Efficient Algorithms for Mumford-Shah and Potts Problems

In this work, we consider Mumford-Shah and Potts models and their higher order generalizations. Mumford-Shah and Potts models are among the most well-known variational approaches to edge-preserving smoothing and partitioning of images. Though their formulations are intuitive, their application is not straightforward as it corresponds to solving challenging, particularly non-convex, minimization problems. The main focus of this thesis is the development of new algorithmic approaches to Mumford-Shah and Potts models, which is to this day an active field of research. We start by considering the situation for univariate data. We find that switching to higher order models can overcome known shortcomings of the classical first order models when applied to data with steep slopes. Though the existing approaches to the first order models could be applied in principle, they are slow or become numerically unstable for higher orders. Therefore, we develop a new algorithm for univariate Mumford-Shah and Potts models of any order and show that it solves the models in a stable way in O(n^2). Furthermore, we develop algorithms for the inverse Potts model. The inverse Potts model can be seen as an approach to jointly reconstructing and partitioning images that are only available indirectly on the basis of measured data. Further, we give a convergence analysis for the proposed algorithms. In particular, we prove the convergence to a local minimum of the underlying NP-hard minimization problem. We apply the proposed algorithms to numerical data to illustrate their benefits. Next, we apply the multi-channel Potts prior to the reconstruction problem in multi-spectral computed tomography (CT). To this end, we propose a new superiorization approach, which perturbs the iterates of the conjugate gradient method towards better results with respect to the Potts prior. In numerical experiments, we illustrate the benefits of the proposed approach by comparing it to the existing Potts model approach from the literature as well as to the existing total variation type methods. Hereafter, we consider the second order Mumford-Shah model for edge-preserving smoothing of images which –similarly to the univariate case– improves upon the classical Mumford-Shah model for images with linear color gradients. Based on reformulations in terms of Taylor jets, i.e. specific fields of polynomials, we derive discrete second order Mumford-Shah models for which we develop an efficient algorithm using an ADMM scheme. We illustrate the potential of the proposed method by comparing it with existing methods for the second order Mumford-Shah model. Further, we illustrate its benefits in connection with edge detection. Finally, we consider the affine-linear Potts model for the image partitioning problem. As many images possess linear trends within homogeneous regions, the classical Potts model frequently leads to oversegmentation. The affine-linear Potts model accounts for that problem by allowing for linear trends within segments. We lift the corresponding minimization problem to the jet space and develop again an ADMM approach. In numerical experiments, we show that the proposed algorithm achieves lower energy values as well as faster runtimes than the method of comparison, which is based on the iterative application of the graph cut algorithm (with α-expansion moves)

Bewertung gesellschaftlicher Nebenleistungen von ökologischen und konventionellen Milchviehbetrieben Süddeutschlands innerhalb der Treibhausgasbilanzierung

Allocation of greenhouse gas emissions with economic allocation for milk and beef is well established in carbon foot printing, but many organic and extensive farms fulfill a wide range of additional ecosystem services for society such as management of renewable natural resources as well as preservation of biodiversity and cultural landscapes. Farms are compensated for these ecosystem services by the second pillar of the Common Agricultural Policy of the European Union. This study introduces a new aspect by examining an economic allocation for greenhouse gas emissions including ecosystem services besides milk and beef for 113 dairy farms located in grassland-based areas of Southern Germany. Results are carbon footprints of 1.66 kg CO2eq/kg fat and protein corrected milk (FPCM) on average in “conventional economic allocation”. Economic allocation, which includes ecosystem services based on the farm net income, results in a carbon footprint of 1.5 kg CO2eq/kg FPCM on average. Especially organic and extensive systems are favored with this approach. This approach shows that carbon footprints of dairy farms should not be examined one-dimensionally based solely on the amount of milk and meat that is produced on the farm; rather, a broader approach is necessary especially in organic farms

Weniger (Kraftfutter) ist manchmal mehr (Gewinn) – ein Plädoyer für hohe Grundfutterleistungen in der ökologischen Milchproduktion

High concentrate use in milk production disregards the inborn ability of ruminants to convert into valuable foodstuffs cellulose, which monogastrics cannot digest. The present paper builds upon the analyses of 36 organic dairy farms and compares farms with high concentrate use per cow against those with low usage. The cluster of farms with 6.7 dt concentrates performs slightly better economically than those with a higher concentrate usage of 13.3 dt per cow. But the efficient usage of forage is more decisive for farm profitability. Therefore, organic farms should improve their milk yields by high forage qualities and add a limited quantity of efficiently utilized concentrate

Vorzüglichkeit der ökologischen Weidemilchproduktion im Kontext steigender Kraftfutterpreise

Owing to strongly volatile and temporarily very low milk payout over the last years with operational costs showing an upward trend, organic milk production associated with intense pasture utilization has gained in excellence. Our contribution compares a sample of 38 randomly selected South German pasture farms with conventionally farming top enterprises in the financial years 2009 – 2011. The results obtained demonstrate that in spite of the smaller sizes of the 34 selected firms, organic pasture farms can generate higher hourly earnings than conventionally farming top enterprises thanks to high basic ration performance from cheap pasture grass and low input of concentrated feed with high prices for organic milk. This advantage will even be greater with increasing prices for concentrated feed and/or operating resources if the milk prices are kept at the level of the previous years

Boundary Conditions in Quantum String Cosmology

We discuss in detail how to consistently impose boundary conditions in quantum string cosmology. Since a classical time parameter is absent in quantum gravity, such conditions must be imposed with respect to intrinsic variables. Constructing wave packets for minisuperspace models from different tree-level string effective actions, we explain in particular the meaning of a transition between ``pre-big-bang" and ``post-big-bang" branches. This leads to a scenario different from previous considerations.Comment: 16 pages, REVTEX, minor changes, two references adde

Einfluss von Milchleistung und Nutzungsdauer auf den Product Carbon Footprint von Milch bei ökologisch wirtschaftenden Betrieben in Süddeutschland

Quantification and mitigation of greenhouse gas emissions is an intensively discussed topic. For dairy farms many studies consider a higher milk yield per cow for greenhouse gas mitigation but this often results in a reduction in herd fertility and thus more heifers are needed which may lead to more emissions in total. This paper presents the Product Carbon Footprint of 36 organic dairy farms and analyses the influence of milk yield per cow and longevity of dairy cows. Results are: (1) a product carbon footprint of 1,61 kg CO2eq/kg fat and protein corrected milk on average, (2) increasing milk yield per cow causes decreasing product carbon footprints (coefficient of determination 48 %) and (3) decreasing longevity per cow causes decreasing product carbon footprints but to a lower degree of influence (coefficient of determination 16 %). With regard to climate protection, not considering ethical aspects, a high milk yield per cow should be achieved rather than to focus on longevity

Erhebliche Effizienzpotenziale in der Färsenaufzucht der ökologischen Milchproduktion

In many organic farms there is a huge potential to increase efficiency in rearing heifers for replacement. This is the result of a study in 36 organic dairy farms with pasture from South Germany, which were analyzed economically in the years 2009 – 2011. In particular farms with high production efficiency and low production costs per heifer show decreased production times per cow for some months, but this effect is overcompensated by higher milk yields per cow. This is one reason why they perform economically better with regard to the dairy farm. The most important factors influencing the production costs per heifer are the costs for forage and labor. Based on the results of this study, more efficient rearing of heifers with lower production costs seems necessary and worthwhil