Fractal-based analysis and interpolation of 3D natural surface shapes and their application to terrain modeling

Yokoya, Naokazu; Yamamoto, Kazuhiko; Funakubo, Noboru

doi:10.1016/0734-189x(89)90034-0

Cited by 106 publications

(24 citation statements)

References 11 publications

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“…However, the pixels in new interpolated image can not maintain the information of the original image. Yokoya proposed an image interpolation method based on fractal geometry (Yokoya (1989)), which used the statistical self-similarity between gray levels of neighboring pixels to interpolate. Whereas it is difficult to accurately compute the self-similarity transformation using the traditional fractal scheme.…”

Section: Heterogeneous Object Slicing With Geometric Constraintmentioning

confidence: 99%

Heterogeneous Object Modeling for Rapid Prototyping

Xiao-jun¹

2011

Rapid Prototyping Technology - Principles and Functional Requirements

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Section: Heterogeneous Object Slicing With Geometric Constraintmentioning

confidence: 99%

Heterogeneous Object Modeling for Rapid Prototyping

Xiao-jun¹

2011

Rapid Prototyping Technology - Principles and Functional Requirements

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“…However, the pixels in new interpolated image can not maintain the information of the original image. Yokoya proposed an image interpolation method based on fractal geometry [25], which used the statistical self-similarity between gray levels of neighboring pixels to interpolate. Whereas it is difficult to accurately compute the self-similarity transformation using the traditional fractal scheme.…”

Section: Materials Layer Interpolationmentioning

confidence: 99%

Heterogeneous Object Slicing with Geometric Contour Constraint

Xiao-jun¹,

Wang²,

Liu³

2009

Computer-Aided Design and Applications

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Slicing contour generation for geometric model is a vital process in rapid prototyping manufacturing. When slicing a heterogeneous object (HO), we take into account not only the geometric slicing but also the gradient material information. In this paper, we develop a new method to slice a heterogeneous object where the geometric contours are taken as constraints to resample the heterogeneous information through pixel overlap interpolation and tri-linear interpolation, which can maintain the original heterogeneous material information as much as possible and the slicing boundary as accurate as possible. The novelty of our method is that the gradient material resampling with geometry constraint can guarantee the crisp boundary of the HO slices when the gradient information is converted for geometric space to image space. Experimental results validate that our method can create heterogeneous object slices with more accurate boundary than simple interpolation scheme.

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“…Yokoya [38] also assumed that intensity in images is distributed by a fractal Brownian function, and that…”

Section: B(rt) = R'12b(t)mentioning

confidence: 99%

Fractal Modeling of Natural Terrain: Analysis and Surface Reconstruction with Range Data

Arakawa

Krotkov

1996

Graphical Models and Image Processing

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In this paper we address two issues in modeling natural terrain using fractal geometry: estimation of fractal dimension, and fractal surface reconstruction. For estimation of fractal dimension, we extend the fractal Brownian function approach to accommodate irregularly sampled data, and we develop methods for segmenting sets of points exhibiting self-similarity over only certain scales. For fractal surface reconstruction, we extend Szeliski's regularization with fractal priors method to use a temperature parameter that depends on fractal dimension. We demonstrate both estimation and reconstruction with noisy range imagery of natural terrain. D 1% Academic press, Inc.

show abstract

Fractal-based analysis and interpolation of 3D natural surface shapes and their application to terrain modeling

Cited by 106 publications

References 11 publications

Heterogeneous Object Modeling for Rapid Prototyping

Heterogeneous Object Modeling for Rapid Prototyping

Heterogeneous Object Slicing with Geometric Contour Constraint

Fractal Modeling of Natural Terrain: Analysis and Surface Reconstruction with Range Data

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