Background Camera-based photoplethysmography (cbPPG) is a measurement technique which enables remote vital sign monitoring by using cameras. To obtain valid plethysmograms, proper regions of interest (ROIs) have to be selected in the video data. Most automated selection methods rely on specific spatial or temporal features limiting a broader application. In this work, we present a new method which overcomes those drawbacks and, therefore, allows cbPPG to be applied in an intraoperative environment. Methods We recorded 41 patients during surgery using an RGB and a near-infrared (NIR) camera. A Bayesian skin classifier was employed to detect suitable regions, and a level set segmentation approach to define and track ROIs based on spatial homogeneity. Results The results show stable and homogeneously illuminated ROIs. We further evaluated their quality with regards to extracted cbPPG signals. The green channel provided the best results where heart rates could be correctly estimated in 95.6% of cases. The NIR channel yielded the highest contribution in compensating false estimations. Conclusions The proposed method proved that cbPPG is applicable in intraoperative environments. It can be easily transferred to other settings regardless of which body site is considered.

This dissertation deals with customised image analysis tools in cancer research. In the field of biomedical sciences, mathematical imaging has become crucial in order to account for advancements in technical equipment and data storage by sound mathematical methods that can process and analyse imaging data in an automated way. This thesis contributes to the development of such mathematically sound imaging models in four ways: (i) automated cell segmentation and tracking. In cancer drug development, time-lapse light microscopy experiments are conducted for performance validation. The aim is to monitor behaviour of cells in cultures that have previously been treated with chemotherapy drugs, since atypical duration and outcome of mitosis, the process of cell division, can be an indicator of successfully working drugs. As an imaging modality we focus on phase contrast microscopy, hence avoiding phototoxicity and influence on cell behaviour. As a drawback, the common halo- and shade-off effect impede image analysis. We present a novel workflow uniting both automated mitotic cell detection with the Hough transform and subsequent cell tracking by a tailor-made level-set method in order to obtain statistics on length of mitosis and cell fates. The proposed image analysis pipeline is deployed in a MATLAB software package called MitosisAnalyser. For the detection of mitotic cells we use the circular Hough transform. This concept is investigated further in the framework of image regularisation in the general context of imaging inverse problems, in which circular objects should be enhanced, (ii) exploiting sparsity of first-order derivatives in combination with the linear circular Hough transform operation. Furthermore, (iii) we present a new unified higher-order derivative-type regularisation functional enforcing sparsity of a vector field related to an image to be reconstructed using curl, divergence and shear operators. The model is able to interpolate between well-known regularisers such as total generalised variation and infimal convolution total variation. Finally, (iv) we demonstrate how we can learn sparsity promoting parametrised regularisers via quotient minimisation, which can be motivated by generalised Eigenproblems. Learning approaches have recently become very popular in the field of inverse problems. However, the majority aims at fitting models to favourable training data, whereas we incorporate knowledge about both fit and misfit data. We present results resembling behaviour of well-established derivative-based sparse regularisers, introduce novel families of non-derivative-based regularisers and extend this framework to classification problems.

After a review of the notions of Hausdorff and Fourier dimensions from fractal geometry and Fourier analysis and the properties of local times of Brownian motion, we study the Fourier structure of Brownian level sets. We show that if δa(X) is the Dirac measure of one-dimensional Brownian motion X at the level a, that is the measure defined by the Brownian local time La at level a, and μ is its restriction to the random interval [0, L−1 a (1)], then the Fourier transform of μ is such that, with positive probability, for all 0 ≤ β < 1/2, the function u → |u|β|μ(u)|2, (u ∈ R), is bounded. This growth rate is the best possible. Consequently, each Brownian level set, reduced to a compact interval, is with positive probability, a Salem set of dimension 1/2. We also show that the zero set of X reduced to the interval [0, L−1 0 (1)] is, almost surely, a Salem set. Finally, we show that the restriction μ of δ0(X) to the deterministic interval [0, 1] is such that its Fourier transform satisfies E (|ˆμ(u)|2) ≤ C|u|−1/2, u 6= 0 and C > 0. Key words: Hausdorff dimension, Fourier dimension, Salem sets, Brownian motion, local times, level sets, Fourier transform, inverse local times. / Decision Sciences / PhD. (Operations Research)

Background Camera-based photoplethysmography (cbPPG) is a measurement technique which enables remote vital sign monitoring by using cameras. To obtain valid plethysmograms, proper regions of interest (ROIs) have to be selected in the video data. Most automated selection methods rely on specific spatial or temporal features limiting a broader application. In this work, we present a new method which overcomes those drawbacks and, therefore, allows cbPPG to be applied in an intraoperative environment. Methods We recorded 41 patients during surgery using an RGB and a near-infrared (NIR) camera. A Bayesian skin classifier was employed to detect suitable regions, and a level set segmentation approach to define and track ROIs based on spatial homogeneity. Results The results show stable and homogeneously illuminated ROIs. We further evaluated their quality with regards to extracted cbPPG signals. The green channel provided the best results where heart rates could be correctly estimated in 95.6% of cases. The NIR channel yielded the highest contribution in compensating false estimations. Conclusions The proposed method proved that cbPPG is applicable in intraoperative environments. It can be easily transferred to other settings regardless of which body site is considered.

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