Stochastic processes with imbedded marked point processes (pmp) and thcir application in queneing

König, Dieter; Rolski, Tomasz; Schmidt, V.; Stoyan, Dietrich

doi:10.1080/02331937808842475

Cited by 32 publications

(30 citation statements)

References 16 publications

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“…1, both the source and the target images are referring to the same cross‐section of the prostate but differ due to in‐plane deformation. After converting the source and target images to the tri‐grayscale‐images, the intensity conservation principle is readily applicable and a relationship can be established between the source and target images. With this established relationship, the mapping relation between the source and target image can subsequently be derived with the help of assumption No.…”

Section: Methodsmentioning

confidence: 99%

Registration of in vivo prostate MRI and pseudo‐whole mount histology using Local Affine Transformations guided by Internal Structures (LATIS)

Kalavagunta

Zhou

Schmechel

et al. 2014

Magnetic Resonance Imaging

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Purpose To present a novel registration approach called LATIS (Local Affine Transformation assisted by Internal Structures) for co-registering post prostatectomy pseudo-whole mount (PWM) pathological sections with in vivo MRI (Magnetic Resonance Imaging) images. Materials and Methods Thirty-five patients with biopsy-proven prostate cancer were imaged at 3T with an endorectal coil. Excised prostate specimens underwent quarter mount step-section pathologic processing, digitization, annotation and assembly into a PWM. Manually annotated macro-structures on both pathology and MRI were used to assist registration using a relaxed local affine transformation approximation. Registration accuracy was assessed by calculation of the dice similarity coefficient (DSC) between transformed and target capsule masks and least square distance between transformed and target landmark positions. Results LATIS registration resulted in a DSC value of 0.991±0.004 and registration accuracy of 1.54±0.64 mm based on identified landmarks common to both datasets. Image registration performed without the use of internal structures led to an 87% increase in landmark based registration error. Derived transformation matrices were used to map regions of pathologically defined disease to MRI. Conclusion LATIS was used to successfully co-register digital pathology with in vivo MRI to facilitate improved correlative studies between pathologically identified features of prostate cancer and multi-parametric MRI.

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Section: Methodsmentioning

confidence: 99%

Registration of in vivo prostate MRI and pseudo‐whole mount histology using Local Affine Transformations guided by Internal Structures (LATIS)

Kalavagunta

Zhou

Schmechel

et al. 2014

Magnetic Resonance Imaging

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“…Conversely, if the cycles x, are considered as marks of the embedded points t,, a PMP can be interpreted as aRMPP with mark space Cr Therefore, the following statements for PMP can be considered as modifications of the corresponding theorems for RXPP. This was pointed out and directly used in the previous representations of PMP's [ I ] , [S], [B], [14].…”

Section: Remarkmentioning

confidence: 89%

“…Simultaneously turned out that PMP include a number of ciasses of ~t o c h~t i c processes important for applications such as regenerative, semi-Piarkov, semi-regenerative processes etc. 191, [14]. Therefore, PMP are of general interest, outside of the areas mentioned above also.…”

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confidence: 97%

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On stochastie processes with an embedded marked point process

Streller

1982

Series Statistics

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Sommary. I n the paper stoehastio processes with an embedded marked point process (PMP) are investigated. The en~hedded points pplit the P M P up to so-called cyoles. A great number of classes of stochastic processes, such as piecewise Markov, regenerative, semiregenerative etc., can be understood as special PMP where the cycles form a i?Iarkov chain. It is shown that there exists a one-to-one correspondence between distributions of stationary sequences of cycles and distributions of stationary PMP, where no independence assumptions about the cycles have to be made. Further, an ergodictheorsm for PMP is stated that shows in which way the distribution of a stationary PNIP arises as a limit clistribution of the associated sequence of cycles. This is the basis farproviding s n elementary proof of the Orey-Jacod-Kesten theorem for se~ni~regenerative processes.K e y words: Random masked paint process, stationary process, ergodic theorem, semi regenerative process, Orey-Jacod-Kesten theorem.

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“…The theory presented below gives a very general method which, in a uniform way, produces known as well as unknown results and explains them in terms of a rate-conservative principle. The fact that SPMP'S give a very general method for obtaining formulae which relate the distributions of a process and some process imbedded in it was noticed by Konig et al (1978) and a general theory of such relations was set up there. Their paper contains many examples of piecewise Markov processes.…”

Section: Introductionmentioning

confidence: 99%

A rate-conservative principle for stationary piecewise Markov processes

Rolski¹

1978

Advances in Applied Probability

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A stationary process yt, t ∈ R1 is considered which is Markov between points of changeover from a stationary point process, and at these points it changes over according to a distribution dependent only on the value of yt just before the change is analysed. An explicit form of a rate-conservative principle is stated, and its relationship with formulae relating the distribution of the process at an instant t and the distribution at a point of changeover is shown. The theory is applied to discrete state processes and to processes which are generalizations of the Takács processes, and is also applied in the theory of G/M/l and G/G/k queues to obtain relations between distributions of a process and some process imbedded in it.

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Stochastic processes with imbedded marked point processes (pmp) and thcir application in queneing

Cited by 32 publications

References 16 publications

Registration of in vivo prostate MRI and pseudo‐whole mount histology using Local Affine Transformations guided by Internal Structures (LATIS)

Registration of in vivo prostate MRI and pseudo‐whole mount histology using Local Affine Transformations guided by Internal Structures (LATIS)

On stochastie processes with an embedded marked point process

A rate-conservative principle for stationary piecewise Markov processes

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