Segmentation of Stochastic Images using ... - Jacobs University

Chapter 8 Segmentation of Classical Images Using Stochastic Parameters
Figure 8.4: Ambrosio-Tortorelli model applied on the expected value of the liver data set using a
stochastic parameter µ. The upper row shows the expected value (left) and the variance
(right) of the smoothed image, the lower row the expected value (left) and the variance
(right) of the phase field.
Results
We applied the Ambrosio-Tortorelli segmentation with stochastic parameters on the liver data set.
Again, we use the expected value of the stochastic data set as deterministic input and construct a
stochastic input image that contains one random variable and a maximal polynomial chaos degree
of four. As in the random walker tests, the remaining stochastic dimensions are filled up with zeros.
To separate the influence of the stochasticity of the parameters in the Ambrosio-Tortorelli model, we
use one stochastic parameter for the first tests and keep the other parameters deterministic.
Fig. 8.4 shows the result for a uniformly distributed parameter µ. To be precise, µ is uniformly
distributed between 200 and 600, i.e. µ ∼ U [200,600]. The parameter µ controls the influence of the
smoothing term in the image equation. For large µ we get sharper images with sharp edges. Thus,
a stochastic parameter µ influences the smoothing of the image. This is visible from the variance of
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