Introduction

2017 ◽  
pp. 1-43
Keyword(s):  
Computer Vision ◽  
Computer Science ◽  
Shape Representation ◽  
Contour Reconstruction ◽  
Curve Modeling

Computer vision needs suitable methods of shape representation and contour reconstruction. One of them, invented by the author and called method of Hurwitz-Radon Matrices (MHR), can be used in representation and reconstruction of shapes of the objects in the plane. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. 2D shape is represented by the set of successive nodes. It is shown how to create the orthogonal and discrete OHR operator and how to use it in a process of shape representation and reconstruction. Contour of the object, represented by successive contour points, consists of information which allows us to describe many important features of the object as shape coefficients. 2D curve modeling is a basic subject in many branches of industry and computer science.

Introduction

2018 ◽  
pp. 187-220
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Computer Vision ◽  
Computer Science ◽  
Shape Representation ◽  
Contour Reconstruction ◽  
Curve Modeling

Computer vision needs suitable methods of shape representation and contour reconstruction. One of them, invented by the author and called method of Hurwitz-Radon Matrices (MHR), can be used in representation and reconstruction of shapes of the objects in the plane. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. 2D shape is represented by the set of successive nodes. It is shown how to create the orthogonal and discrete OHR operator and how to use it in a process of shape representation and reconstruction. Contour of the object, represented by successive contour points, consists of information which allows us to describe many important features of the object as shape coefficients. 2D curve modeling is a basic subject in many branches of industry and computer science.

Data Analyzing via Probabilistic Modeling

2021 ◽  
pp. 25-51
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Artificial Intelligence ◽  
Image Processing ◽  
Computer Vision ◽  
Object Recognition ◽  
Computer Science ◽  
Classical Problem ◽  
Contour Reconstruction ◽  
Curve Interpolation ◽  
Characteristic Features ◽  
Unknown Object

Object recognition is one of the topics of artificial intelligence, computer vision, image processing, and machine vision. The classical problem in these areas of computer science is that of determining object via characteristic features. An important feature of the object is its contour. Accurate reconstruction of contour points leads to possibility to compare the unknown object with models of specified objects. The key information about the object is the set of contour points which are treated as interpolation nodes. Classical interpolations (Lagrange or Newton polynomials) are useless for precise reconstruction of the contour. The chapter is dealing with proposed method of contour reconstruction via curves interpolation. First stage consists in computing the contour points of the object to be recognized. Then one can compare models of known objects, given by the sets of contour points, with coordinates of interpolated points of unknown object. Contour points reconstruction and curve interpolation are possible using a new method of Hurwitz-Radon matrices.

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.

Object Recognition via Contour Points Reconstruction Using Hurwitz - Radon Matrices

2013 ◽  
pp. 998-1018
Author(s):  
Dariusz Jakóbczak
Keyword(s):  
Artificial Intelligence ◽  
Image Processing ◽  
Computer Vision ◽  
Object Recognition ◽  
Computer Science ◽  
Classical Problem ◽  
Contour Reconstruction ◽  
Curve Interpolation ◽  
Characteristic Features ◽  
Unknown Object

Object recognition is one of the topics of artificial intelligence, computer vision, image processing and machine vision. The classical problem in these areas of computer science is that of determining object via characteristic features. Important feature of the object is its contour. Accurate reconstruction of contour points leads to possibility to compare the unknown object with models of specified objects. The key information about the object is the set of contour points which are treated as interpolation nodes. Classical interpolations (Lagrange or Newton polynomials) are useless for precise reconstruction of the contour. The chapter is dealing with proposed method of contour reconstruction via curves interpolation. First stage consists in computing the contour points of the object to be recognized. Then one can compare models of known objects, given by the sets of contour points, with coordinates of interpolated points of unknown object. Contour points reconstruction and curve interpolation is possible using new method of Hurwitz - Radon Matrices.

Object Recognition via Contour Points Reconstruction Using Hurwitz - Radon Matrices

2011 ◽  
pp. 87-107 ◽  
Author(s):  
Dariusz Jakóbczak
Keyword(s):  
Artificial Intelligence ◽  
Image Processing ◽  
Computer Vision ◽  
Object Recognition ◽  
Computer Science ◽  
Classical Problem ◽  
Contour Reconstruction ◽  
Curve Interpolation ◽  
Characteristic Features ◽  
Unknown Object

Object recognition is one of the topics of artificial intelligence, computer vision, image processing and machine vision. The classical problem in these areas of computer science is that of determining object via characteristic features. Important feature of the object is its contour. Accurate reconstruction of contour points leads to possibility to compare the unknown object with models of specified objects. The key information about the object is the set of contour points which are treated as interpolation nodes. Classical interpolations (Lagrange or Newton polynomials) are useless for precise reconstruction of the contour. The chapter is dealing with proposed method of contour reconstruction via curves interpolation. First stage consists in computing the contour points of the object to be recognized. Then one can compare models of known objects, given by the sets of contour points, with coordinates of interpolated points of unknown object. Contour points reconstruction and curve interpolation is possible using new method of Hurwitz - Radon Matrices.

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.

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.

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