Learning a Fast Emulator of a Binary Decision Process Center for Machine Perception Czech Technical University, Prague ACCV 2007, Tokyo, Japan Jan Šochman and Jiří Matas TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

2 Importance of Classification Speed Time-to-decision vs. precision trade-off is inherent in many detection, recognition and matching problems in computer vision Often the trade-off is not explicitly stated in the problem formulation, but decision time clearly influences impact of a method Example: face detection Viola-Jones (2001) – real-time performance citations Schneiderman-Kanade (1998) - smaller error rates, but 1000x slower -250 citations Time is implicitly considered as an important characteristic of detection and recognition algorithms

3 Fast Emulation of A Decision Process The Idea Given a black box algorithm A performing some useful binary decision task Train a sequential classifier S to (approximately) emulate detection performance of algorithm A while minimizing time-to-decision Allow user to control quality of the approximation Contribution A general framework for speeding up existing algorithms by a sequential classifier learned by the WaldBoost algorithm [1] Demonstrated on two interest point detectors Advantages Instead of spending man-months on code optimization, choose relevant feature class and train sequential classifier S Your (slow) Matlab code can be speeded up this way! [1] J. Šochman and J. Matas. Waldboost – Learning For Time Constrained Sequential Detection. CVPR 2005

4 Black-box Generated Training Set Emulator approximates behavior of the black-box algorithm The black-box algorithm can potentially provide almost unlimited number of training samples Efficiency of training is important Suitable for incremental or online methods

5 WaldBoost Optimization Task Basic notions: Sequential strategy S is characterized by: Problem formulation:

6 WaldBoost Sequential Classifier Training Combines AdaBoost training (provides measurements) with Wald’s sequential decision making theory (for sequential decisions) Sequential WaldBoost classifier Set of weak classifiers (features) and thresholds are found during training

7 Emulation of Similarity-Invariant Regions Motivation Hessian-Laplace is close to state of the art Kadir’s detector very slow (100x slower than Difference of Gaussians) Standard testing protocol exists Executables of both methods available at robots.ox.ac.uk Both detectors are scale-invariant which is easily implemented via a scanning window + a sequential test Implementation Choice of : various filters computable with integral images - difference of rectangular regions, variance in a window Positive samples: Patches twice the size of original interest point scale [1] K. Mikolajczyk, C. Schmid. Scale and Affine Invariant Interest Point Detectors. ICCV [2] T. Kadir, M. Brady. Saliency, Scale and Image Description. IJCV The approach tested on Hessian-Laplace [1] and Kadir-Brady salient [2] interest point detectors

8 Results: Hessian-Laplace – boat sequence Repeatability comparable (left graph) Matching score almost identical (middle graph) Higher number of correspondences and correct matches in WaldBoost. Speed comparison (850x680 image) Original1.3 sec WaldBoost1.3 sec

9 Results: Kadir-Brady – east-south sequence Repeatability slightly higher (left graph) Matching score slightly higher (middle graph) Higher number of correspondences and correct matches in WaldBoost. Speed comparison (850x680 image) Original1 min 44 sec WaldBoost1.4 sec

10 Approximation Quality – Hesian-Laplace Yellow circles Yellow circles: repeated detections (85% coverage) Red circles Red circles: original detections not found by the WaldBoost detector

11 Approximation Quality – Kadir-Brady Yellow circles Yellow circles: repeated detections (96% coverage) Red circles Red circles: original detections not found by the WaldBoost detector

12 Conclusions and Future Work A general framework for speeding up existing binary decision algorithms has been presented To optimize the emulator’s time-to-decision a WaldBoost sequential classifier was trained The approach was demonstrated on (but is not limited to) two interest point detectors emulation Future work Precise localization of the detections by interpolation on the grid Using real value output of the black-box algorithm (“sequential regression”) To emulate or to be repeatable?

13 Conclusions and Future Work A general framework for speeding up existing binary decision algorithms has been presented To optimize the emulator’s time-to-decision a WaldBoost sequential classifier was trained The approach was demonstrated (but is not limited to) on two interest point detectors Future work Precise localization of the detections by interpolation on the grid Using real value output of the black-box algorithm (“sequential regression”) To emulate or to be repeatable? Thank you for your attention