Shape Representation and Shape Coefficients via Method of Hurwitz-Radon Matrices

Jakóbczak, Dariusz Jacek

doi:10.1007/978-3-642-15910-7_47

Cited by 21 publications

(7 citation statements)

References 4 publications

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“…Key questions look as follows: how can we compute coordinates of points settled between the interpolation nodes [18] and how the curve is parameterized? The answers are connected with novel MHR method [19].…”

Section: Mhr Methods and Curve Parameterizationmentioning

confidence: 99%

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Curve Parameterization and Curvature via Method of Hurwitz-Radon Matrices

Jakóbczak¹

2011

Image Processing & Communications

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Section: Mhr Methods and Curve Parameterizationmentioning

confidence: 99%

“…Here are the examples of curvature calculations: Parameterization of the curve (13)- (14), curvature (18) and local maximum curvature for parameter α (19) are possible to be applied via MHR method.…”

Section: Curvaturementioning

confidence: 99%

Curve Parameterization and Curvature via Method of Hurwitz-Radon Matrices

Jakóbczak¹

2011

Image Processing & Communications

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“…Curve modeling [12] by MHR method is connected with possibility of changing the nodes coordinates nodes, what is connected with smaller computational costs then uses all nodes. Future works are connected with: geometrical transformations of curve (translations, rotations, scaling)-only nodes are transformed and new curve (for example contour of the object) for new nodes is reconstructed; estimation of curve length [13]; possibility to apply MHR method to three-dimensional curves [8] [9]; object recognition [14], shape representation [15] [16] and parameterization [17] in image processing; curve extrapolation [18].…”

Section: Discussionmentioning

confidence: 99%

Numerical Quadratures Using the Interpolation Method of Hurwitz-Radon Matrices

Jakóbczak¹

2014

ALAMT

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Mathematics and computer sciences need suitable methods for numerical calculations of integrals. Classical methods, based on polynomial interpolation, have many weak sides: they are useless to interpolate the function that fails to be differentiable at one point or differs from the shape of polynomials considerably. We cannot forget about the Runge's phenomenon. To deal with numerical interpolation and integration dedicated methods should be constructed. One of them, called by author the method of Hurwitz-Radon Matrices (MHR), can be used in reconstruction and interpolation of curves in the plane. This novel method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from that matrices, is described. It is shown how to create the orthogonal and discrete OHR and how to use it in a process of function interpolation and numerical integration. Created from the family of N-1 HR matrices and completed with the identical matrix, system of matrices is orthogonal only for vector spaces of dimensions N = 2, 4 or 8. Orthogonality of columns and rows is very significant for stability and high precision of calculations. MHR method is interpolating the curve point by point without using any formula of function. Main features of MHR method are: accuracy of curve reconstruction depending on number of nodes and method of choosing nodes; interpolation of L points of the curve is connected with the computational cost of rank O(L); MHR interpolation is not a linear interpolation.

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“…So this paper wants to answer the question: how do we interpolate the curve by a set of knots [26]? Nodes on Fig.…”

Section: Shape Representation and Curve Reconstructionmentioning

confidence: 99%

Curve interpolation and shape modeling via probabilistic nodes combination

Jakóbczak

2014

Vietnam J Comput Sci

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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 γ 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.

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Shape Representation and Shape Coefficients via Method of Hurwitz-Radon Matrices

Cited by 21 publications

References 4 publications

Curve Parameterization and Curvature via Method of Hurwitz-Radon Matrices

Curve Parameterization and Curvature via Method of Hurwitz-Radon Matrices

Numerical Quadratures Using the Interpolation Method of Hurwitz-Radon Matrices

Curve interpolation and shape modeling via probabilistic nodes combination

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