Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities

Intensity inhomogeneities in images constitute a considerable challenge in image segmentation. In this paper we propose a novel biconvex variational model to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. Our method assumes that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of our biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled by our model. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images which was indeed the motivation of our work

Study of polyhydroxyalkanoates production using acetic, propionic and butyric acids

Treballs Finals de Grau d'Enginyeria Química, Facultat de Química, Universitat de Barcelona, Curs: 2019-2020, Tutors: Joan Dosta Parras, Carme Vidal AntichNowadays, to replace the use of plastic is needed due to its low degradation capacity and its low efficiency in recycling, which usually leads to pollutants and toxic substances. To promote a circular system, the use of a bio-polymer such as polyhydroxyalkanoates (PHA) is proposed. This bio-polymer is produced from a four-stage system: fermentation, selection of microorganisms, accumulation of intracellular PHA and extraction, using wastewater or other wastes as the municipal waste organic fraction as substrates. In this work, a selection of PHA-producing microorganisms with an organic loading ratio of 3.5 g COD · L-1·d-1 with synthetic feeding is carried out in a 3L reactor where the ratio carbon- nitrogen is decreased (56.39 g COD /g N, 48.59 g COD / g N and 43.00 g COD / g N) to find the appropriate ratio. The process is performed with an HRT of 1.16 days and an SRT of 4.87 days. Accumulation test have also been carried out in a 1 L reactor where a ratio of 43.00 g COD / gN is worked. The pH, oxygen concentration, ammonium concentration and volatile fatty acids consume are monitored along the process. Moreover, the effect of added the PHA production process in a wastewater treatment plant where secondary sludge is mixed with municipal organic fraction has studied. The results obtained are to see the evolution of a system that it is trying to stabilize. Nevertheless, a reactor that works with a coupled feeding have a volatile suspended solid and totals ratio lower than another that works with an uncoupled feeding. In addition to that, the microorganism PHA content is twice as many in a reactor with coupled feeding as in an uncoupled feeding, according to the bibliography. However, it is observed that the microorganisms have the same maxim PHA content independent of the organic rate load, according to the bibliography. Regarding the nitrogen limitation, a correlation is observed between the increase in biomass and the increase in the nitrogen dose. Besides the C-N ratios of this study were insufficient. It is also observed that the acid consumption speed on the number of carbon in the molecular chain. Lastly, it has been concluded that the PHA production process could be implemented in a municipal wastewater treatment plant using VFA produced by the acidogenic fermentation of waste secondary sludge and squeezed OFMS

Religion in the Public Schools after Santa Fe Independent School District v. Doe: Time for a New Strategy

In this Essay, Steven Fitschen, President of the National Legal Foundation, argues against the Supreme Court\u27s ruling in Santa Fe Independent School District v. Doe, and calls for a new strategy in litigating similar cases. Fitschen proposes a thirty-year plan because he believes that the current Court composition, which he sees as driven by personal predilections rather than by precedent, was partly responsible for the outcome of Santa Fe. Fitschen argues that the current Court has largely ignored Establishment Clause precedent, and that any new, effective strategy will be slowly implemented The thirty-year plan calls for less perfunctory reliance on free-exercise-as-free-speech strategy, and asserts that the Establishment and Free Exercise Clauses are really two sides of the same coin, rather than in tension with each other. Fitschen also draws upon historical arguments that although establishment of religion is prohibited by the First Amendment, acknowledgment, accommodation, and even encouragement of religion is not. The thirty-year plan will be successful when everything short of establishment passes constitutional muster, and when mere acknowledgment, accommodation,and encouragement are not falsely characterized as establishment by opponents. Fitschen is hopeful that a reminder of historical reality, as articulated by Justice Story, will make the thirty-year plan a feasible new strategy for the futur

Disparity and Optical Flow Partitioning Using Extended Potts Priors

This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notation of asymptotically level stable functions we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of minimizers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method

From Civil Rights to Blackmail: How the Civil Rights Attorney\u27s Fees Awards Act of 1976 (42 U.S.C. § 1988) Has Perverted One of America\u27s Most Historic Civil Rights Statutes

For fourteen years, members of Congress repeatedly introduced legislation directed at a single subject. A key underpinning for the necessity of the legislation was provided by the opinions of two Supreme Court justices. Yet, for the past nine years, Congress has gone silent on the same topic. This Article argues that it is past time for Congress to reconsider this topic, and that if it will not do so, the Supreme Court can rectify the situation without engaging in judicial legislation. Perhaps the best view of Congress\u27s efforts can be seen by examining the high-water mark of those efforts, which occurred in 2006. In that year, it was the belief of 247 United States representatives that the Establishment Clause [of the United States Constitution] does not secure an individual right. Therefore, they believed attorney\u27s fees should not be available in Establishment Clause cases under 42 U.S.C. §§ 1983 and 1988, the federal civil rights and fee shifting statutes that make such awards possible. Similarly, by 2006, two Supreme Court Justices had indicated that the Establishment Clause did not protect individual rights. Indeed, the 247 Congressmen explicitly relied on the words of one of those justices, Anthony Kennedy, for this proposition; and Justice Thomas had by then made the even more emphatic, unequivocal statement that [t]he Establishment Clause does not purport to protect individual rights. And yet, here were are, fourteen years later, and attorney\u27s fees are still being awarded in Establishment Clause cases under 42 U.S.C. § 1988. This Article will argue that this practice should stop, either by amendment of 42 U.S.C. §§ 1983 and 1988 or through a pronouncement by the Supreme Court that Establishment Clause claims can no longer be brought under 42 U.S.C. § 1983