Information measures for object recognition accommodating signature variability

Abstract

This paper presents measures characterizing the information content of remote observations of ground scenes imaged via optical and infrared sensors. Object recognition is posed in the context of deformable templates; the special Euclidean group is used to accommodate geometric variation of object pose. Principal component analysis of object signatures is used to represent and efficiently accommodate variation in object signature due to changes in the thermal state of the object surface. Mutual information measures, which are independent of the recognition system, are calculated quantifying both the information gain due to remote observations of the scene and the information loss due to signature variability. Signature model mismatch is quantitatively examined using the Kullback-Leibler divergence. Expressions are derived quadratically approximating the posterior conditional entropy on the orthogonal group for high signal-to-noise ratio. It is demonstrated that quadratic modules accurately characterize the posterior entropy for broad ranges of signal-to-noise ratio. Information gain in multiple-sensor scenarios is quantified, and it is demonstrated that the cost of signature uncertainty for the Comanche series of FLIR images collected by the U.S. Army Night Vision Electronic Sensors Directorate is approximately 0.8 bits with an associated near doubling of mean-squared error uncertainty in pose.

On data-driven histogram-based estimation for mutual information

“…with ξ [1−q] (A) denoting the set operator that returns the collection of projected elements of A in the range of coordinate dimensions [1 − q] 3 . Then, the following collections of events are associated to the partition rule π n (·):…”

“…3 By construction any set A ∈ πn(z n 1 ) can be expressed by A = A 1 × A 2 , with A 1 ∈ R q and A 2 ∈ R p , and consequently ξ [1−q] …”

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