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Computation time is an important performance characteristic of computer vision algorithms. This paper shows how existing (slow) binary-valued decision algorithms can be approximated by a trained WaldBoost classifier, which minimises the decision time while guaranteeing predefined approximation precision. The core idea is to take an existing algorithm as a black box performing some useful binary decision task and to train the WaldBoost classifier as its emulator. Two interest point detectors, Hessian-Laplace and Kadir-Brady saliency detector, are emulated to demonstrate the approach. The experiments show similar repeatability and matching score of the original and emulated algorithms while achieving a 70-fold speed-up for Kadir-Brady detector.