Image Analysis, Random Fields and Markov Chain Monte Carlo Methods

Winkler, Gerhard

doi:10.1007/978-3-642-55760-6

Cited by 280 publications

(226 citation statements)

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“…The MCMC fitting is non-deterministic alternative and tests a wider range of values in parameter space than fminsearch, causing it to be more capable of locating sinks that contain global minima (Winkler, 2003;Gilks et al, 1996;Brooks et al, 2011). Markov chain fitting itself starts by choosing an initial condition, a point in parameter space, denoted by p 0 .…”

Section: Markov Chain Fitting With Simulated Annealingmentioning

confidence: 99%

“…This serves two purposes-to escape more easily from a local minimum that is not a global minimum, and to allow repeated iterations of the same algorithm to increase the accuracy of the results. The stochasticity in the algorithm allows for different outcomes even among trials with the same initial conditions (Winkler, 2003;Gilks et al, 1996;Brooks et al, 2011). This process is repeated n times-where n is an arbitrary number chosen by the user-before stopping.…”

Section: Markov Chain Fitting With Simulated Annealingmentioning

confidence: 99%

“…This algorithm reduces the chances that a minimization function will converge to a local minimum instead of a global minimum, since the act of raising the distance function to a power less than 1 reduces the prominence of local minima (Winkler, 2003). In this case, we ran 10 trials with simulated annealing, corresponding to ten iterations.…”

Section: Markov Chain Fitting With Simulated Annealingmentioning

confidence: 99%

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A Comparison and Catalog of Intrinsic Tumor Growth Models

2014

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Determining the dynamics and parameter values that drive tumor growth is of great interest to mathematical modelers, experimentalists and practitioners alike. We provide a basis on which to estimate the growth dynamics of ten different tumors by fitting growth parameters to at least five sets of published experimental data per type of tumor. These timescale tumor growth data are also used to determine which of the most common tumor growth models (exponential, power law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each type of tumor. In order to compute the best-fit parameters, we implemented a hybrid local-global least squares minimization algorithm based on a combination of Nelder-Mead simplex direct search and Monte Carlo Markov Chain methods.

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Section: Markov Chain Fitting With Simulated Annealingmentioning

confidence: 99%

Section: Markov Chain Fitting With Simulated Annealingmentioning

confidence: 99%

Section: Markov Chain Fitting With Simulated Annealingmentioning

confidence: 99%

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A Comparison and Catalog of Intrinsic Tumor Growth Models

2014

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“…We can see that SA provides lower energies (and hence better approximations to the global fibrous structure according to our model) than classical ICM. The proposed deterministic optimization strategy (ICM with α-relaxation and (t 2 )+(t 4 )-moves) shows similar performance to SA with communication q 1 , and the corresponding computational gain is 20 6 ∼ 3.33. The graph-based approach together with either SA or our modified ICM algorithm presents longer fiber bundles and lower fiber-length dispersion.…”

Section: Quantitative Analysismentioning

confidence: 91%

A graph‐based approach for automatic cardiac tractography

Frindel

Robini

Schaerer

et al. 2010

Magnetic Resonance in Med

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A new automatic algorithm for assessing fiber-bundle organization in the human heart using diffusion-tensor magnetic resonance imaging is presented. The proposed approach distinguishes from the locally "greedy" paradigm, which uses voxel-wise seed initialization intrinsic to conventional tracking algorithms. It formulates the fiber tracking problem as the global problem of computing paths in a boolean-weighted undirected graph, where each voxel is a vertex and each pair of neighboring voxels is connected with an edge. This leads to a global optimization task that can be solved by iterated conditional modes-like algorithms or Metropolis-type annealing. A new deterministic optimization strategy, namely iterated conditional modes with α-relaxation using (t 2 )-and (t 4 )-moves, is also proposed; it has similar performance to annealing but offers a substantial computational gain. This approach offers some important benefits. The global nature of our tractography method reduces sensitivity to noise and modeling errors. The discrete framework allows an optimal balance between the density of fiber bundles and the amount of available data. Besides, seed points are no longer needed; fibers are predicted in one shot for the whole diffusion-tensor magnetic resonance imaging volume, in a completely automatic way. Magn Reson Med 64:1215-1229, 2010.

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“…The inversion was based on the exponential Markov Random Fields (MRF) model. The MRF is a global model uniquely determined by a local statistical description of a single image or multispectral images for image pattern analysis, texture modeling and image classification [58][59][60][61][62][63][64]. In this paper, we use MRF model to determine relative surface roughness from standard deviation of cross-polarized ratio of series of SAR imagery.…”

Section: Methodsmentioning

confidence: 99%

Use of Radarsat-2 and Landsat TM Images for Spatial Parameterization of Manning’s Roughness Coefficient in Hydraulic Modeling

et al. 2015

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Vegetation resistance influences water flow in floodplains. Characterization of vegetation for hydraulic modeling includes the description of the spatial variability of vegetation type, height and density. In this research, we explored the use of dual polarized Radarsat-2 wide swath mode backscatter coefficients (σ°) and Landsat 5 TM to derive spatial hydraulic roughness. The spatial roughness parameterization included four steps: (i) land use classification from Landsat 5 TM; (ii) establishing a relationship between σ° statistics and vegetation parameters; (iii) relative surface roughness (Ks) determination from Synthetic Aperture Radar (SAR) backscatter temporal variability; (iv) derivation of the spatial distribution of the spatial hydraulic roughness both from Manning's roughness coefficient look up table (LUT) and relative surface roughness. Hydraulic simulations were performed using the FLO-2D hydrodynamic model to evaluate model performance under three different hydraulic modeling simulations results with different Manning's coefficient parameterizations, which includes SWL1, SWL2 and SWL3. SWL1 is simulated water OPEN ACCESSRemote Sens. 2015, 7 837 levels with optimum floodplain roughness (np) with channel roughness nc = 0.03 m −1/3 /s; SWL2 is simulated water levels with calibrated values for both floodplain roughness np = 0.65 m −1/3 /s and channel roughness nc = 0.021 m −1/3 /s; and SWL3 is simulated water levels with calibrated channel roughness nc and spatial Manning's coefficients as derived with aid of relative surface roughness. The model performance was evaluated using Nash-Sutcliffe model efficiency coefficient (E) and coefficient of determination (R 2 ), based on water levels measured at a gauging station in the wetland. The overall performance of scenario SWL1 was characterized with E = 0.75 and R 2 = 0.95, which was improved in SWL2 to E = 0.95 and R 2 = 0.99. When spatially distributed Manning values derived from SAR relative surface values were parameterized in the model, the model also performed well and yielding E = 0.97 and R 2 = 0.98. Improved model performance using spatial roughness shows that spatial roughness parameterization can support flood modeling and provide better flood wave simulation over the inundated riparian areas equally as calibrated models.

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Image Analysis, Random Fields and Markov Chain Monte Carlo Methods

Cited by 280 publications

References 0 publications

A Comparison and Catalog of Intrinsic Tumor Growth Models

A Comparison and Catalog of Intrinsic Tumor Growth Models

A graph‐based approach for automatic cardiac tractography

Use of Radarsat-2 and Landsat TM Images for Spatial Parameterization of Manning’s Roughness Coefficient in Hydraulic Modeling

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