The geometry of the generalized gamma manifold and an application to medical imaging

作者: Sana Rebbah , Florence Nicol , Stéphane Puechmorel

DOI: 10.3390/MATH7080674

关键词:

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

参考文章(19)
Hirohiko Shima, Geometry of Hessian Structures International Conference on Geometric Science of Information. pp. 37- 55 ,(2013) , 10.1007/978-3-642-40020-9_4
Mayuresh S. Korgaonkar, Leanne M. Williams, Adam M. Brickman, Edgar Busovaca, Molly E. Zimmerman, Irene B. Meier, Erica Y. Griffith, Stuart M. Grieve, Is the Alzheimer’s disease cortical thickness signature a biological marker for memory? Brain Imaging and Behavior. ,vol. 10, pp. 517- 523 ,(2016) , 10.1007/S11682-015-9413-5
Gavin E. Crooks, The Amoroso Distribution arXiv: Statistics Theory. ,(2010)
Mara Cercignani, Giancarlo Comi, Matilde Inglese, Massimo Filippi, Elisabetta Pagani, Mean diffusivity and fractional anisotropy histograms of patients with multiple sclerosis. American Journal of Neuroradiology. ,vol. 22, pp. 952- 958 ,(2001)
Prashanthi Vemuri, Clifford R Jack, Role of structural MRI in Alzheimer's disease Alzheimer's Research & Therapy. ,vol. 2, pp. 23- 23 ,(2010) , 10.1186/ALZRT47
E. W. Stacy, G. A. Mihram, Parameter Estimation for a Generalized Gamma Distribution Technometrics. ,vol. 7, pp. 349- 358 ,(1965) , 10.1080/00401706.1965.10490268
E. W. Stacy, A Generalization of the Gamma Distribution Annals of Mathematical Statistics. ,vol. 33, pp. 1187- 1192 ,(1962) , 10.1214/AOMS/1177704481
Luigi Amoroso, Ricerche intorno alla curva dei redditi Annali di Matematica Pura ed Applicata. ,vol. 2, pp. 123- 159 ,(1925) , 10.1007/BF02409935
M. Garey, D. Johnson, H. Witsenhausen, The complexity of the generalized Lloyd - Max problem (Corresp.) IEEE Transactions on Information Theory. ,vol. 28, pp. 255- 256 ,(1982) , 10.1109/TIT.1982.1056488
J. J. Duistermaat, On Hessian Riemannian structures Asian Journal of Mathematics. ,vol. 5, pp. 79- 91 ,(2001) , 10.4310/AJM.2001.V5.N1.A6