A technique is proposed for choosing the thresholds for a number of object detection tasks, based on a prototype selection technique. The chosen prototype subset has to be correctly classified. The positive and negative objects are introduced in order to provide the optimization via empirical risk minimization. A Boolean function and its derivatives are obtained for each object. A special technique, based on the fastest gradient descent, is proposed for the sum of Boolean functions maximization. The method is applied to the detection task of house edges, using its images in aerial photos. It is shown that proposed method can be expanded to solving of a wide range of tasks, connected to the function optimization, while the function is given in vertices of a 2ⁿ single hyper - cube.