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The Automatic Design of Feature Spaces for Local Image Descriptors using an Ensemble of Non-linear Feature Extractors. Gustavo Carneiro. Set of Matching Problems. Wide baseline Matching. Visual Class Recognition. Visual Object Recognition. Set of Matching Problems.

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## Gustavo Carneiro

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**The Automatic Design of Feature Spaces for Local Image**Descriptors using anEnsemble of Non-linear Feature Extractors Gustavo Carneiro**Set of Matching Problems**Wide baseline Matching Visual Class Recognition Visual Object Recognition**Set of Matching Problems**1- Design a feature space that facilitates certain matching problems SIFT [Lowe,ICCV09] Shape Context [Belongie et al. PAMI02] HOG [Dalal & Triggs,CVPR05]**Set of Matching Problems**2- Given a matching problem, and a set of feature spaces, combine them in order to minimize probability of error (mismatches) [Varma & Ray, CVPR07] SIFT Target Matching Problem Shape Context HOG**Set of Matching Problems**3- Given a matching problem, find the feature space and respective parameters θ that minimizes probability of error (mismatches) [Hua et al.ICCV07] Target Matching Problem Feature Transform 2 (θ*) Feature Transform 1 (θ) Feature Transform 2 (θ) Feature Transform 1 (θ*)**Set of Matching Problems**4- Given future unknown matching problems, find the feature space that minimizes probability of error (mismatches) Feature Transform Matching Problem 3 Feature Transform Matching Problem 1 Target Matching Problem 1 Target Matching Problem 2 Feature Transform Matching Problem 4 Feature Transform Matching Problem 2 Feature Transform Matching Problem 5**The Universal Feature Transform**• Solve random and simple matching problems • The more matching problems solved, the easier it will be to solve new problems • Restriction: problems should be in similar feature ranges and similar class statistics**(Linear) Distance Metric Learning[Chopra et**al.CVPR05,Goldberger et al.NIPS04, Weinberger & Saul JMLR09] • Image patches: • Linear transform: • Distance in T space:**(Non-Linear) Distance Metric Learning [Sugiyama JMLR07]**• Rewrite S(b) and S(w): • By taking the following transformation: • Generalized Eigenvalue Problem: Dot product replaced by non-linear kernel function • Feature Transform**Linear vs Non-linear DML**LINEAR Points not belonging to any class collapse at the origin NON-LINEAR Points from the same class collapse and are far from each other**Intuition**• Train several feature transforms • Random matching problems • Aggregate distances[Breiman 01]: • Threshold-based classifier**ROC**Aggregated distances Intuition Unkown target problem T Small dist. Large dist. Random training problem 1**ROC**Aggregated distances Intuition Unkown target problem T Small dist. Largedist. Random training problem 2**Toy Example**• Combing 100 feature spaces... NLMSL trained UFT Original Error decreases with number of feature spaces No matter the error for each space**Experiments**• Dataset of for training [Winder & Brown,CVPR07]: • Backprojecting 3D points to 2D images from scene reconstructions • Variations in scene location, brightness and partial occlusion • Similar pre-processing of [Winder & Brown,CVPR07] • Train: all patch classes from Trevi & Yosemite dataset • Test: 50K matching and 50K non-matching pairs from Notre Dame dataset**Experiments**• Using cross validation • 50 training classes for training each feature space • 50 training feature spaces Error decreases with number of feature spaces UFT (2.28%) SIFT (6.3%) @95% TP No matter the error in each space**Experiments**• Matching database [Mikolajczyk & Schmid,PAMI’05]**Conclusion**• Competitive performance • Simple ensemble classifier (can be efficiently implemented) • Adapt to new classification problems (no re-training)**Linear vs Non-linear DML**10 runs, 100 points per class Classifier: threshold matching LINEAR NON-LINEAR Non-linear: low bias, high variance Linear: High bias, low variance**Combining Feature Spaces**• Breiman’s idea about ensemble classifiers [Breiman 01]: • combine low-bias, high-variance (unstable) classifiers to produce low-bias, low-variance classifiers. • Distance

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