Rational Cubic Spline Interpolation for Monotonic Interpolating Curve with C<sup>2</sup> Continuity

Karim, Samsul Ariffin Abdul

doi:10.1051/matecconf/201713104016

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…Among the spline functions, the cubic spline functions [25][26][27][28] are the most preferred functions. The cubic spline functions fit the data very smoothly.…”

Section: Cubic Spline Interpolationmentioning

confidence: 99%

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Exploring Optimality of Piecewise Polynomial Interpolation Functions for Lung Field Modeling in 2D Chest X-Ray Images

2021

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In this paper, a landmark based approach, using five different interpolating polynomials (linear, cubic convolution, cubic spline, PCHIP, and Makima) for modeling of lung field region in 2D chest X-ray images have been presented. Japanese Society of Radiological Technology (JSRT) database which is publicly available has been used for evaluation of the proposed method. Selected radiographs are anatomically landmarked using 17 and 16 anatomical landmark points to represent left and right lung field regions, respectively. Local, piecewise polynomial interpolation is then employed to create additional semilandmark points to form the lung contour. Jaccard similarity coefficients and Dice coefficients have been used to find accuracy of the modeled shape through comparison with the prepared ground truth. With the optimality condition of three intermediate semilandmark points, PCHIP interpolation method with an execution time of 5.04873 s is found to be the most promising candidate for lung field modeling with an average Dice coefficient (DC) of 98.20 and 98.54% (for the left and right lung field, respectively) and with the average Jaccard similarity coefficient (JSC) of 96.47 and 97.13% for these two lung field regions. While performance of Makima and cubic convolution is close to the PCHIP with the same optimality condition, i.e., three intermediate semilandmark points, the optimality condition for the cubic spline method is of at least seven intermediate semilandmark points which, however, does not result in better performance in terms of accuracy or execution time.

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“…Among the spline functions, the cubic spline functions [25][26][27][28] are the most preferred functions. The cubic spline functions fit the data very smoothly.…”

Section: Cubic Spline Interpolationmentioning

confidence: 99%

“…This characteristic makes it differ from the cubic spline function. If h j is the length of jth subinterval given by h j x j+1 − x j (28) then the divided difference δ j will be…”

Section: Piecewise Cubic Hermite Interpolationmentioning

confidence: 99%

Exploring Optimality of Piecewise Polynomial Interpolation Functions for Lung Field Modeling in 2D Chest X-Ray Images

2021

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Wind Velocity Data Interpolation Using Rational Cubic Spline

Karim

Raju

2018

MATEC Web Conf.

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Wind velocity data is always having positive value and the minimum value approximately close to zero. The standard cubic spline interpolation (not-a-knot and natural) as well as cubic Hermite polynomial may be produces interpolating curve with negative values on some subintervals. To cater this problem, a new rational cubic spline with three parameters is constructed. This rational spline will be used to preserve the positivity of the wind velocity data. Numerical results shows that the proposed scheme work very well and give visually pleasing interpolating curve on the given domain.

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Preserving monotone or convex data using quintic trigonometric Bézier curves

Mahzir,

Misro,

Miura

2024

MATH

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<abstract><p>Bézier curves are essential for data interpolation. However, traditional Bézier curves often fail to detect special features that may exist in a data set, such as monotonicity or convexity, leading to invalid interpolations. This study aims to improve the deficiency of Bézier curves by imposing monotonicity or convexity-preserving conditions on the shape parameter and control points. For this purpose, the quintic trigonometric Bézier curves with two shape parameters are used. These techniques constrain only one of the shape parameters, leaving the other free to provide users with more freedom and flexibility in modifying the final curve. To guarantee smooth interpolation, the curvature profiles of the curves are analyzed, which aids in selecting the optimal shape parameter values. The effectiveness of the developed schemes was evaluated by implementing real-life data and data obtained from the existing schemes. Compared with the existing schemes, the developed schemes produce low-curvature interpolation curves with unnoticeable wiggles and turns. The proposed methods also work effectively for both nonuniformly spaced data and negative-valued convex data in real-life applications. When the shape parameter is correctly chosen, the developed interpolants exhibit continuous curvature plots, assuring $ C^2 $ continuity.</p></abstract>

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Rational Cubic Spline Interpolation for Monotonic Interpolating Curve with C² Continuity

Cited by 3 publications

References 15 publications

Exploring Optimality of Piecewise Polynomial Interpolation Functions for Lung Field Modeling in 2D Chest X-Ray Images

Exploring Optimality of Piecewise Polynomial Interpolation Functions for Lung Field Modeling in 2D Chest X-Ray Images

Wind Velocity Data Interpolation Using Rational Cubic Spline

Preserving monotone or convex data using quintic trigonometric Bézier curves

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Rational Cubic Spline Interpolation for Monotonic Interpolating Curve with C2 Continuity

Cited by 3 publications

References 15 publications

Exploring Optimality of Piecewise Polynomial Interpolation Functions for Lung Field Modeling in 2D Chest X-Ray Images

Exploring Optimality of Piecewise Polynomial Interpolation Functions for Lung Field Modeling in 2D Chest X-Ray Images

Wind Velocity Data Interpolation Using Rational Cubic Spline

Preserving monotone or convex data using quintic trigonometric Bézier curves

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Product

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Rational Cubic Spline Interpolation for Monotonic Interpolating Curve with C² Continuity