Segmentation of Stochastic Images using ... - Jacobs University

8.2 Ambrosio-Tortorelli Segmentation with Stochastic Parameters
Figure 8.5: Ambrosio-Tortorelli model applied on the expected value of the liver data set using a
stochastic parameter ε. The upper row shows the expected value (left) and the variance
(right) of the smoothed image and the lower row the expected value (left) and the variance
(right) of the phase field.
the smoothed image in Fig. 8.4, where a smoothing across the object boundaries leads to a variance
that looks similar to the original image. This is due to the cartoon-like initial image. Once energy is
transported across the edge, it is equally distributed in the whole region due to the smoothing term.
The smooth image resulting from the image equation influences the phase field, because it leads to
diffuse boundaries and to a wide phase field that is visible in the phase field variance in Fig. 8.4.
In Fig. 8.5 we used a stochastic parameter ε uniformly distributed between 0.0015 and 0.0035,
i.e. ε ∼ U [0.0015,0.0035]. The parameter ε influences the width of the phase field, but has no
influence on the smoothing parts of the equations. We observe changes in the variance around the
edges in Fig. 8.5. Directly, the parameter ε influences the width of the phase field and due to the
wider phase field, the image is smoothed differently close to edges.
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