Segmentation of Stochastic Images using ... - Jacobs University

7.5 Segmentation of Stochastic Images Using Stochastic Level Sets
Figure 7.12: Mean (left) of the stochastic liver image and the variance of the stochastic Chan-Vese
solution. In addition, we show the expected value contour at different time steps.
Figure 7.13: Variance of the stochastic image to segment (left), the expected value is not depicted,
because the expected value is an image with the same gray value at every pixel. On
the right, the segmentation result is depicted on one realization (one sample) of the
stochastic image to segment.
tion of the random variable for the mean inside the regions. The realizations drawn from the final
stochastic level set fit to each other and to the final contour of the level set evolution from Fig. 7.12.
The extension of the stochastic Chan-Vese approach that tries to homogenize the variance of the
object and the background allows to segment objects in images with constant mean, i.e. it allows to
segment objects from constant images where the classical method fails. Fig. 7.13 shows the result
of the segmentation of an image with constant mean, but non-constant variance. Drawing samples
of this image (cf. Fig. 7.13) the object is visible on samples through the different variance levels, but
again, the classical Chan-Vese approach cannot segment the object in the image due to the constant
mean value, whereas the variance extension of the stochastic Chan-Vese approach yields the correct
result. In fact, the Chan-Vese approach without variance homogenization would not move the initial
contour because the driving force is zero due to the constant mean value.
Conclusion
We presented an extension of the level set approach to use random variables or random fields as
propagation speed. The use of this uncertain speed leadss to an uncertain interface position char-
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