Segmentation of Stochastic Images using ... - Jacobs University

6.2 Ambrosio-Tortorelli Segmentation on Stochastic Images
Samples E(φ) Var(φ)
Monte Carlo
GSD
Figure 6.13: Segmentation result of the street scene. On the left we show the five samples the stochastic
input image is computed from. On the right we compare the results computed via
the GSD method and a Monte Carlo sampling.
in Section 5.2. It is visible from the pictures that the gray value uncertainty is high close to the edges
of moving objects. Thus, we expect the highest phase field variance in these regions. The results
depicted in Fig. 6.13 match with these expectations. Indeed, in the region around the wheels of the
car and around the right shoulder of the person, the edge detection is most influenced by the moving
camera, respectively the varying gray values between the samples at the edges. Also around the
edges in the background, the variance increases due to the moving camera. However, the stochastic
method can detect the edges in the image properly. The result of the stochastic method contains
much more information than the deterministic method. The expected value of the stochastic method
is comparable to the result of the classical method, the stochastic information like chaos coefficients,
variance, etc. are the real benefit of the method. Thus, we use the variance, indicating the robustness
of the detected edges to get information, which is not available in the classical model.
To verify the intrusive GSD method, we compared the results of the GSD implementation with
a simple Monte Carlo method with 10000 sample computations. Fig. 6.13 shows the results and
Figure 6.14: Expected value and variance of the stochastic input image of the street scene.
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