  scale highlights specifically for same cost Integral picture Viola & Jones, CVPR 2001 22 K. Grauman, B. Leibe K. Grauman, B. Leibe

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Large library of channels Considering all conceivable channel parameters: position, scale, and sort: 180,000+ conceivable elements related with every 24 x 24 window Use AdaBoost both to choose the instructive components and to frame the classifier Viola & Jones, CVPR 2001 K. Grauman, B. Leibe

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AdaBoost for feature+classifier choice Want to choose the single rectangle highlight and edge that best isolates positive (faces) and negative (non-confronts) preparing cases, as far as weighted mistake. Coming about frail classifier: For next round, reweight the cases as indicated by mistakes, pick another channel/edge combo. … Outputs of a conceivable rectangle highlight on countenances and non-faces. Viola & Jones, CVPR 2001 K. Grauman, B. Leibe

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AdaBoost: Intuition Consider a 2-d include space with positive and negative cases. Each powerless classifier parts the preparation cases with no less than half exactness. Illustrations misclassified by a past powerless learner are given more accentuation at future rounds. Figure adjusted from Freund and Schapire 25 K. Grauman, B. Leibe K. Grauman, B. Leibe

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AdaBoost: Intuition 26 K. Grauman, B. Leibe K. Grauman, B. Leibe

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AdaBoost: Intuition Final classifier is blend of the powerless classifiers 27 K. Grauman, B. Leibe K. Grauman, B. Leibe

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AdaBoost Algorithm Start with uniform weights on preparing cases {x 1 ,… x n } For T rounds Evaluate weighted blunder for each component, pick best. Re-weight the cases: Incorrectly grouped - > more weight Correctly arranged - > less weight Final classifier is mix of the feeble ones, weighted by mistake they had. Freund & Schapire 1995 K. Grauman, B. Leibe

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Cascading classifiers for identification Fleuret & Geman, IJCV 2001 Rowley et al., PAMI 1998 Viola & Jones, CVPR 2001 For productivity, apply less exact however quicker classifiers first to instantly dispose of windows that plainly seem, by all accounts, to be negative; e.g., Filter for promising districts with an underlying economical classifier Build a chain of classifiers, picking modest ones with low false negative rates ahead of schedule in the chain 29 Figure from Viola & Jones CVPR 2001 K. Grauman, B. Leibe K. Grauman, B. Leibe

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Viola-Jones Face Detector: Summary Train course of classifiers with AdaBoost Apply to each subwindow Faces New picture Selected elements, edges, and weights Non-confronts Train with 5K positives, 350M negatives Real-time locator utilizing 38 layer course 6061 elements in conclusive layer [Implementation accessible in OpenCV: http://www.intel.com/innovation/registering/opencv/] 30 K. Grauman, B. Leibe

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Viola-Jones Face Detector: Results First two components chose 31 K. Grauman, B. Leibe K. Grauman, B. Leibe

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Viola-Jones Face Detector: Results K. Grauman, B. Leibe

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Viola-Jones Face Detector: Results K. Grauman, B. Leibe

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Viola-Jones Face Detector: Results K. Grauman, B. Leibe

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Detecting profile faces? Recognizing profile faces requires preparing separate indicator with profile illustrations. K. Grauman, B. Leibe

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Viola-Jones Face Detector: Results Paul Viola, ICCV instructional exercise K. Grauman, B. Leibe

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