We consider discrimination between mammary cancer and mastopathy tissues, which plays a crucial role in clinical practice.  Based on my recent projects, I will discuss results of how stochastic processes can model both tissue modalities, mammary cancer and mastopathies.

I will use exponential families with geometric-topological canonical parameters, like Euler characteristic.  Application of such discrimination techniques has been applied to real biopsy images from patients in German clinics with reasonable improvement of false positive rates.  Such approach can be considered as stochastic and statistic modelling for image processing which can provide good benchmarks for false-positive rates in most typical cancers assessments.

Pure machine learning techniques can benefit from these to obtain results and thus contribute to addressing “inherent data ambiguity” in medical imaging.  The inter-patient variability of fractal dimension for mammary cancer is high and therefore multi-fractality can serve as a better concept. This is a feasible and parsimonious solution for a more delicate problem of multi-objective aggregation of information, relevant in modeling clinical assessor intervariability.  Such problem is well visible if one considers several fractal and texture characteristics of biopsy images. This helps to refine a fractal cancer hypothesis, well applicable for several standard cancers, e.g. mammary or prostate cancer.

In this talk I will also introduce a very different type of cancer growth which is not related to fractal cancer hypothesis. Nephroblastoma (given by Wilms tumor) is the typical tumor of the kidneys appearing in childhood, which does not satisfy fractal cancer hypothesis. I will illustrate by recent pre/post clinical study the effect on invasive treatments to Euclidean volumes of such tumors.