Abstract
The proposed method, called probabilistic nodes combination (PNC), is the method of 2D curve interpolation and modeling using the set of key points (knots or nodes). Nodes can be treated as characteristic points of the object for modeling. The model of each individual symbol or data can be built by choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter $$\gamma $$ ? as probability distribution function enables curve parameterization and interpolation for each specific data or handwritten symbol. Two-dimensional curve is modeled and interpolated via nodes combination and different functions as discrete or continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arccot or power function. The 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.
Highlights
Probabilistic modeling is still a developing branch of computer science: operational research [1], decision making techniques andD
The significance of this paper consists in generalization for the MHR method: the computations are done without matrices in curve fitting and shape modeling, with clear point interpolation formula based on probability distribution function and nodes combination
Curve interpolation [5] represents one of the most important problems in mathematics and computer science: how do we model the curve [6] via a discrete set of two-dimensional points [7]? the matter of shape representation and curve parameterization is still open [8]
Summary
Probabilistic modeling is still a developing branch of computer science: operational research (for example probabilistic model-based prognosis) [1], decision making techniques and. The proposed curve modeling is based on two agents: probability distribution and nodes combination. The significance of this paper consists in generalization for the MHR method: the computations are done without matrices in curve fitting and shape modeling, with clear point interpolation formula based on probability distribution function (continuous or discrete) and nodes combination. The proposed method relies on nodes combination and functional modeling of curve points situated between the basic set of key points. The functions that are used in calculations represent a whole family of elementary functions with inverse functions: polynomials, trigonometric, cyclometric, logarithmic, exponential and power function These functions are treated as probability distribution functions in the range [0; 1]
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