Learning detectors quickly with stationary statistics

Computer vision is increasingly becoming interested in the rapid estimation of object detectors. The canonical strategy of using Hard Negative Mining to train a Support Vector Machine is slow, since the large negative set must be traversed at least once per detector. Recent work has demonstrated that, with an assumption of signal stationarity, Linear Discriminant Analysis is able to learn comparable detectors without ever revisiting the negative set. Even with this insight, the time to learn a detector can still be on the order of minutes. Correlation filters, on the other hand, can produce a detector in under a second. However, this involves the unnatural assumption that the statistics are periodic, and requires the negative set to be re-sampled per detector size. These two methods differ chie y in the structure which they impose on the co- variance matrix of all examples. This paper is a comparative study which develops techniques (i) to assume periodic statistics without needing to revisit the negative set and (ii) to accelerate the estimation of detectors with aperiodic statistics. It is experimentally verified that periodicity is detrimental.