Experiments in Binning Image Statistics

Various vision tasks require the computation of image statistics and aggregating them into histograms. These histograms are usually compared using the χ distance which gives a rough idea of the similarity of the two image patches. For example, in [2] a histogram of key-points is collected on a rectangular grid for the category recognition task. Other researchers, [3], have used local image statistics around a point to find corresponding points. In general, image statistics produce a vast array of number of varying magnitudes. Some form of aggregation is required to ensure robustness. Although k-means clustering is a commonly used device in this setting, the Euclidean distance on which it is based is not always the appropriate measure of distance. A pre-processing step where the statistics are aggregated into histograms is quite helpful. In this study, we study the issues surrounding binning these statistics by feature location and feature magnitude. Where, a feature can be interpreted as the response of an arbitrary filter or key-point detection algorithm. We claim that the optimal binning strategy depends on the particular feature being computed. Towards this end, we try various strategies on a fixed set of features and evaluate their performance on a specific task. The task that we consider is object categorization using the CalTech 101 dataset [1]. The overall approach is to use a nearest neighbour classifier using the χ distance between the feature histograms of the test image and the training images. In the subsequent sections we describe the features that we collected and the performance of various binning strategies that we evaluated on these features.