A Shape Preserving Verification Technique for Parametric Curves

Dejdumrong, Natasha

doi:10.1109/cgiv.2007.12

Cited by 7 publications

(3 citation statements)

References 11 publications

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“…Our paper aims at giving the positive answer to this question. There exists several well established methods: spline functions [13], shape-preserving techniques [14], subdivision algorithms [15], Bezier curves, B-splines, NURBS [16] and others [12] to overcome difficulties of polynomial interpolation, but matrix interpolation MHR (based on simple matrix calculations with low computational costs) seems to be quite novel in the area of shape reconstruction. In comparison MHR method with Bézier curves, Hermite curves and B-curves (B-splines) or NURBS one unpleasant feature of these curves must be mentioned: small change of one characteristic point can make big change of whole reconstructed curve [17].…”

Section: Shape Reconstruction Via Mhr Methodsmentioning

confidence: 99%

Implementation of Hurwitz-Radon Matrices in Shape Representation

Jakóbczak

2010

Advances in Intelligent and Soft Computing

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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. Shape is represented by the set of 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. MHR method is interpolating the curve point by point without using any formula or function.

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Section: Shape Reconstruction Via Mhr Methodsmentioning

confidence: 99%

Implementation of Hurwitz-Radon Matrices in Shape Representation

Jakóbczak

2010

Advances in Intelligent and Soft Computing

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“…Relation between two surfaces is determined by convex hull property and cuboidal smallest convection hull property in both the cases intersection of segment of line done by approximation final patch by first order cubic Bézier patch and planer triangle and then intersection done using recursive subdivision and incremental tracing. [18] expressed Cubic Bézier curve parametric forms shape preservation is difficu lt and various parameters effects like position and order of curve, types of curve, weight of curve and duplicat ion of control points. A technique is derived based on these to preserve shape of CBC by normalizing total positivity and corner cutting algorithm.…”

Section: Additional Associated Workmentioning

confidence: 99%

Cubic Bézier Surface Machining: A State of an Art Review

2014

IJAERD

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“…These methods have many weak sides [21] and are not sufficient for curve interpolation in the situations when the curve cannot be built by polynomials or trigonometric functions. Also, there exist several well-established methods of curve modeling, for example shape-preserving techniques [22], subdivision algorithms [23] and others [24] to overcome the difficulties of polynomial interpolation, but probabilistic interpolation with nodes combination seems to be quite novel in the area of shape modeling. The proposed 2D curve interpolation is the functional modeling via any elementary functions and it helps us to fit the curve during the computations.…”

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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A Shape Preserving Verification Technique for Parametric Curves

Cited by 7 publications

References 11 publications

Implementation of Hurwitz-Radon Matrices in Shape Representation

Implementation of Hurwitz-Radon Matrices in Shape Representation

Cubic Bézier Surface Machining: A State of an Art Review

Curve interpolation and shape modeling via probabilistic nodes combination

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