1Object recognitionMethods for classification andimage representationCredits• Slides by Pete Barnum• Slides by Fei-Fei Li• Paul Viola, Michael Jones, Robust Real-time Object Detection, IJCV 04• Navneet Dalal and Bill Triggs, Histograms of Oriented Gradients forHuman Detection, CVPR05• Kristen Grauman, Gregory Shakhnarovich, and Trevor Darrell, VirtualVisual Hulls: Example-Based 3D Shape Inference from Silhouettes• S. Lazebnik, C. Schmid, and J. Ponce. Beyond Bags of Features:Spatial Pyramid Matching for Recognizing Natural Scene Categories.• Yoav Freund Robert E. Schapire, A Short Introduction to BoostingObject recognition• What is it?– Instance– Category– Something with a tail• Where is it?– Localization– Segmentation• How many are there?(CC) By Yannic Meyer(CC) By Peter Hellberg(CC) By Paul Godden2Object recognition• What is it?– Instance– Category– Something with a tail• Where is it?– Localization– Segmentation• How many are there?(CC) By DunechaserFace detectionfeatures?classify+1 face-1 not face• We slide a window over the image• Extract features for each window• Classify each window into face/non-facexF(x) y? ?What is a face?• Eyes are dark (eyebrows+shadows)• Cheeks and forehead are bright.• Nose is brightPaul Viola, Michael Jones, Robust Real-time Object Detection, IJCV 043Basic feature extraction• Information type:– intensity• Sum over:– gray and white rectangles• Output: gray-white• Separate output value for– Each type– Each scale– Each position in the window• FEX(im)=x=[x1,x2,…….,xn]Paul Viola, Michael Jones, Robust Real-time Object Detection, IJCV 04x120x357x629x834Face detectionfeatures?classify+1 face-1 not face• We slide a window over the image• Extract features for each window• Classify each window into face/non-facexF(x) yClassification• Examples are points in Rn• Positives are separated fromnegatives by the hyperplane w• y=sign(wTx-b)++++++++--------w4Classification• x ∈ Rn - data points• P(x) - distribution of the data• y(x) - true value of y for each x• F - decision function:y=F(x, θ)• θ - parameters of F,e.g. θ=(w,b)• We want F that makes fewmistakes++++++++--------wLoss function• Our decision may have severeimplications• L(y(x),F(x, θ)) - loss functionHow much we pay for predictingF(x,θ), when the true value is y(x)• Classification error:• Hinge loss++++++++--------wPOSSIBLE CANCERABSOLUTELY NORISK OF CANCERLearning• Total loss shows how good a function (F, θ) is:• Learning is to find a function to minimize theloss:• How can we see all possible x?5Datasets• Dataset is a finite sample {xi} from P(x)• Dataset has labels {(xi,yi)}• Datasets today are big to ensure thesampling is fair10363204340Pascal VOC3060825630608Caltech 256414687???176975LabelMe#instances#classes#imagesOverfitting• A simple dataset.• Two models++++++++--------++++++++--------++LinearNon-linearOverfitting++++++++--------+++++----------++++++++++++--------+++++----------++++• Let’s get more data.• Simple model has better generalization.6Overfitting• As complexityincreases, the modeloverfits the data• Training lossdecreases• Real loss increases• We need to penalizemodel complexity= to regularizeModel complexityTraining lossReal lossLossOverfitting• Split the dataset– Training set– Validation set– Test set• Use training set tooptimize modelparameters• Use validation test tochoose the best model• Use test set only tomeasure the expectedlossModel complexityTraining set lossTest set lossLossValidation set lossStopping pointClassification methods• K Nearest Neighbors• Decision Trees• Linear SVMs• Kernel SVMs• Boosted classifiers7K Nearest Neighbors• Memorize all trainingdata• Find K closest pointsto the query• The neighbors votefor the label:Vote(+)=2Vote(–)=1++++++++-------++o------K-Nearest NeighborsKristen Grauman, Gregory Shakhnarovich, and Trevor Darrell,Virtual Visual Hulls: Example-Based 3D Shape Inference from SilhouettesNearest Neighbors (silhouettes)K-Nearest NeighborsKristen Grauman, Gregory Shakhnarovich, and Trevor Darrell,Virtual Visual Hulls: Example-Based 3D Shape Inference from SilhouettesSilhouettes from other views3D Visual hull8Decision treeoX1>2X2>1V(+)=8V(-)=2V(+)=2V(-)=8V(+)=0V(-)=4YesNoYesNo+V(+)=8V(-)=4V(-)=8Decision Tree Training• Partition data into pure chunks• Find a good rule• Split the training data– Build left tree– Build right tree• Count the examples in the leavesto get the votes: V(+), V(-)• Stop when– Purity is high– Data size is small– At fixed level++++++++--------+----V(-)=57%V(-)=80% V(+)=64%V(+)=80%V(-)=100%Decision trees• Stump:– 1 root– 2 leaves• If xi > athen positiveelse negative• Very simple• “Weak classifier”Paul Viola, Michael Jones, Robust Real-time Object Detection, IJCV 04x120x357x629x8349Support vector machines• Simple decision• Good classification• Good generalization++++++++--------+----wmarginSupport vector machines++++++++--------+----wSupport vectors:How do I solve the problem?• It’s a convex optimization problem– Can solve in Matlab (don’t)• Download from the web– SMO: Sequential Minimal Optimization– SVM-Light http://svmlight.joachims.org/– LibSVM http://www.csie.ntu.edu.tw/~cjlin/libsvm/– LibLinear http://www.csie.ntu.edu.tw/~cjlin/liblinear/– SVM-Perf http://svmlight.joachims.org/– Pegasos http://ttic.uchicago.edu/~shai/10Linear SVM for pedestriandetectionSlides by Pete BarnumNavneet Dalal and Bill Triggs, Histograms of Oriented Gradients for Human Detection, CVPR05uncenteredcenteredcubic-correcteddiagonalSobelSlides by Pete BarnumNavneet Dalal and Bill Triggs, Histograms of Oriented Gradients for Human Detection, CVPR0511• Histogram of gradientorientations-OrientationSlides by Pete BarnumNavneet Dalal and Bill Triggs, Histograms of Oriented Gradients for Human Detection, CVPR05X=15x7 cells8 orientationsSlides by Pete BarnumNavneet Dalal and Bill Triggs, Histograms of Oriented Gradients for Human Detection, CVPR05pedestrianSlides by Pete BarnumNavneet Dalal and Bill Triggs, Histograms of Oriented Gradients for Human Detection, CVPR0512Kernel SVMDecision function is a linear combination of support vectors:Prediction is a dot product:Kernel is a function that computes the dot product ofdata points in some unknown space:We can compute the decision without knowing the space:Useful kernels•