The Geometry of the Generalized Gamma Manifold and an Application to Medical Imaging

Abstract

The Fisher information metric provides a smooth family of probability measures with a Riemannian manifold structure, which is an object in information geometry. The information geometry of the gamma manifold associated with the family of gamma distributions has been well studied. However, only a few results are known for the generalized gamma family that adds an extra shape parameter. The present article gives some new results about the generalized gamma manifold. This paper also introduces an application in medical imaging that is the classification of Alzheimer's disease population. In the medical field, over the past two decades, a growing number of quantitative image analysis techniques have been developed, including histogram analysis, which is widely used to quantify the diffuse pathological changes of some neurological diseases. This method presents several drawbacks. Indeed, all the information included in the histogram is not used and the histogram is an overly simplistic estimate of a probability distribution. Thus, in this study, we present how using information geometry and the generalized gamma manifold improved the performance of the classification of Alzheimer's disease population.

Image Analysis Using Human Body Geometry and Size Proportion Science for Action Classification

“…In this case, D TLR evaluates to less than the armLength resulting in it being classified out of the SHSW class. These actions don't even fall into the SHTW class as rule (5); the class does not get satisfied as the example image shown in Figure 7a. These are the cases where TL(θ) are greater than 125, but D TLR is less than armLength or TL(θ) ≤ 125 but armLength > D TLR > ( 2 3 ) * armLength.…”

“…The "BHTW" actions are misclassified as "Standing" as they are not able to fulfill the two halves of (18) i.e., (i) (TL(θ) > 97. 5 AND TL(θ) ≤ 125) AND (TR(theta) < 82.5 AND TR(theta) ≥ 55)) and (ii) (D TLR > f orearm AND D TLR ≤ 1.5 * armLength)). Figure 12b is the example of the "BHTW" action images where left and right hands touch each other.…”

“…The classification rule for the right-hand wave is given as: TL(θ) > 97. 5 The proposed rule for Classifying both hands side wave is a combination of the left and right-hand side wave along with taking D TLR into account. As defined by [44], the size of the Wingspan of a human is the same as his height.…”

“…Much of the work carried out in the field of action recognition includes silhouette-based features through depth images or vision-based generic features for 2D images with inherent limitations. Geometric features can be a good source of information used to solve the classification problem [5] and domain-specific features may perform better than the generic nature of global or local features [6].…”

Fisher-Rao geometry of Dirichlet distributions

“…The family of gamma distributions has been studied by Lauritzen in [19], and more recently by Arwini and Dodson in [6], who also focus on the log-normal, log-gamma, and families of bivariate distributions. Power inverse Gaussian distributions [35], location-scale models and in particular the von Mises distribution [28], and the generalized gamma distributions [27] have also received attention.…”