Constant-time Extraction of Statistical Moments for Object Detection Procedures

We propose a computational technique, backed with special integral images, allowing for constant-time extraction of statistical moments within detection procedures. The moments under study are formulated in their normalized central version. The set of proposed integral images needs to be prepared prior to the detection procedure. Its size grows quadratically with the imposed maximum order of moments, but the time invested in the preparation is amortized sufficiently well at the scanning stage. We give exact counts of the number of operations involved in extraction according to the proposed algorithm. The main idea is coupled with an auxiliary technique for detection window partitioning. In the experimental part, we demonstrate two examples of detection tasks. Detectors have been trained on the proposed features by the RealBoost learning algorithm and achieve both: satisfactory time performance and accuracy.