PNC in 2D Curve Modeling

2017 ◽  
pp. 87-131
Keyword(s):  
Curve Fitting ◽  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Shape Representation ◽  
Linear Interpolation ◽  
Distribution Functions ◽  
Novel Approach ◽  
Curve Modeling ◽  
Basic Probability ◽  
Pros And Cons

Interpolation methods and curve fitting represent so huge problem that each individual interpolation is exceptional and requires specific solutions. PNC method is such a novel tool with its all pros and cons. The user has to decide which interpolation method is the best in a single situation. The choice is yours if you have any choice. Presented method is such a new possibility for curve fitting and interpolation when specific data (for example handwritten symbol or character) starts up with no rules for polynomial interpolation. This chapter consists of two generalizations: generalization of previous MHR method with various nodes combinations and generalization of linear interpolation with different (no basic) probability distribution functions and nodes combinations. This probabilistic view is novel approach a problem of modeling and interpolation. Computer vision and pattern recognition are interested in appropriate methods of shape representation and curve modeling.

Applications of PNC in Artificial Intelligence

2020 ◽  
pp. 509-538
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Artificial Intelligence ◽  
Computer Vision ◽  
Curve Fitting ◽  
Polynomial Interpolation ◽  
Shape Representation ◽  
Shape Reconstruction ◽  
Contour Representation ◽  
Novel Approach ◽  
Curve Interpolation ◽  
Curve Modeling

Interpolation methods and curve fitting represent so huge problem that each individual interpolation is exceptional and requires specific solutions. Presented method is such a new possibility for curve fitting and interpolation when specific data (for example handwritten symbol or character) starts up with no rules for polynomial interpolation. The method of Probabilistic Nodes Combination (PNC) enables interpolation and modeling of two-dimensional curves using nodes combinations and different coefficients γ. This probabilistic view is novel approach a problem of modeling and interpolation. Computer vision and pattern recognition are interested in appropriate methods of shape representation and curve modeling. PNC method represents the possibilities of shape reconstruction and curve interpolation via the choice of nodes combination and probability distribution function for interpolated points. It seems to be quite new look at the problem of contour representation and curve modeling in artificial intelligence and computer vision.

Applications of PNC in Artificial Intelligence

2017 ◽  
pp. 269-308
Keyword(s):  
Artificial Intelligence ◽  
Computer Vision ◽  
Curve Fitting ◽  
Polynomial Interpolation ◽  
Shape Representation ◽  
Shape Reconstruction ◽  
Contour Representation ◽  
Novel Approach ◽  
Curve Interpolation ◽  
Curve Modeling

Interpolation methods and curve fitting represent so huge problem that each individual interpolation is exceptional and requires specific solutions. Presented method is such a new possibility for curve fitting and interpolation when specific data (for example handwritten symbol or character) starts up with no rules for polynomial interpolation. The method of Probabilistic Nodes Combination (PNC) enables interpolation and modeling of two-dimensional curves using nodes combinations and different coefficients ?. This probabilistic view is novel approach a problem of modeling and interpolation. Computer vision and pattern recognition are interested in appropriate methods of shape representation and curve modeling. PNC method represents the possibilities of shape reconstruction and curve interpolation via the choice of nodes combination and probability distribution function for interpolated points. It seems to be quite new look at the problem of contour representation and curve modeling in artificial intelligence and computer vision.

Applications of PNC in Numerical Methods

2017 ◽  
pp. 235-268
Keyword(s):  
Probability Distribution ◽  
Shape Representation ◽  
Mathematical Problem ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Key Points ◽  
Characteristic Points ◽  
Curve Modeling ◽  
Curve Contour ◽  
Dimensional Object

Nodes are treated as characteristic points of data for modeling and analyzing. The model of data can be built by choice of probability distribution function and nodes combination. Two-dimensional object is extrapolated and interpolated via nodes combination and different functions as discrete or continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot or power function. Curve interpolation represents one of the most important problems in mathematics and computer science: how to model the curve via discrete set of two-dimensional points? Also the matter of shape representation (as closed curve - contour) and curve parameterization is still opened. For example pattern recognition, signature verification or handwriting identification problems are based on curve modeling via the choice of key points. So interpolation is not only a pure mathematical problem but important task in computer vision and artificial intelligence.

The Method of Probabilistic Nodes Combination in Decision Making and Risk Analysis

2016 ◽  
pp. 32-60
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Decision Making ◽  
Distribution Function ◽  
Probability Distribution ◽  
Risk Analysis ◽  
Probability Distribution Function ◽  
Linear Interpolation ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
Characteristic Points ◽  
Basic Probability

Proposed method, called Probabilistic Nodes Combination (PNC), is the method of 2D curve interpolation and extrapolation using the set of key points (knots or nodes). Nodes can be treated as characteristic points of data for modeling and analyzing. The model of data can be built by choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter ? as probability distribution function enables value anticipation in risk analysis and decision making. Two-dimensional curve is extrapolated and interpolated via nodes combination and different functions as discrete or continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot or power function. Novelty of the paper consists of two generalizations: generalization of previous MHR method with various nodes combinations and generalization of linear interpolation with different (no basic) probability distribution functions and nodes combinations.

Probabilistic Nodes Combination (PNC)

2020 ◽  
pp. 1026-1057
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Computer Vision ◽  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Shape Representation ◽  
Shape Reconstruction ◽  
Novel Approach ◽  
Curve Modeling ◽  
Inverse Functions ◽  
Vision Function

The method of Probabilistic Nodes Combination (PNC) enables interpolation and modeling of two-dimensional curves using nodes combinations and different coefficients γ: polynomial, sinusoidal, cosinusoidal, tangent, cotangent, logarithmic, exponential, arc sin, arc cos, arc tan, arc cot or power function, also inverse functions. This probabilistic view is novel approach a problem of modeling and interpolation. Computer vision and pattern recognition are interested in appropriate methods of shape representation and curve modeling. PNC method represents the possibilities of shape reconstruction and curve interpolation via the choice of nodes combination and probability distribution function for interpolated points. It seems to be quite new look at the problem of contour representation and curve modeling in artificial intelligence and computer vision. Function for γ calculations is chosen individually at each curve modeling and it is treated as probability distribution function: γ depends on initial requirements and curve specifications.

Probabilistic Nodes Combination (PNC)

2017 ◽  
pp. 44-86
Keyword(s):  
Computer Vision ◽  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Shape Representation ◽  
Shape Reconstruction ◽  
Novel Approach ◽  
Curve Modeling ◽  
Inverse Functions ◽  
Vision Function

The method of Probabilistic Nodes Combination (PNC) enables interpolation and modeling of two-dimensional curves using nodes combinations and different coefficients ?: polynomial, sinusoidal, cosinusoidal, tangent, cotangent, logarithmic, exponential, arc sin, arc cos, arc tan, arc cot or power function, also inverse functions. This probabilistic view is novel approach a problem of modeling and interpolation. Computer vision and pattern recognition are interested in appropriate methods of shape representation and curve modeling. PNC method represents the possibilities of shape reconstruction and curve interpolation via the choice of nodes combination and probability distribution function for interpolated points. It seems to be quite new look at the problem of contour representation and curve modeling in artificial intelligence and computer vision. Function for ? calculations is chosen individually at each curve modeling and it is treated as probability distribution function: ? depends on initial requirements and curve specifications.

A cell-based smoothed point interpolation method (CS-PIM) for 2D thermoelastic problems

2017 ◽  
Vol 27 (6) ◽  
pp. 1249-1265 ◽  
Author(s):  
Yijun Liu ◽  
Guiyong Zhang ◽  
Huan Lu ◽  
Zhi Zong
Keyword(s):  
Thermal Stresses ◽  
Interpolation Method ◽  
Content Type ◽  
Novel Approach ◽  
Convergence Results ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Thermoelastic Problems ◽  
Gradient Smoothing ◽  
Practical Implications

Purpose Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and the solutions of automated generated linear elements are generally of poor accuracy about especially gradient results. The proposed cell-based smoothed point interpolation method (CS-PIM) aims to improve the results accuracy of the thermoelastic problems via properly softening the overly-stiff stiffness. Design/methodology/approach This novel approach is based on the newly developed G space and weakened weak (w2) formulation, and of which shape functions are created using the point interpolation method and the cell-based gradient smoothing operation is conducted based on the linear triangular background cells. Findings Owing to the property of softened stiffness, the present method can generally achieve better accuracy and higher convergence results (especially for the temperature gradient and thermal stress solutions) than the FEM does by using the simplest linear triangular background cells, which has been examined by extensive numerical studies. Practical implications The CS-PIM is capable of producing more accurate results of temperature gradients as well as thermal stresses with the automated generated and unstructured background cells, which make it a better candidate for solving practical thermoelastic problems. Originality/value It is the first time that the novel CS-PIM was further developed for solving thermoelastic problems, which shows its tremendous potential for practical implications.

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

An experimental study on optimal spark timing control for improved performance of a flex fuel vehicle engine

2019 ◽  
Vol 234 (5) ◽  
pp. 1294-1303
Author(s):  
Junsang Yoo ◽  
Taeyong Lee ◽  
Pyungsik Go ◽  
Yongseok Cho ◽  
Kwangsoon Choi ◽  
...  
Keyword(s):  
Empirical Equation ◽  
Interpolation Method ◽  
Linear Interpolation ◽  
Combustion Characteristics ◽  
Combustion Stability ◽  
Timing Control ◽  
Vehicle Engine ◽  
Spark Timing ◽  
Linear Interpolation Method ◽  
Blended Fuels

In the American continent, the most frequently used alternative fuel is ethanol. Especially in Brazil, various blends of gasoline–ethanol fuels are widely spread. The vehicle using blended fuel is called flexible fuel vehicle. Because of several selections for the blending ratios in gas stations, the fuel properties may vary after refueling depending on a driver’s selection. Also, the combustion characteristics of the flexible fuel vehicle engine may change. In order to respond to the flexible fuel vehicle market in Brazil, a study on blended fuels is performed. The main purpose of this study is to enhance performance of the flexible fuel vehicle engine to target Brazilian market. Therefore, we investigated combustion characteristics and optimal spark timings of the blended fuels with various blending ratios to improve the performance of the flexible fuel vehicle engine. As a tool for prediction of the optimal spark timing for the 1.6L flexible fuel vehicle engine, the empirical equation was suggested. The validity of the equation was investigated by comparing the predicted optimal spark timings with the stock spark timings through engine tests. When the stock spark timings of E0 and E100 were optimal, the empirical equation predicted the actual optimal spark timings for blended fuels with a good accuracy. In all conditions, by optimizing spark timing control, performance was improved. Especially, torque improvements of E30 and E50 fuels were 5.4% and 1.8%, respectively, without affecting combustion stability. From these results, it was concluded that the linear interpolation method is not suitable for flexible fuel vehicle engine control. Instead of linear interpolation method, optimal spark timing which reflects specific octane numbers of gasoline–ethanol blended fuels should be applied to maximize performance of the flexible fuel vehicle engine. The results of this study are expected to save the effort required for engine calibration when developing new flexible fuel vehicle engines and to be used as a basic strategy to improve the performance of other flexible fuel vehicle engines.

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