Discrete Curvature Estimation Methods for Triangulated Surfaces

2012 ◽  
pp. 28-42 ◽  
Author(s):  
Mohammed Mostefa Mesmoudi ◽  
Leila De Floriani ◽  
Paola Magillo
Keyword(s):  
Estimation Methods ◽  
Discrete Curvature ◽  
Triangulated Surfaces ◽  
Curvature Estimation

Estimation and Display of Triangular Mesh Curvature in Reverse Engineering

2010 ◽  
Vol 136 ◽  
pp. 95-102
Author(s):  
Hui Cun Shen ◽  
J.J. Nie ◽  
W.S. Zong ◽  
J. Wang ◽  
B.G. Yang
Keyword(s):  
Reverse Engineering ◽  
Surface Fitting ◽  
Triangular Mesh ◽  
Surface Curvature ◽  
Estimation Methods ◽  
Quadric Surface ◽  
Fitting Method ◽  
Curvature Estimation ◽  
Curvature Group ◽  
Paraboloid Surface

The estimation of triangular mesh curvature is implemented by establishing local quadric surface at vertexes of mesh. Deduction course of quadric surface curvature calculation is presented. Errors and complexity of two curvature estimation methods, which are the ecumenical quadric surface fitting method and the quadric paraboloid surface fitting method respectively, are compared. Technique for curvature group display is put forward. This technique can display features of mesh distinctly, even though the curvature values of mesh distribute non-uniformly in their variety range.

scholarly journals A Discrete Curvature Estimation Based Low-Distortion Adaptive Savitzky–Golay Filter for ECG Denoising

Sensors ◽  
2019 ◽  
Vol 19 (7) ◽  
pp. 1617 ◽  
Author(s):  
Hui Huang ◽  
Shiyan Hu ◽  
Ye Sun
Keyword(s):  
Consumer Electronics ◽  
High Signal ◽  
Wearable Electronics ◽  
Signal Distortion ◽  
Data Smoothing ◽  
Discrete Curvature ◽  
Ecg Denoising ◽  
Curvature Estimation ◽  
Low Distortion ◽  
Distortion Reduction

Electrocardiogram (ECG) sensing is an important application for the diagnosis of cardiovascular diseases. Recently, driven by the emerging technology of wearable electronics, massive wearable ECG sensors are developed, which however brings additional sources of noise contamination on ECG signals from these wearable ECG sensors. In this paper, we propose a new low-distortion adaptive Savitzky-Golay (LDASG) filtering method for ECG denoising based on discrete curvature estimation, which demonstrates better performance than the state of the art of ECG denoising. The standard Savitzky-Golay (SG) filter has a remarkable performance of data smoothing. However, it lacks adaptability to signal variations and thus often induces signal distortion for high-variation signals such as ECG. In our method, the discrete curvature estimation is adapted to represent the signal variation for the purpose of mitigating signal distortion. By adaptively designing the proper SG filter according to the discrete curvature for each data sample, the proposed method still retains the intrinsic advantage of SG filters of excellent data smoothing and further tackles the challenge of denoising high signal variations with low signal distortion. In our experiment, we compared our method with the EMD-wavelet based method and the non-local means (NLM) denoising method in the performance of both noise elimination and signal distortion reduction. Particularly, for the signal distortion reduction, our method decreases in MSE by 33.33% when compared to EMD-wavelet and by 50% when compared to NLM, and decreases in PRD by 18.25% when compared to EMD-wavelet and by 25.24% when compared to NLM. Our method shows high potential and feasibility in wide applications of ECG denoising for both clinical use and consumer electronics.

CIRCULAR ARC SEGMENTATION BY CURVATURE ESTIMATION AND GEOMETRIC VALIDATION

2012 ◽  
Vol 12 (04) ◽  
pp. 1250024 ◽  
Author(s):  
SHYAMOSREE PAL ◽  
RAHUL DUTTA ◽  
PARTHA BHOWMICK
Keyword(s):  
Geometric Analysis ◽  
Circular Arc ◽  
Discrete Curvature ◽  
Circular Arcs ◽  
Initial Stage ◽  
Benchmark Datasets ◽  
Curvature Estimation ◽  
Digital Curve ◽  
Curvature Information ◽  
Novel Algorithm

A novel algorithm to detect circular arcs from a digital image is proposed. The algorithm is based on discrete curvature estimated for the constituent points of digital curve segments, followed by a fast geometric analysis. The curvature information is used in the initial stage to find the potentially circular segments. In the final stage, the circular arcs are merged and maximized in length using the radius and center information of the potentially circular segments. Triplets of longer segments are given higher priorities; doublets and singleton arcs are processed at the end. Detailed experimental results on benchmark datasets demonstrate its efficiency and robustness.

Research of Discrete Curvature Estimation Method Based on Local Space Parabola

2014 ◽  
Vol 577 ◽  
pp. 802-805 ◽  
Author(s):  
Jian Wei Ma ◽  
Zhen Yuan Jia ◽  
Fu Ji Wang
Keyword(s):  
Point Cloud ◽  
Simulation Experiment ◽  
Estimation Method ◽  
Circular Arc ◽  
Discrete Curvature ◽  
Fitting Method ◽  
Local Space ◽  
Scan Line ◽  
Curvature Estimation ◽  
Line Point

Curvature estimation of 3-dimension discrete points performs an important role in dealing with scan line point cloud and is difficult to calculate. A discrete curvature estimation method based on local space parabola is proposed. Method in this paper is contrasted with circular arc fitting method and simulation experiment shows that the proposed method is feasible and effective with high precision.

Investigating the Segmentation of Freeform Triangulated Surfaces Using a Self-Organizing Map

2006 ◽  
Author(s):  
Alexander D. MacLennan ◽  
Geoff West ◽  
Michael Cardew-Hall
Keyword(s):  
Point Clouds ◽  
Free Form ◽  
Complex Object ◽  
Self Organizing Map ◽  
Discrete Curvature ◽  
Planar Surfaces ◽  
Object Based ◽  
Triangulated Surfaces ◽  
Free Form Surfaces ◽  
Self Organizing

Freeform surfaces can be used to describe manufactured objects. These surfaces can be represented as point clouds, triangulated surfaces and range images. Before these objects can be analysed in any way they need to be broken down into their constituent parts. Using this description stamped parts can be indexed and retrieved to assist in determining how to manufacture a part that has similar properties. One means of performing this task is to segment the object based upon its surface properties. Curvature can be used to describe the behaviour of a surface. In order to use these metrics a single Self-Organizing Map is used to automatically categorise surface into regions of similar curvature. The SOM is first trained using a small number of simple shapes and curvature metrics. It is then used to segment an object that is a mixture of free form surfaces and planes. The combination of these metrics, shapes and the use of a SOM allows for the representation of many types of surfaces. The shapes and curvature metrics used to train the model determine how sensitive it is to different surface descriptions. This technique is successfully applied to a complex object that combines free form surfaces and planar surfaces using robust discrete curvature metrics.

Contour Representation by Clustering Curvatures of the 3D Objects

2009 ◽  
Vol 147-149 ◽  
pp. 633-638
Author(s):  
Arūnas Lipnickas ◽  
Vidas Raudonis
Keyword(s):  
Free Form ◽  
Distance Measurements ◽  
3D Object ◽  
Human Foot ◽  
3D Objects ◽  
Large Size ◽  
Contour Representation ◽  
Triangulated Surfaces ◽  
Curvature Estimation ◽  
Free Form Surfaces

The purpose of this work is to segment large size triangulated surfaces and the contours extraction of the 3D object by the use of the object curvature value. The curvatures values allow categorizing the type of the local surface of the 3D object. In present work the curvature was estimated for the free-form surfaces obtained by the 3D range scanner. A free-form surface is the surface such that the surface normal is defined and continuous everywhere, except at sharp corners and edges [2, 5]. Two types of distance measurements functions based on Euclidian distance, bounded box and topology of surface were used for the curvature estimation. Clustering technique has been involved to cluster the values of the curvature for 3D object contour representation. The described technique was applied to the 3D objects with free-form surfaces such as the human foot and cube.

scholarly journals Estimation of Membrane Curvature for Cryo-Electron Tomography

2019 ◽  
Author(s):  
Maria Kalemanov ◽  
Javier F. Collado ◽  
Wolfgang Baumeister ◽  
Rubén Fernández-Busnadiego ◽  
Antonio Martínez-Sánchez
Keyword(s):  
Electron Tomography ◽  
Membrane Curvature ◽  
Quantization Noise ◽  
Estimation Methods ◽  
Tensor Voting ◽  
Triangle Mesh ◽  
Membrane Morphology ◽  
Morphological Descriptor ◽  
Cryo Electron Tomography ◽  
Curvature Estimation

AbstractCurvature is an important morphological descriptor of cellular membranes. Cryo-electron tomography (cryo-ET) is particularly well-suited to visualize and analyze membrane morphology in a close-to-native state and high resolution. However, current curvature estimation methods cannot be applied directly to membrane segmentations in cryo-ET. Additionally, a reliable estimation requires to cope with quantization noise. Here, we developed and implemented a method for membrane curvature estimation from tomogram segmentations.From a membrane segmentation, a signed surface (triangle mesh) is first extracted. The triangle mesh is then represented by a graph (vertices and edges), which facilitates finding neighboring triangles and the calculation of geodesic distances necessary for local curvature estimation. Here, we present several approaches for accurate curvature estimation based on tensor voting. Beside curvatures, these methods also provide robust estimations of surface normals and principal directions.We tested the different methods on benchmark surfaces with known curvature, demonstrating the validity of these methods and their robustness to quantization noise. We also applied two of these approaches to biological cryo-ET data. The results allowed us to determine the best approach to estimate membrane curvature in cellular cryo-ET data.

Curvature Estimation Modeling Using Machine Learning for CLSVOF Method: Comparison With Conventional Methods

2019 ◽  
Author(s):  
Majid Haghshenas ◽  
Ranganathan Kumar
Keyword(s):  
Machine Learning ◽  
Distance Function ◽  
Volume Fraction ◽  
Estimation Methods ◽  
Learning Approach ◽  
Curvature Function ◽  
Estimation Model ◽  
Machine Learning Approach ◽  
Curvature Estimation ◽  
Conventional Methods

Abstract Despite extensive progress in recent decades, curvature estimation in two-phase models remains a challenge. Well-established curvature computing techniques such as distance function, smoothed volume fraction and height-function directly estimate the interface curvature from the implicit representation of the interface. Most recently, machine learning approach has been incorporated in computational physics simulation. Machine learning is a set of algorithms that can be utilized for training a system which allows predicting the output in the future. In this work, we train a curvature estimation model using machine learning approach for Coupled Level Set Volume of Fluid (CLSVOF) method in which both distance function and volume fraction implicitly represent the interface. Three datasets for the curvature are generated: a) curvature as a function of volume fraction (nine inputs), b) curvature as a function of distance function (nine inputs), and c) curvature as a function of both volume fraction and distance function (eighteen inputs). For each interfacial cell, curvature and input parameters (nine volume fraction and nine distance function values) at nine grid points across the interface are stored. Datasets are utilized to train different curvature computing models using neural network (NN) learning algorithm. Comparison of different datasets reveals that the distance function dataset is the best input for curvature function training. Different available learning algorithms on built-in NN toolbox in Matlab are examined. The curvature estimation function is examined for a dimensional 2D well-defined droplet on different grid resolution. In addition, the curvature estimation model by machine learning approach is compared with conventional methods such as the level set method and height function method for couple of cases. First, the case of elliptical droplet is used to evaluate curvature estimation of different methods in comparison with the analytical solution. Then, the standard case of equilibrium droplet is simulated by CLSVOF solver using different curvature estimation methods to evaluate parasitic currents generation and droplet pressure prediction. The results show that the machine learning curvature function outperforms conventional methods even on coarse grids. Finally, the curvature estimation methods are is utilized to solve a practical case of rising bubble. We observed that the terminal velocity of capped bubble reported by curvature function simulation has the lowest error.

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