Rational Bi-Quartic Spline With Six Parameters for Surface Interpolation With Application in Image Enlargement

Karim, Samsul Ariffin Abdul

doi:10.1109/access.2020.3002387

Cited by 14 publications

(4 citation statements)

References 20 publications

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“…In terms of application in computer graphics, the resulting curves are smooth and highly suitable in designing any computer graphics shape and model. One possible future extension is the generalization of the proposed subdivision scheme in scattered data interpolation and image interpolation problems [33,34].…”

Section: Discussionmentioning

confidence: 99%

A 3-point point quinary approximating subdivision schemes and its application in geometric modeling and computer graphics

Ghaffar,

Mustafa,

Abdul Karim

2024

ITM Web Conf.

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This article discusses the significance of a subdivision scheme with shape parameters in geometric modeling and computational geometry. A new recursive method for generating the mask of 3-point quinary approximating subdivision schemes (ASSs) is presented. The proposed subdivision scheme exhibits all the geometric properties and offers better shape control than non-parametric subdivision schemes. The article includes several numerical examples to demonstrate the high practical value of the proposed schemes in geometric modeling and computer graphics.

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Section: Discussionmentioning

confidence: 99%

A 3-point point quinary approximating subdivision schemes and its application in geometric modeling and computer graphics

Ghaffar,

Mustafa,

Abdul Karim

2024

ITM Web Conf.

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“…This will increase the resolution when we deal with the upscaling images especially for RGB type images. Future studies will be focusing on the application of the proposed subdivision scheme in RGB image interpolation such as fruit and medical imaging images [11,12].…”

Section: Discussionmentioning

confidence: 99%

Advancing Curve and Surface Images Modeling with Two-Parameters Polynomial-Based Quaternary Subdivision Schemes

Mustafa,

Iqbal,

Mustafa

et al. 2024

ITM Web Conf.

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In the context of this paper, we introduce a novel polynomial function that relies on two parameters. This polynomial enables the creation of a family of quaternary subdivision schemes for curve and surface modeling. One of these parameters is responsible for determining the specific member of the family while the other parameter provides the means to finely control the shape of the resulting curve or the regular surface images. This two-parameter approach adds significant versatility to the subdivision schemes to meet specific requirements and preferences. The exploration of various family members within this class of quaternary schemes is a focal point of our research. By adjusting the parameters, we investigate and delineate the distinctive characteristics of specific family members. This provides valuable insights into how these schemes can be harnessed to achieve various modeling goals. This insight empowers users to select the most suitable family members in accordance with their specific needs and design objectives.

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“…Moreover, it can also be observed from Tables 2, 4, 6 and 8 that this technique is efficient because it needed fewer iterations to obtain the subdivision depths of the scheme within the user-defined error tolerance. Furthermore, other possible extensions are in image processing and scattered data interpolation [47][48][49].…”

Section: Discussionmentioning

confidence: 99%

An Efficient Computational Approach for Computing Subdivision Depth of Non-Stationary Binary Subdivision Schemes

et al. 2023

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Subdivision schemes are equipped with some rules that take a polygon as an input and produce smooth curves or surfaces as an output. This presents the issue of how accurately the polygon approximates the limit curve and surface. What number of iterations/levels would be necessary to achieve the required shape at a user-specified error tolerance? In fact, several methods have been introduced in the case of stationary schemes to address the issue in terms of the error bounds (distance between polygon/polyhedron and limiting shape) and subdivision depth (the number of iterations required to obtain the result at a user-specified error tolerance). However, in the case of non-stationary schemes, this topic needs to be further studied to meet the requirements of new practical applications. This paper highlights a new approach based on a convolution technique to estimate error bounds and subdivision depth for non-stationary schemes. The given technique is independent of any condition on the coefficient of the non-stationary subdivision schemes, and it also produces the best results with the least amount of computational effort. In this paper, we first associated constants with the vectors generated by the given non-stationary schemes, then formulated an expression for the convolution product. This expression gives real values, which monotonically decrease with the increase in the order of the convolution in both the curve and surface cases. This convolution feature plays an important role in obtaining the user-defined error tolerance with fewer iterations. It achieves a trade-off between the number of iterations and user-specified errors. In practice, more iterations are needed to achieve a lower error rate, but we achieved this goal by using fewer iterations.

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Rational Bi-Quartic Spline With Six Parameters for Surface Interpolation With Application in Image Enlargement

Cited by 14 publications

References 20 publications

A 3-point point quinary approximating subdivision schemes and its application in geometric modeling and computer graphics

A 3-point point quinary approximating subdivision schemes and its application in geometric modeling and computer graphics

Advancing Curve and Surface Images Modeling with Two-Parameters Polynomial-Based Quaternary Subdivision Schemes

An Efficient Computational Approach for Computing Subdivision Depth of Non-Stationary Binary Subdivision Schemes

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