ciency issues related to probability density function comparisonPatrick

The CANDID project (Comparison Algorithm for Navigating Digital Image Databases) employs probability density functions (PDFs) of localized feature information to represent the content of an image for search and retrieval purposes. A similarity measure between PDFs is used to identify database images that are similar to a user-provided query image. Unfortunately, signature comparison involving PDFs is a very time-consuming operation. In this paper, we look into some eeciency considerations when working with PDFs. Since PDFs can take on many forms, we look into tradeoos between accurate representation and eeciency of manipulation for several data sets. In particular, we typically represent each PDF as a Gaussian mixture (e.g. as a weighted sum of Gaussian kernels) in the feature space. We nd that by constraining all Gaussian kernels to have principal axes that are aligned to the natural axes of the feature space, computations involving these PDFs are simpliied. We can also constrain the Gaussian kernels to be hyperspherical rather than hyperellipsoidal, simplifying computations even further, and yielding an order of magnitude speedup in signature comparison. This paper illustrates the tradeoos encountered when using these constraints.