scholarly journals Fuzzy Bit-Plane-Dependence Region Competition

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2392
Author(s):  
Siukai Choy ◽  
Tszching Ng ◽  
Carisa Yu ◽  
Benson Lam
Keyword(s):  
Energy Functional ◽  
Superior Performance ◽  
Projection Algorithm ◽  
Variational Model ◽  
Fuzzy Membership Function ◽  
Probability Models ◽  
Closed Form Solutions ◽  
Additional Information ◽  
Minimization Procedure ◽  
Bit Plane

This paper presents a novel variational model based on fuzzy region competition and statistical image variation modeling for image segmentation. In the energy functional of the proposed model, each region is characterized by the pixel-level color feature and region-level spatial/frequency information extracted from various image domains, which are modeled by the windowed bit-plane-dependence probability models. To efficiently minimize the energy functional, we apply an alternating minimization procedure with the use of Chambolle’s fast duality projection algorithm, where the closed-form solutions of the energy functional are obtained. Our method gives soft segmentation result via the fuzzy membership function, and moreover, the use of multi-domain statistical region characterization provides additional information that can enhance the segmentation accuracy. Experimental results indicate that the proposed method has a superior performance and outperforms the current state-of-the-art superpixel-based and deep-learning-based approaches.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

The Dynamics of Cumulative Step Size Adaptation on the Ellipsoid Model

2016 ◽  
Vol 24 (1) ◽  
pp. 25-57 ◽  
Author(s):  
Hans-Georg Beyer ◽  
Michael Hellwig
Keyword(s):  
Steady State ◽  
Linear Convergence ◽  
Search Space ◽  
Mean Value ◽  
Superior Performance ◽  
Noisy Environments ◽  
Step Size ◽  
State Behavior ◽  
Closed Form Solutions ◽  
The Mean

The behavior of the [Formula: see text]-Evolution Strategy (ES) with cumulative step size adaptation (CSA) on the ellipsoid model is investigated using dynamic systems analysis. At first a nonlinear system of difference equations is derived that describes the mean value evolution of the ES. This system is successively simplified to finally allow for deriving closed-form solutions of the steady state behavior in the asymptotic limit case of large search space dimensions. It is shown that the system exhibits linear convergence order. The steady state mutation strength is calculated, and it is shown that compared to standard settings in [Formula: see text] self-adaptive ESs, the CSA control rule allows for an approximately [Formula: see text]-fold larger mutation strength. This explains the superior performance of the CSA in non-noisy environments. The results are used to derive a formula for the expected running time. Conclusions regarding the choice of the cumulation parameter c and the damping constant D are drawn.

scholarly journals Pangenome Graphs

2020 ◽  
Vol 21 (1) ◽  
pp. 139-162 ◽  
Author(s):  
Jordan M. Eizenga ◽  
Adam M. Novak ◽  
Jonas A. Sibbesen ◽  
Simon Heumos ◽  
Ali Ghaffaari ◽  
...  
Keyword(s):  
Graphical Models ◽  
Genome Assembly ◽  
Association Studies ◽  
Low Cost ◽  
Variant Calling ◽  
Superior Performance ◽  
Whole Genome ◽  
Coordinate Systems ◽  
Multiple Sequence ◽  
Additional Information

Low-cost whole-genome assembly has enabled the collection of haplotype-resolved pangenomes for numerous organisms. In turn, this technological change is encouraging the development of methods that can precisely address the sequence and variation described in large collections of related genomes. These approaches often use graphical models of the pangenome to support algorithms for sequence alignment, visualization, functional genomics, and association studies. The additional information provided to these methods by the pangenome allows them to achieve superior performance on a variety of bioinformatic tasks, including read alignment, variant calling, and genotyping. Pangenome graphs stand to become a ubiquitous tool in genomics. Although it is unclear whether they will replace linearreference genomes, their ability to harmoniously relate multiple sequence and coordinate systems will make them useful irrespective of which pangenomic models become most common in the future.

scholarly journals Nonlocal Variational Model for Saliency Detection

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Meng Li ◽  
Yi Zhan ◽  
Lidan Zhang
Keyword(s):  
Visual Attention ◽  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Temporal Evolution ◽  
Lagrange Equation ◽  
Saliency Detection ◽  
Energy Functional ◽  
Experimental Results ◽  
Variational Model ◽  
Still Images

We present a nonlocal variational model for saliency detection from still images, from which various features for visual attention can be detected by minimizing the energy functional. The associated Euler-Lagrange equation is a nonlocalp-Laplacian type diffusion equation with two reaction terms, and it is a nonlinear diffusion. The main advantage of our method is that it provides flexible and intuitive control over the detecting procedure by the temporal evolution of the Euler-Lagrange equation. Experimental results on various images show that our model can better make background details diminish eventually while luxuriant subtle details in foreground are preserved very well.

Multi-Phase Texture Segmentation Using Gabor Features Histograms Based on Wasserstein Distance

2014 ◽  
Vol 15 (5) ◽  
pp. 1480-1500 ◽  
Author(s):  
Motong Qiao ◽  
Wei Wang ◽  
Michael Ng
Keyword(s):  
Gabor Filter ◽  
Error Function ◽  
Feature Space ◽  
Wasserstein Distance ◽  
Energy Functional ◽  
Phase Image ◽  
Minimization Method ◽  
Closed Form Solutions ◽  
Gabor Feature ◽  
Multi Phase

AbstractWe present a multi-phase image segmentation method based on the histogram of the Gabor feature space, which consists of a set of Gabor-filter responses with various orientations, scales and frequencies. Our model replaces the error function term in the original fuzzy region competition model with squared 2-Wasserstein distance function, which is a metric to measure the distance of two histograms. The energy functional is minimized by alternative minimization method and the existence of closed-form solutions is guaranteed when the exponent of the fuzzy membership term being 1 or 2. We test our model on both simple synthetic texture images and complex natural images with two or more phases. Experimental results are shown and compared to other recent results.

Bond Behavior of FRCM Carbon Yarns Embedded in a Cementitious Matrix: Experimental and Numerical Results

2017 ◽  
Vol 747 ◽  
pp. 305-312 ◽  
Author(s):  
Jacopo Donnini ◽  
Giovanni Lancioni ◽  
Tiziano Bellezze ◽  
Valeria Corinaldesi
Keyword(s):  
Mechanical Performance ◽  
Stress Transfer ◽  
Polymer Coatings ◽  
Energy Functional ◽  
Numerical Results ◽  
Variational Model ◽  
Experimental Session ◽  
Cementitious Matrix ◽  
Pull Out ◽  
Multifilament Yarns

The use of inorganic cement based composite systems, known as Fiber Reinforced Cementitious Matrix (FRCM), is a very promising technique for retrofitting and strengthening the existing masonry or concrete structures. The effectiveness of FRCM systems is strongly related to the interface bond between inorganic matrix and fabric reinforcement, and, since the major weakness is often located on this interface, the study of stress-transfer mechanisms between fibers and matrix becomes of fundamental importance.FRCM are usually reinforced with uni-directional or bi-directional fabrics consisting of multifilament yarns made of carbon, glass, basalt or PBO fibers, disposed along two orthogonal directions. The difficulty of the mortar to penetrate within the filaments that constitute the fabric yarns and the consequent non-homogeneous stress distribution through the yarn cross section makes difficult to access the characterization of the composite material. The use of polymer coatings on the fibers surface showed to enhance the bond strength of the interface between fibers and mortar and, as a consequence, to improve the mechanical performance of the composite. The coating does not allow the mortar to penetrate within the filaments while is able to improve the bond between the two materials and to increase the shear stress transfer capacity at the interface.An experimental session of several pull out tests on carbon yarns embedded in a cementitious matrix was carried out. Different embedded lengths have been analyzed, equal to 20, 30 and 50 mm. The carbon yarns object of this study were pre-impregnated with a flexible epoxy resin enhanced with a thin layer of quartz sand applied on the surface.A variational model was proposed to evaluate the pull-out behaviour and failure mechanisms of the system and to compare numerical results to the experimental outcomes. Evolution of fracture in the yarn-matrix system is determined by solving an incremental energy minimization problem, acting on an energy functional which account for brittle failure of matrix and yarn, and for debonding at the yarn-matrix interface. The model was able to accurately describe the three phases of the pull-out mechanism, depending on the embedded length.

scholarly journals Low-rank Matrix Optimization for Video Segmentation Research

2017 ◽  
Vol 6 (1) ◽  
pp. 36
Author(s):  
Caiyun Huang ◽  
Guojun Qin
Keyword(s):  
Video Segmentation ◽  
Optimal Solution ◽  
Low Rank ◽  
Superior Performance ◽  
Closed Form Solutions ◽  
Matrix Optimization ◽  
Rank Matrix ◽  
Low Rank Representation ◽  
Spatio Temporal ◽  
Low Rank Matrix

This paper investigates how to perform robust and efficient unsupervised video segmentation while suppressing the effects of data noises and/or corruptions. The low-rank representation is pursued for video segmentation. The supervoxels affinity matrix of an observed video sequence is given, low-rank matrix optimization seeks a optimal solution by making the matrix rank explicitly determined. We iteratively optimize them with closed-form solutions. Moreover, we incorporate a discriminative replication prior into our framework based on the obervation that small-size video patterns, and it tends to recur frequently within the same object. The video can be segmented into several spatio-temporal regions by applying the Normalized-Cut algorithm with the solved low-rank representation. To process the streaming videos, we apply our algorithm sequentially over a batch of frames over time, in which we also develop several temporal consistent constraints improving the robustness. Extensive experiments are on the public benchmarks, they demonstrate superior performance of our framework over other approaches．

scholarly journals Jointly Multiple Hash Learning

2019 ◽  
Vol 33 ◽  
pp. 9981-9982
Author(s):  
Xingbo Liu ◽  
Xiushan Nie ◽  
Yingxin Wang ◽  
Yilong Yin
Keyword(s):  
Superior Performance ◽  
Closed Form Solutions ◽  
Fixed Length ◽  
Compact Binary ◽  
Proposed Model ◽  
Efficient Retrieval ◽  
Benchmark Datasets ◽  
One Step ◽  
Types Of Information ◽  
Hash Codes

Hashing can compress heterogeneous high-dimensional data into compact binary codes while preserving the similarity to facilitate efficient retrieval and storage, and thus hashing has recently received much attention from information retrieval researchers. Most of the existing hashing methods first predefine a fixed length (e.g., 32, 64, or 128 bit) for the hash codes before learning them with this fixed length. However, one sample can be represented by various hash codes with different lengths, and thus there must be some associations and relationships among these different hash codes because they represent the same sample. Therefore, harnessing these relationships will boost the performance of hashing methods. Inspired by this possibility, in this study, we propose a new model jointly multiple hash learning (JMH), which can learn hash codes with multiple lengths simultaneously. In the proposed JMH method, three types of information are used for hash learning, which come from hash codes with different lengths, the original features of the samples and label. In contrast to the existing hashing methods, JMH can learn hash codes with different lengths in one step. Users can select appropriate hash codes for their retrieval tasks according to the requirements in terms of accuracy and complexity. To the best of our knowledge, JMH is one of the first attempts to learn multi-length hash codes simultaneously. In addition, in the proposed model, discrete and closed-form solutions for variables can be obtained by cyclic coordinate descent, thereby making the proposed model much faster during training. Extensive experiments were performed based on three benchmark datasets and the results demonstrated the superior performance of the proposed method.

POPULAR WAVELET MODELS

2007 ◽  
Vol 05 (04) ◽  
pp. 655-666
Author(s):  
LOKENATH DEBNATH ◽  
SARALEES NADARAJAH
Keyword(s):  
Superior Performance ◽  
Wavelet Expansion ◽  
Wavelet Coefficients ◽  
Probability Models ◽  
Posterior Density ◽  
Modern Approach ◽  
Prior Model ◽  
Standard Models ◽  
Bayesian Prior

The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for two popular models for the marginal posterior density. We also illustrate the superior performance of these models over the standard models for wavelet coefficients.

scholarly journals Variational model of scoliosis

2018 ◽  
Vol 45 (2) ◽  
pp. 167-175
Author(s):  
Igor Popov ◽  
Nikita Lisitsa ◽  
Yuri Baloshin ◽  
Mikhail Dudin ◽  
Stepan Bober
Keyword(s):  
Mathematical Model ◽  
Variational Principles ◽  
Three Dimensional ◽  
Energy Functional ◽  
Variational Model ◽  
Spinal Diseases ◽  
Clear Understanding ◽  
History Of ◽  
Minimal Curves ◽  
Initiating Factors

Scoliosis, being one of the most widespread spinal diseases among children, has been studied extensively throughout the history of medicine, yet there is no clear understanding of its initiating factors and the mechanogenesis of the monomorphic three-dimensional deformation due to its polyetiological nature. We present a novel mathematical model of the process of emergence of the three-dimensional deformation of the human spine based on variational principles. Typical scoliosis geometry is assumed to be described as minimal curves of a particular energy functional, which are shown to closely resemble actual scoliosis. We investigate the numerical properties of the first stage of scoliosis, which is shown to have the highest influence on the development of the disease.

Sign in / Sign up

Export Citation Format

Share Document