37,642 research outputs found
Breast Cancer: Modelling and Detection
This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection. We then discuss mathematical models that underpin mammographic image analysis, which complements models of tumour growth and facilitates diagnosis and treatment of cancer. Mammographic images are notoriously difficult to interpret, and we give an overview of the primary image enhancement technologies that have been introduced, before focusing on a more detailed description of some of our own recent work on the use of physics-based modelling in mammography. This theoretical approach to image analysis yields a wealth of information that could be incorporated into the mathematical models, and we conclude by describing how current mathematical models might be enhanced by use of this information, and how these models in turn will help to meet some of the major challenges in cancer detection
Aberrations in shift-invariant linear optical imaging systems using partially coherent fields
Here the role and influence of aberrations in optical imaging systems
employing partially coherent complex scalar fields is studied. Imaging systems
require aberrations to yield contrast in the output image. For linear
shift-invariant optical systems, we develop an expression for the output
cross-spectral density under the space-frequency formulation of statistically
stationary partially coherentfields. We also develop expressions for the output
cross{spectral density and associated spectral density for weak-phase,
weak-phase-amplitude, and single-material objects in one transverse spatial
dimension
Challenges in imaging and predictive modeling of rhizosphere processes
Background Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions. Scope In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding. Conclusions We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes
Aberrated dark-field imaging systems
We study generalized dark-field imaging systems. These are a subset of linear
shift-invariant optical imaging systems, that exhibit arbitrary aberrations,
and for which normally-incident plane-wave input yields zero output. We write
down the theory for the forward problem of imaging coherent scalar optical
fields using such arbitrarily-aberrated dark-field systems, and give numerical
examples. The associated images may be viewed as a form of dark-field Gabor
holography, utilizing arbitrary outgoing Green functions as generalized
Huygens-type wavelets, and with the Young-type boundary wave forming the
holographic reference
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