Segmentation of Stochastic Images using ... - Jacobs University

2.6 Work Related to the Stochastic Framework
2.5.2 Robustness
Robustness of segmentation methods is desirable in two ways: The methods should be robust with
respect to the noise and with respect to the segmentation parameters.
Robustness with respect to the segmentation parameters, e.g. the β for random walker segmentation
or µ,ν, and ε for Ambrosio-Tortorelli segmentation, is necessary to get stable results. When the
segmentation result changes significantly for small parameter changes, the results are arbitrary, and
it is not recommendable to base e.g. medical diagnoses on such a segmentation result. It is possible
to investigate this kind of robustness by comparing the results of segmentations with slightly modified
parameters or by treating the segmentation parameters as random variables and investigate the
variance of the segmentation result. Chapter 8 of this thesis is about this.
Robustness with respect to noise is an essential property of a segmentation method for medical
images. The real, noise-free, image is not available, and it is a random choice which noise realization
the image at hand shows. It is desirable for segmentation methods to be robust with respect to the
noise realization, i.e. the segmentation result should not vary much for noise realizations. To investigate
this, it is possible to run the segmentation on noise realizations or to make image pixels random
variables, describing the process leading to the image noise. The first way is time-consuming. We
will see this later in the thesis, e.g. in Section 6.1. The second way is the fundamental idea of this
thesis. It needs a theoretical foundation, which the following chapters will present.
2.5.3 Error Propagation
Image processing widely neglects error propagation. Nearly all methods in image processing consider
the available data as the “truth”, but as we saw, the real data is not available. Instead, we have to
use an image corrupted by a random noise realization. When neglecting this error introduced by the
noise and other imaging artifacts we end up with results looking precise, but ignoring the influence
of the noise. It is desirable to have image processing methods that are able to deal with information
about the image noise, e.g. via the mentioned description of noise via the introduction of random
variables for the image pixels. The next chapters deal exactly with this new idea for the processing
of images and provide a theoretical background.
2.6 Work Related to the Stochastic Framework
In this section, we review work sounding similar to the work presented in this thesis and identify the
differences and similarities. A lot of authors presented methods for image segmentation that take
more or less stochasticity into account, e.g. via a modeling with Markov random fields or stochastic
annealing, but none of the methods mentioned can propagate stochastic information from the input
to the output of the segmentation process or model pixels as random variables.
Markov Random Fields for Image Segmentation
The literature [39, 65, 153] uses Markov random fields (MRFs) for image segmentation frequently.
MRFs are a possibility to model the noise in the input image, but the result of MRF segmentation
is a deterministic segmentation result along with a map to remove the noise from the input image.
Thus, this method tries to incorporate the noise via a stochastic modeling approach, but is not able
to propagate uncertainty information from the input to the output.
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