Weighting of Words

In the most simple bag of words approach, histograms are created for each image, with each histogram bin having equal wieght. Inverse document frequency (IDF) weighting \cite{IDF} is a technique drawn from bag of word implementations in the field of text retieval. IDF assumes that words that appear less frequently are more discriminative. Tirilly, et al. ("A review of weighting schemes for bag of visual words image retrieval") propose a modified version of IDF, called Mean-term-frequency*IDF^2 which makes the additional assumption that words which on average appear numerous times in images they are present in are more discriminative than words that tend to appear less frequently when present in an image.

We implemented this weighting technique and it increased our probability of detection while decreasing our probability of false alarm.

Additionally, we explored soft-weighting. In the basic bag of words approach, word assignments are made on a binary basis: descriptors are assigned to the closest word center, even if they may be located a similar distance away from other words. In "Towards optimal bag-of-features for object categorization and semantic video retrieval," Jiang et al propose a soft-assignment scheme in which descriptors are assigned to multiple words. Columbia University implemented a soft-assignment scheme in their 2008 submission with very successful results.

We implemented the above equation in our system and the soft assignment improved both the probability of detection and the probability of false alarm. And when combined with TF-IDF^2, the results improved even more. Unfortuanately, when implemented with bootstrapping, there seemed to be a bug which we could not resolve in time for our final submission.