Fuzzy Ideas Explain Fechner Law and Help Detect Relation Between Objects in Video

How to find relation between objects in a video? If two objects are closely related - e.g., a computer and it mouse - then they almost always appear together, and thus, their numbers of occurrences are close. However, simply computing the differences between numbers of occurrences is not a good idea: objects with 100 and 110 occurrences are most probably related, but objects with 1 and 5 occurrences probably not, although 5 - 1 is smaller than 110 - 100. A natural idea is, instead, to compute the difference between re-scaled numbers of occurrences, for an appropriate nonlinear re-scaling. In this paper, we show that fuzzy ideas lead to the selection of logarithmic re-scaling, which indeed works very well in video analysis - and which also explains Fechner Law in psychology, that our perception of difference between two stimuli is determined by the difference between the logarithms of their intensities.