scholarly journals Comparison of minimization methods for nonsmooth image segmentation

2018 ◽  
Vol 9 (1) ◽  
pp. 68-86 ◽  
Author(s):  
L. Antonelli ◽  
V. De Simone
Keyword(s):  
Optimization Problem ◽  
Convex Relaxation ◽  
Numerical Comparison ◽  
Two Phase ◽  
Piecewise Constant ◽  
First Order ◽  
Smoothing Methods ◽  
Minimization Methods ◽  
Basic Approaches ◽  
Nonsmooth Optimization Problem

Abstract Segmentation is a typical task in image processing having as main goal the partitioning of the image into multiple segments in order to simplify its interpretation and analysis. One of the more popular segmentation model, formulated by Chan-Vese, is the piecewise constant Mumford-Shah model restricted to the case of two-phase segmentation. We consider a convex relaxation formulation of the segmentation model, that can be regarded as a nonsmooth optimization problem, because the presence of the l1-term. Two basic approaches in optimization can be distinguished to deal with its non differentiability: the smoothing methods and the nonsmoothing methods. In this work, a numerical comparison of some first order methods belongs of both approaches are presented. The relationships among the different methods are shown, and accuracy and efficiency tests are also performed on several images.

scholarly journals A Study on the Chain Ratio-Type Estimator of Finite Population Variance

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yunusa Olufadi ◽  
Cem Kadilar
Keyword(s):  
Finite Population ◽  
Numerical Comparison ◽  
Mean Square ◽  
Auxiliary Variables ◽  
Population Variance ◽  
Two Phase ◽  
First Order ◽  
Phase Sampling ◽  
The Mean ◽  
Two Phase Sampling

We suggest an estimator using two auxiliary variables for the estimation of the unknown population variance. The bias and the mean square error of the proposed estimator are obtained to the first order of approximations. In addition, the problem is extended to two-phase sampling scheme. After theoretical comparisons, as an illustration, a numerical comparison is carried out to examine the performance of the suggested estimator with several estimators.

scholarly journals Stabilised bias field: segmentation with intensity inhomogeneity

2016 ◽  
Vol 10 (4) ◽  
pp. 302-313 ◽  
Author(s):  
Jack Spencer ◽  
Ke Chen
Keyword(s):  
Convex Relaxation ◽  
Intensity Variation ◽  
Bias Field ◽  
Intensity Inhomogeneity ◽  
Variational Model ◽  
Great Success ◽  
Two Phase ◽  
Relaxation Methods ◽  
Piecewise Constant ◽  
Field Estimation

Automatic segmentation in the variational framework is a challenging task within the field of imaging sciences. Achieving robustness is a major problem, particularly for images with high levels of intensity inhomogeneity. The two-phase piecewise-constant case of the Mumford-Shah formulation is most suitable for images with simple and homogeneous features where the intensity variation is limited. However, it has been applied to many different types of synthetic and real images after some adjustments to the formulation. Recent work has incorporated bias field estimation to allow for intensity inhomogeneity, with great success in terms of segmentation quality. However, the framework and assumptions involved lead to inconsistencies in the method that can adversely affect results. In this paper we address the task of generalising the piecewise-constant formulation, to approximate minimisers of the original Mumford-Shah formulation. We first review existing methods for treating inhomogeneity, and demonstrate the inconsistencies with the bias field estimation framework. We propose a modified variational model to account for these problems by introducing an additional constraint, and detail how the exact minimiser can be approximated in the context of this new formulation. We extend this concept to selective segmentation with the introduction of a distance selection term. These models are minimised with convex relaxation methods, where the global minimiser can be found for a fixed fitting term. Finally, we present numerical results that demonstrate an improvement to existing methods in terms of reliability and parameter dependence, and results for selective segmentation in the case of intensity inhomogeneity.

scholarly journals AN ADAPTIVE VARIATIONAL MODEL FOR MEDICAL IMAGES RESTORATION

2019 ◽  
Vol XLII-2/W12 ◽  
pp. 219-224
Author(s):  
T. T. T. Tran ◽  
C. T. Pham ◽  
A. V. Kopylov ◽  
V. N. Nguyen
Keyword(s):  
Optimization Problem ◽  
Medical Images ◽  
Variational Model ◽  
Imaging Analysis ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Piecewise Constant ◽  
First Order ◽  
Proposed Model ◽  
Staircase Effect

<p><strong>Abstract.</strong> Image denoising is one of the important tasks required by medical imaging analysis. In this work, we investigate an adaptive variation model for medical images restoration. In the proposed model, we have used the first-order total variation combined with Laplacian regularizer to eliminate the staircase effect in the first-order TV model while preserve edges of object in the piecewise constant image. We also propose an instance of Split Bregman method to solve the proposed denoising model as an optimization problem. Experimental results from mixed Poisson-Gaussian noise are given to demonstrate that our proposed approach outperforms the related methods.</p>

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

scholarly journals Enhancing methane production from the invasive macroalga Rugulopteryx okamurae through anaerobic co-digestion with olive mill solid waste: process performance and kinetic analysis

2021 ◽  
Author(s):  
D. de la Lama-Calvente ◽  
M. J. Fernández-Rodríguez ◽  
J. Llanos ◽  
J. M. Mancilla-Leytón ◽  
R. Borja
Keyword(s):  
Anaerobic Digestion ◽  
Solid Waste ◽  
Methane Production ◽  
Methane Yield ◽  
Specific Rate ◽  
Order Kinetic ◽  
Two Phase ◽  
First Order ◽  
Olive Mill Solid Waste ◽  
Olive Mill

AbstractThe biomass valorisation of the invasive brown alga Rugulopteryx okamurae (Dictyotales, Phaeophyceae) is key to curbing the expansion of this invasive macroalga which is generating tonnes of biomass on southern Spain beaches. As a feasible alternative for the biomass management, anaerobic co-digestion is proposed in this study. Although the anaerobic digestion of macroalgae barely produced 177 mL of CH4 g−1 VS, the co-digestion with a C-rich substrate, such as the olive mill solid waste (OMSW, the main waste derived from the two-phase olive oil manufacturing process), improved the anaerobic digestion process. The mixture improved not only the methane yield, but also its biodegradability. The highest biodegradability was found in the mixture 1 R. okamurae—1 OMSW, which improved the biodegradability of the macroalgae by 12.9% and 38.1% for the OMSW. The highest methane yield was observed for the mixture 1 R. okamurae—3 OMSW, improving the methane production of macroalgae alone by 157% and the OMSW methane production by 8.6%. Two mathematical models were used to fit the experimental data of methane production time with the aim of assessing the processes and obtaining the kinetic constants of the anaerobic co-digestion of different combination of R. okamurae and OMSW and both substrates independently. First-order kinetic and the transference function models allowed for appropriately fitting the experimental results of methane production with digestion time. The specific rate constant, k (first-order model) for the mixture 1 R. okamurae- 1.5 OMSW, was 5.1 and 1.3 times higher than that obtained for the mono-digestion of single OMSW and the macroalga, respectively. In the same way, the transference function model revealed that the maximum methane production rate (Rmax) was also found for the mixture 1 R. okamurae—1.5 OMSW (30.4 mL CH4 g−1 VS day−1), which was 1.6 and 2.2 times higher than the corresponding to the mono-digestions of the single OMSW and sole R. okamurae (18.9 and 13.6 mL CH4 g−1 VS day−1), respectively.

History Matching in Two-Phase Petroleum Reservoirs

1980 ◽  
Vol 20 (06) ◽  
pp. 521-532 ◽  
Author(s):  
A.T. Watson ◽  
J.H. Seinfeld ◽  
G.R. Gavalas ◽  
P.T. Woo
Keyword(s):  
Optimal Control ◽  
Parameter Estimation ◽  
Objective Function ◽  
History Matching ◽  
Computing Time ◽  
Absolute Permeability ◽  
Two Phase ◽  
Automatic History Matching ◽  
Control Approach ◽  
First Order

Abstract An automatic history-matching algorithm based onan optimal control approach has been formulated forjoint estimation of spatially varying permeability andporosity and coefficients of relative permeabilityfunctions in two-phase reservoirs. The algorithm usespressure and production rate data simultaneously. The performance of the algorithm for thewaterflooding of one- and two-dimensional hypotheticalreservoirs is examined, and properties associatedwith the parameter estimation problem are discussed. Introduction There has been considerable interest in thedevelopment of automatic history-matchingalgorithms. Most of the published work to date onautomatic history matching has been devoted tosingle-phase reservoirs in which the unknownparameters to be estimated are often the reservoirporosity (or storage) and absolute permeability (ortransmissibility). In the single-phase problem, theobjective function usually consists of the deviationsbetween the predicted and measured reservoirpressures at the wells. Parameter estimation, orhistory matching, in multiphase reservoirs isfundamentally more difficult than in single-phasereservoirs. The multiphase equations are nonlinear, and in addition to the porosity and absolutepermeability, the relative permeabilities of each phasemay be unknown and subject to estimation. Measurements of the relative rates of flow of oil, water, and gas at the wells also may be available forthe objective function. The aspect of the reservoir history-matchingproblem that distinguishes it from other parameterestimation problems in science and engineering is thelarge dimensionality of both the system state and theunknown parameters. As a result of this largedimensionality, computational efficiency becomes aprime consideration in the implementation of anautomatic history-matching method. In all parameterestimation methods, a trade-off exists between theamount of computation performed per iteration andthe speed of convergence of the method. Animportant saving in computing time was realized insingle-phase automatic history matching through theintroduction of optimal control theory as a methodfor calculating the gradient of the objective functionwith respect to the unknown parameters. Thistechnique currently is limited to first-order gradientmethods. First-order gradient methods generallyconverge more slowly than those of higher order.Nevertheless, the amount of computation requiredper iteration is significantly less than that requiredfor higher-order optimization methods; thus, first-order methods are attractive for automatic historymatching. The optimal control algorithm forautomatic history matching has been shown toproduce excellent results when applied to field problems. Therefore, the first approach to thedevelopment of a general automatic history-matchingalgorithm for multiphase reservoirs wouldseem to proceed through the development of anoptimal control approach for calculating the gradientof the objective function with respect to theparameters for use in a first-order method. SPEJ P. 521＾

Treatment of VX Hydrolysate with Ultraviolet Light and Hydrogen Peroxide

1997 ◽  
Vol 2 (3) ◽  
Author(s):  
Michael G. MacNaughton ◽  
James R. Scott
Keyword(s):  
Hydrogen Peroxide ◽  
Ultraviolet Light ◽  
Pilot Scale ◽  
Methylphosphonic Acid ◽  
Chemical Agent ◽  
Organosulfur Compounds ◽  
Two Phase ◽  
First Order ◽  
Engineering Study ◽  
Inorganic Sulfate

AbstractAn engineering study was performed to evaluate the use of ultraviolet light and hydrogen peroxide to destroy caustic-neutralized VX nerve agent in the U.S. chemical agent stockpile as an alternative to incineration. Whereas caustic neutralization completely destroys VX, (3-ethyl-S-2-(diisopropylamino)ethyl methylphosphonothiolate, the reaction leaves a complex two-phase mixture containing organic phosphates and organosulfur compounds which require treatment prior to ultimate disposal. Studies performed in laboratory-scale (320-mL), bench-scale (10-L) and pilot-scale (20-L) reactors demonstrated that the principal products of the caustic neutralization-ethyl methylphosphonic acid (EMPA), methylphosphonic acid (MPA), 2-(diisopropylamino)ethyl sulfide (RSR), disulfide (RSSR) and the other mixed sulfides-could be oxidized to inorganic sulfate, phosphate, ammonia and carbon dioxide. The reaction was zero order above 1000 mg/L and pseudo first order below. To mineralize 10,000 lb of VX per day to less than 10 mg/L organic carbon would require more than 1100 lamps of 30 kW each.

scholarly journals Monoclinic–orthorhombic first-order phase transition in K2ZnSi5O12 leucite analogue; transition mechanism and spontaneous strain analysis.

2021 ◽  
pp. 1-20
Author(s):  
Anthony M.T. Bell ◽  
Francis Clegg ◽  
Christopher M.B. Henderson
Keyword(s):  
Phase Transition ◽  
Strain Analysis ◽  
Phase Region ◽  
Martensitic Transition ◽  
Two Phase ◽  
Spontaneous Strain ◽  
First Order ◽  
Transition Mechanism ◽  
First Order Phase Transition ◽  
Increasing Temperature

Abstract Hydrothermally synthesised K2ZnSi5O12 has a polymerised framework structure with the same topology as leucite (KAlSi2O6, tetragonal I41/a), which has two tetrahedrally coordinated Al3+ cations replaced by Zn2+ and Si4+. At 293 K it has a cation-ordered framework P21/c monoclinic structure with lattice parameters a = 13.1773(2) Å, b = 13.6106(2) Å, c = 13.0248(2) Å and β = 91.6981(9)°. This structure is isostructural with K2MgSi5O12, the first cation-ordered leucite analogue characterised. With increasing temperature, the P21/c structure transforms reversibly to cation-ordered framework orthorhombic Pbca. This transition takes place over the temperature range 848−863 K where both phases coexist; there is an ~1.2% increase in unit cell volume between 843 K (P21/c) and 868 K (Pbca), characteristic of a first-order, displacive, ferroelastic phase transition. Spontaneous strain analysis defines the symmetry- and non-symmetry related changes and shows that the mechanism is weakly first order; the two-phase region is consistent with the mechanism being a strain-related martensitic transition.

scholarly journals Deep Network Guided Proof Search

10.29007/8mwc ◽  
2018 ◽  
Author(s):  
Sarah Loos ◽  
Geoffrey Irving ◽  
Christian Szegedy ◽  
Cezary Kaliszyk
Keyword(s):  
Deep Learning ◽  
Program Analysis ◽  
Network Models ◽  
Theorem Prover ◽  
Neural Network Models ◽  
Two Phase ◽  
First Order ◽  
Proof Search ◽  
System Verification ◽  
Theory Reasoning

Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.Automated first-order theorem provers can aid in the formalization and verification of mathematical theorems and play a crucial role in program analysis, theory reasoning, security, interpolation, and system verification.Here we suggest deep learning based guidance in the proof search of the theorem prover E. We train and compare several deep neural network models on the traces of existing ATP proofs of Mizar statements and use them to select processed clauses during proof search. We give experimental evidence that with a hybrid, two-phase approach, deep learning based guidance can significantly reduce the average number of proof search steps while increasing the number of theorems proved.Using a few proof guidance strategies that leverage deep neural networks, we have found first-order proofs of 7.36% of the first-order logic translations of the Mizar Mathematical Library theorems that did not previously have ATP generated proofs. This increases the ratio of statements in the corpus with ATP generated proofs from 56% to 59%.

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