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Computation time is an important performance characteristic of computer vision algorithms. The paper shows how existing (slow) binary decision algorithms can be approximated by a (fast) trained WaldBoost classifier.WaldBoost learning minimises the decision time of the classifier while guaranteeing predefined precision. We show that the WaldBoost algorithm together with bootstrapping is able to efficiently handle an effectively unlimited number of training examples provided by the implementation of the approximated algorithm.Two interest point detectors, the Hessian-Laplace and the Kadir-Brady saliency detectors, are emulated to demonstrate the approach. Experiments show that while the repeatability and matching scores are similar for the original and emulated algorithms, a 9-fold speed-up for the Hessian-Laplace detector and a 142-fold speed-up for the Kadir-Brady detector is achieved. For the Hessian-Laplace detector, the achieved speed is similar to SURF, a popular and very fast handcrafted modification of Hessian-Laplace; the WaldBoost emulator approximates the output of the Hessian-Laplace detector more precisely.