4.10.3 Fractal Representations, Fractal Dimension

Chapter Contents (Back)
Fractals. Representation, Fractals. See also Fractal Texture Segmentation. See also Fractals for Texture Analysis and Description, Fractal Dimension.

Mandelbrot, B.B.,
The Fractal Geometry of Nature,
San Francisco: Freeman1968. Fractals. The basic BibRef 6800 Bookon fractals. BibRef

Mandelbrot, B.B.,
Fractals: Form, Chance, and Dimension,
San Francisco: Freeman1977. Fractals. The basic BibRef 7700 Bookon fractals. BibRef

Musgrave, F.K., and Mandelbrot, B.B.,
The art of fractal landscapes,
IBMRD(35), No. 4, 539, July 1991, pp. 535-536. BibRef 9107

Stevens, R.J., Lehar, A.F., and Perston, F.H.,
Manipulation and Presentation of Multidimensional Image Data Using the Peano Scan,
PAMI(5), No. 5, September 1983, pp. 520-526. BibRef 8309

Kube, P.R.[Paul R.], and Pentland, A.P.[Alex P.],
On the Imaging of Fractal Surfaces,
PAMI(10), No. 5, September 1988, pp. 704-707.
IEEE DOI Relate power spectrum of a surface with that of the image. BibRef 8809

Yokoya, N., Yamamoto, K., Funakubo, N.,
Fractal-Based Analysis of 3D Natural Surface Shapes and Their Application to Terrain Modeling,
CVGIP(46), No. 3, June 1989, pp. 284-302.
WWW Link. BibRef 8906

Heijmans, H.J.A.M., Toet, A.,
Morphological Sampling,
CVGIP(54), No. 3, November 1991, pp. 384-400.
WWW Link. BibRef 9111

Super, B.J., Bovik, A.C.,
Localized Measurement of Image Fractal Dimension Using Gabor Filters,
JVCIR(2), 1991, pp. 114-128. BibRef 9100

Jaggard, D.L., (Ed.)
Special Section on Fractals in Electrical Engineering,
PIEEE(81), No. 10, October 1993, pp. 1423-1533. BibRef 9310

Huang, Q., Lorch, J.R., Dubes, R.C.,
Can the Fractal Dimension of Images Be Measured,
PR(27), No. 3, March 1994, pp. 339-349.
WWW Link. BibRef 9403

Bell, S.B.M.,
Fractals: A Fast, Accurate and Illuminating Algorithm,
IVC(13), No. 4, May 1995, pp. 253-257.
WWW Link. BibRef 9505

Krueger, W.M., Jost, S.D., Rossi, K., Axen, U.,
On Synthesizing Discrete Fractional Brownian-Motion with Applications to Image-Processing,
GMIP(58), No. 4, July 1996, pp. 334-344. 9609
For Fractal Dimension estimation. BibRef

Tang, Y.Y., Li, B.F., Ma, H., Liu, J.M.,
Ring-Projection-Wavelet-Fractal Signatures: A Novel-Approach To Feature-Extraction,
CirSysSignal(45), No. 8, August 1998, pp. 1130-1134. 9809
BibRef

Tang, Y.Y., Li, B.F., Ma, H., Liu, J.M., Suen, C.,
A Novel Approach to Optical Character Recognition Based on Ring-Projection-Wavelet-Fractal Signatures,
ICPR96(II: 325-329).
IEEE DOI 9608
(Hong Kong Baptist Univ., HK) BibRef

Lonardi, S.[Stefano], Sommaruga, P.[Paolo],
Fractal image approximation and orthogonal bases,
SP:IC(14), No. 5, March 1999, pp. 413-423.
WWW Link. BibRef 9903

Zeng, X., Koehl, L., Vasseur, C.,
Design and implementation of an estimator of fractal dimension using fuzzy techniques,
PR(34), No. 1, January 2001, pp. 151-169.
WWW Link. 0010
BibRef

Carlin, M.[Mats],
Measuring the complexity of non-fractal shapes by a fractal method,
PRL(21), No. 11, October 2000, pp. 1013-1017. 0010
BibRef

McGunnigle, G., Chantler, M.J.,
Evaluating Kube and Pentland's fractal imaging model,
IP(10), No. 4, April 2001, pp. 534-542.
IEEE DOI 0104
See also On the Imaging of Fractal Surfaces. BibRef

Lundmark, A., Wadströmer, N., Li, H.,
Hierarchical Subsampling Giving Fractal Regions,
IP(10), No. 1, January 2001, pp. 167-173.
IEEE DOI 0101
BibRef

Tolle, C.R., McJunkin, T.R., Gorsich, D.J.,
Suboptimal minimum cluster volume cover-based method for measuring fractal dimension,
PAMI(25), No. 1, January 2003, pp. 32-41.
IEEE DOI 0301
BibRef

Marsh, R.[Ronald],
FractalNet: A biologically inspired neural network approach to fractal geometry,
PRL(24), No. 12, August 2003, pp. 1881-1887.
WWW Link. 0304
BibRef

Chang, H.T.[Hsuan T.],
Arbitrary affine transformation and their composition effects for two-dimensional fractal sets,
IVC(22), No. 13, 1 November 2004, pp. 1117-1127.
WWW Link. 0410
BibRef

Duh, D.J., Jeng, J.H., Chen, S.Y.,
DCT based simple classification scheme for fractal image compression,
IVC(23), No. 13, 29 November 2005, pp. 1115-1121.
WWW Link. 0512
BibRef

Xu, S.J.[Shu-Jian], Weng, Y.J.[Yong-Ji],
A new approach to estimate fractal dimensions of corrosion images,
PRL(27), No. 16, December 2006, pp. 1942-1947.
WWW Link. 0611
Corrosion image; FD determination; Image FD; Pit diameter distribution; Pit depth distribution; Relativity analysis BibRef

Ozawa, K.[Kuzumasa],
Dual fractals,
IVC(26), No. 5, May 2008, pp. 622-631.
WWW Link. 0803
BibRef
Earlier:
Dual Fractals: Theory and Applications,
SCIA01(P-W5). 0206
Dual fractals; Dual-similarity; Hutchinson operator; Image coding; Template matching; Secret sharing; Feature extraction BibRef


Zhang, K.[Kai], Wang, S.[Shucai],
Application of slit island method in the measure of the fractal dimensions of pore section border in eggshells,
IASP11(484-487).
IEEE DOI 1112
BibRef

Vrscay, E.R.[Edward R.],
Continuous Evolution of Fractal Transforms and Nonlocal PDE Imaging,
ICIAR06(I: 446-457).
Springer DOI 0610
BibRef

Bouridane, A., Alexander, A., Nibouche, M., Crookes, D.,
Application of Fractals to the Detection and Classification of Shoeprints,
ICIP00(Vol I: 474-477).
IEEE DOI 0008
BibRef

Chu, H.T., Chen, C.C.,
A Fast Algorithm for Generating Fractals,
ICPR00(Vol III: 302-305).
IEEE DOI 0009
BibRef

Shen, J., Zhang, T.X., Li, J.,
New Fractal Feature with Application in Image Analysis,
SCIA99(Image Analysis). BibRef 9900

Skarbek, W.[Wladyslaw],
On Convergence of Discrete and Selective Fractal Operators,
CAIP99(201-208).
Springer DOI 9909
BibRef

Vehel, J.L.[J. Levy],
About Lacunarity, Some Links Between Fractal and Integral Geometry and an Application to Texture Segmentation,
ICCV90(380-384).
IEEE DOI BibRef 9000

Feng, J., Lin, W., Chen, C.,
Fractional Box-Counting Approach to Fractal Dimension Estimation,
ICPR96(II: 854-858).
IEEE DOI 9608
(Northwestern Univ., USA) BibRef

Chernov, V.,
Tauber Theorems for Dirichlet Series and Fractals,
ICPR96(II: 656-661).
IEEE DOI 9608
(Image Processing Systems Inst., RUS) BibRef

Nikiel, S.S.,
Noise suppression based on the fractal dimension estimates,
ICIP96(II: 193-196).
IEEE DOI 9610
BibRef

Swarnakar, V., Acharya, R.S.,
Fractal dimension estimation using continuous alternating sequential filter pyramid,
ICIP95(III: 652-655).
IEEE DOI 9510
BibRef

Talukdar, D., Acharya, R.,
Estimation of fractal dimension using alternating sequential filters,
ICIP95(I: 231-234).
IEEE DOI 9510
BibRef

Chapter on Computational Vision, Regularization, Connectionist, Morphology, Scale-Space, Perceptual Grouping, Wavelets, Color, Sensors, Optical, Laser, Radar continues in
Fractal Based Coding and Compression, Fractal Coding, Fractal Compression .


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