Real-time thresholding with Euler numbers

The problem of finding an automatic thresholding technique is well known in applications involving image differencing like visual-based surveillance systems, autonomous vehicle driving, etc. Among the algorithms proposed in the past years, the thresholding technique based on the stable Euler number method is considered one of the most promising in terms of visual results. Unfortunately its high computational complexity made it an impossible choice for real-time applications. The implementation here proposed, called fast Euler numbers, overcomes the problem since it calculates all the Euler numbers in just one single raster scan of the image. That is, it runs in O(hw), where h and w are the image's height and width, respectively. A technique for determining the optimal threshold, called zero crossing, is also proposed.