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Keywords
(6)
Level Set
Surface Fitting
Surface Model
Surface Reconstruction
Gradient Descent
Radon Transform
Related Publications
(6)
Geometric Surface Processing via Normal Maps
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A direct approach to estimating surfaces in tomographic data
A direct approach to estimating surfaces in tomographic data,10.1016/S13618415(02)000828,Medical Image Analysis,Ross T. Whitaker,Vidya Elangovan
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A direct approach to estimating surfaces in tomographic data
(
Citations: 19
)
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Ross T. Whitaker
,
Vidya Elangovan
Under ideal circumstances, the inverse of the
radon transform
is computable, and sequences of measured projections are sufficient to obtain accurate estimates of volume densities. In situations where the sinogram data is incomplete, the
radon transform
is noninvertable, and attempts to reconstruct greyscale density values result in reconstruction artifacts that can undermine the effectiveness of subsequent processing. This paper presents a direct approach to the segmentation of incomplete tomographic data. The strategy is to impose a fairly simple model on the data, and treat segmentation as a problem of estimating the interface between two substances of somewhat homogeneous density. The segmentation is achieved by simultaneously deforming a
surface model
and updating density parameters in order to achieve a best fit between the projected model and the measured sinograms. The deformation is implemented with levelset surface models, calculated at the resolution of the input data. Relative to previous work, this paper makes several contributions. First is a proper derivation of the deformation of surface models that move according to a
gradient descent
on a likelihood measure. We also present a series of computational innovations that make this direct surfacefitting approach feasible with stateoftheart computers. Another contribution is the demonstration of the effectiveness of this approach on underconstrained tomographic problems, using both simulated and real datasets.
Journal:
Medical Image Analysis  MED IMAGE ANAL
, vol. 6, no. 3, pp. 235249, 2002
DOI:
10.1016/S13618415(02)000828
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Citation Context
(9)
...The main difference between traditional level set methods [26, 35, 12, 33, 27, 40,
45
] and our algorithm is that we represent the attenuation coefficient as f (Φ), as opposed to the traditional form H(Φ) with H the Heaviside function...
Ville Kolehmainen
,
et al.
Limited Data XRay Tomography Using Nonlinear Evolution Equations
...Examples for situations where this model is used are computerized tomography (CT) [66, 67,
168
], singleparticle emission computerized tomography (SPECT), positron emission tomography (PET), diffuse optical tomography (DOT) [11, 52, 55, 58, 59], or fluorescence tomography [74, 92]...
Oliver Dorn
,
et al.
TOPICAL REVIEW: Level set methods for inverse scattering
...Previous work on estimating the alignment of highresolution information directly from projection data includes [5], [6], [18]‐[
21
]...
...Estimation methods have included gradient ascent [18], [
21
], Levenberg‐Marquardt [5], [6], and variable metric methods using adjoint differentiation [19][20]...
...As in [5], [6], [19]‐[
21
], the present work assumes uniform radiotracer concentration within each tissue type...
James E. Bowsher
,
et al.
Aligning emission tomography and MRI images by optimizing the emission...
...Several curve evolution methods and their related application to tomographic image reconstruction can be found in [3][4][
5
][6]...
Jian Zhou
,
et al.
PET Image Reconstruction Using MumfordShah Regularization Coupled wit...
...Alternatively, the motion of the level set can depend on a variational formulation that positions the interface to create discontinuities that best model the discontinuities in the input data (Tsai et al., 2000; Chan and Vese, 2001;
Whitaker and Elangovan, 2002
)...
Joshua E. Cates
,
et al.
GIST: an interactive, GPUbased level set segmentation tool for 3D med...
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Citations
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