• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.9
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• pp.1369-1373
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• 2015

Curve subdivision interpolation reconstructs edge well with low complexity, however it lacks of ability to recover texture components, instead. While, neighbor embedding is superior in texture reconstruction. Therefore, in this paper, a novel Super Resolution technique which combines curve subdivision interpolation and neighbor embedding is proposed. First, edge region and non-edge regions are classified. Then, for edge region, the curve subdivision algorithm is used to make two polynomials derived from discrete pixels and adaptive weights are adapted for gradients of 4 different sides to make smooth edge. For non edge region, neighbor-embedding method is used to conserve texture property in original image. Consequently results show that the proposed technique conserves sharp edges and details in texture better, simultaneously.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.665-672
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• 2005

By its simplicity and efficiency, subdivision is a widely used technique in computer graphics, computer aided design and data compression. In this paper we prove a regularity theorem for ternary interpolatory subdivision scheme that can be applied to non-stationary subdivision. This theorem converts the convergence of the limit curve of a ternary interpolatory subdivision to the analysis of the rate of the contraction of differences of the polygons.

• International Journal of CAD/CAM
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• v.5 no.1
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• pp.29-38
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• 2005

A non-uniform 3-point ternary interpolatory subdivision scheme with variable subdivision weights is introduced. Its support is computed. The $C^0$ and $C^1$ convergence analysis are presented. To elevate its controllability, a modified edition is proposed. For every initial control point on the initial control polygon a shape weight is introduced. These weights can be used to control the shape of the corresponding subdivision curve easily and purposefully. The role of the initial shape weight is analyzed theoretically. The application of the presented schemes in designing smooth interpolatory curves and surfaces is discussed. In contrast to most conventional interpolatory subdivision scheme, the presented subdivision schemes have better locality. They can be used to generate $C^0$ or $C^1$ interpolatory subdivision curves or surfaces and control their shapes wholly or locally.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.6
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• pp.69-74
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• 2023

In this paper we review techniques for building and analyzing wavelets on irregular point sets in one and two dimensions. In particular we focus on subdivision schemes and commutation. Subdivision means the skill that approximates the initial lines or mesh into a tender curve or a curved surface by continuous partitioning operation. The key to generalizing wavelet constructions to non-traditional settings is the use of generalized subdivision. The first generation setting is already connected with subdivision schemes, but they become even more important in the construction of second generation wavelets. Subdivision schemes provide fast algorithms, create a natural multi-resolution structure, and yield the underlying scaling functions and wavelets we seek.