Segmentation of magnetic resonance images into n(0, sigma) stationary regions

Ian R. Greenshields; A. Zoe Leibowitz; Francis DiMario M.D.; Gale Ramsby M.D.

doi:10.1117/12.154566

14 September 1993 Segmentation of magnetic resonance images into n(0, sigma) stationary regions

Ian R. Greenshields, A. Zoe Leibowitz, Francis DiMario M.D., Gale Ramsby M.D.

Proceedings Volume 1898, Medical Imaging 1993: Image Processing; (1993) https://doi.org/10.1117/12.154566
Event: Medical Imaging 1993, 1993, Newport Beach, CA, United States

Abstract

Recall that a random field X(t1 ,t2) = X(t) over R2 is called hornogenous when its mean value (X(t)) = in (1) is a constant, while its core1ation function (X(t1),X(t2)) = B(t1,t2) depends only on the vector 'r t1 — t2, whence B(t1,t2) = B(ti — t2) (2) Absolute precision would require that a random field satisfying (1) and (2) be referred to as a widesense homogeneous random field, since it is not difficult to define strictly homogeneous random fields, which are coiiceptually related to the usual strictly stationary random process[1]. In the following, the term homogeneous field should be taken to mean wide-sense homogeneous field. Sometimes, imaging literature will interchange the terms stationary and homogeneous[2]. This is unfortunate but unavoidable in an imaging context.

Citation Download Citation

Ian R. Greenshields, A. Zoe Leibowitz, Francis DiMario M.D., and Gale Ramsby M.D. "Segmentation of magnetic resonance images into n(0, sigma) stationary regions", Proc. SPIE 1898, Medical Imaging 1993: Image Processing, (14 September 1993); https://doi.org/10.1117/12.154566

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