7.10.8 Fractals for Texture Analysis and Description, Fractal Dimension

Peleg, S., Naor, J., Hartley, R.L., and Avnir, D.,
Multiple Resolution Texture Analysis and classification,
PAMI(6), No. 4, July 1984, pp. 518-523. Refutes the Fractal theory of texture made by Pentland. BibRef 8407

Geronimo, J.S.[Jeffrey S.], Hardin, D.P.[Douglas P.], and Massopust, P.R.[Peter R.],
Fractal Surfaces, Multiresolution Analyses, and Wavelet Transforms,
MDSG94(275) BibRef 9400

Jin, X.C., Ong, S.H., and Jayasooriah,
A Practical Method for Estimating Fractal Dimension,
PRL(16), 1995, pp. 457-464. BibRef 9500

Garding, J.,
Properties of Fractal Intensity Surfaces,
PRL(8), December 1988, pp. 319-324. BibRef 8812
And: ISRN KTH/NA/P-87/16-SE. BibRef

Neil, G., Curtis, K.M.,
Shape-Recognition Using Fractal Geometry,
PR(30), No. 12, December 1997, pp. 1957-1969.
WWW Version. 9805
BibRef

Penn, A.I., Loew, M.H.,
Estimating Fractal Dimension with Fractal Interpolation Function Models,
MedImg(16), No. 6, December 1997, pp. 930-937.
IEEE Top Reference. 9803
BibRef

Biswas, M.K., Ghose, T., Guha, S., Biswas, P.K.,
Fractal Dimension Estimation For Texture Images: A Parallel Approach,
PRL(19), No. 3-4, March 1998, pp. 309-313. 9807
BibRef

Dodd, N.,
Multispectral Texture Synthesis Using Fractal Concepts,
PAMI(9), No. 5, September 1987, pp. 703-707. Texture Synthesis. BibRef 8709

Rinaldo, R., Zakhor, A.,
Inverse and Approximation Problem for Two-Dimensional Fractal Sets,
IP(3), No. 6, November 1994, pp. 802-820.
IEEE DOI Link BibRef 9411

Meisel, L.V., Johnson, M.A.,
Convergence of Numerical Box-Counting and Correlation Integral Multifractal Analysis Techniques,
PR(30), No. 9, September 1997, pp. 1565-1570.
WWW Version. 9708
BibRef

Emerson, C.W.[Charles W.], Lam, N.S.N.[Nina Siu-Ngan], Quattrochi, D.A.[Dale A.],
Multi-Scale Fractal Analysis of Image Texture and Patterns,
PhEngRS(65), No. 1, January 1999, pp. 51-62. How fractal dimension changes with scale BibRef 9901

Qiu, H.L.[Hong-Lie], Lam, N.S.N.[Nina Siu-Ngan], Quattrochi, D.A.[Dale A.], Gamon, J.A.[John A.],
Fractal Characterization of Hyperspectral Imagery,
PhEngRS(65), No. 1, January 1999, pp. 63-72. BibRef 9901

Asvestas, P., Matsopoulos, G.K., Nikita, K.S.,
Estimation of fractal dimension of images using a fixed mass approach,
PRL(20), No. 3, March 1999, pp. 347-354. BibRef 9903

Chen, Y.Q., Bi, G.,
On Texture Classification Using Fractal Dimension,
PRAI(13), No. 6, September 1999, pp. 929. 0005
BibRef

Moon, Y.H., Kim, H.S., Kim, J.H.,
A Fast Fractal Decoding Algorithm Based on the Selection of an Initial Image,
IP(9), No. 5, May 2000, pp. 941-945.
IEEE DOI Link 0005
BibRef

Ilow, J., Leung, H.,
Self-similar texture modeling using FARIMA processes with applications to satellite images,
IP(10), No. 5, May 2001, pp. 792-797.
IEEE DOI Link 0105
BibRef

Brochard, J.[Jacques], Khoudeir, M.[Majdi], Augereau, B.[Bertrand],
Invariant feature extraction for 3D texture analysis using the autocorrelation function,
PRL(22), No. 6-7, May 2001, pp. 759-768.
HTML Version. 0105
BibRef

Brochard, J.[Jacques], Khoudeir, M.[Majdi],
Estimation of movement parameters of 3D textured surfaces using the autocorrelation function,
PRL(24), No. 12, August 2003, pp. 2031-2045.
WWW Version. 0304
BibRef

Brochard, J.[Jacques], Khoudeir, M.[Majdi],
Histogram Characterization of Colored textures Using One-Dimensional Moments and Chromaticity Diagram,
VI02(428).
PDF Version. 0208
BibRef

Bringier, B.[Benjamin], Helbert, D.[David], Khoudeir, M.[Majdi],
Photometric reconstruction of a dynamic textured surface from just one color image acquisition,
JOSA-A(25), No. 3, March 2008, pp. 566-574.
WWW Version. 0804
BibRef

Tao, Y.[Yu], Lam, E.C.M.[Ernest C.M.], Tang, Y.Y.[Yuan Y.],
Feature extraction using wavelet and fractal,
PRL(22), No. 3-4, March 2001, pp. 271-287.
HTML Version. 0105
BibRef
Earlier:
Extraction of Fractal Feature for Pattern Recognition,
ICPR00(Vol II: 527-530).
IEEE DOI Link
HTML Version. 0009
BibRef

Tao, Y.[Yu], Ioerger, T.R., Sacchettini, J.C.,
Extracting fractal features for analyzing protein structure,
ICPR02(II: 482-485).
IEEE DOI Link 0211
BibRef

Tang, Y.Y.[Yuan Y.], Tao, Y.[Yu], Lam, E.C.M.[Ernest C.M.],
New method for feature extraction based on fractal behavior,
PR(35), No. 5, May 2002, pp. 1071-1081.
WWW Version. 0202
BibRef

Tang, Y.Y.[Yuan Y.], Tao, Y.[Yu], Lam, E.C.M.,
The application of fractal analysis to feature extraction,
ICIP99(II:875-879).
IEEE Abstract. IEEE Top Reference. BibRef 9900

Turiel, A.[Antonio],
Relevance of multifractal textures in static images,
ELCVIA(1), No. 1, 2002, pp. 35-49.
WWW Version. 0304
BibRef

Drakopoulos, V., Nikolaou, N.P.,
Efficient computation of the Hutchinson metric between digitized images,
IP(13), No. 12, December 2004, pp. 1581-1588.
IEEE DOI Link 0412
Based on shape as projected on the screen. In Fractal processing. BibRef

Sun, W.[Wanxiao],
Three New Implementations of the Triangular Prism Method for Computing the Fractal Dimension of Remote Sensing Images,
PhEngRS(72), No. 4, April 2006, pp. 373-382.
WWW Version. 0610
BibRef

Levit, M., Roy, D.,
Interpretation of Spatial Language in a Map Navigation Task,
SMC-B(37), No. 3, June 2007, pp. 667-679.
IEEE DOI Link 0706
BibRef

Campisi, P., Maiorana, E., Neri, A.,
Video Textures Fractal Modeling,
SPLetters(14), No. 6, June 2007, pp. 405-408.
IEEE DOI Link 0706
BibRef

Xu, Y.[Yong], Ji, H.[Hui], Fermüller, C.[Cornelia],
Viewpoint Invariant Texture Description Using Fractal Analysis,
IJCV(83), No. 1, June 2009, pp. xx-yy.
Springer DOI Link 0903
BibRef
Earlier:
A Projective Invariant for Textures,
CVPR06(II: 1932-1939).
IEEE DOI Link 0606
Multifractal spectrum to be invariant to projections. BibRef

Jeng, J.H.[Jyh-Horng], Tseng, C.C.[Chun-Chieh], Hsieh, J.G.[Jer-Guang],
Study on Huber Fractal Image Compression,
IP(18), No. 5, May 2009, pp. 995-1003.
IEEE DOI Link 0904
Huber regression embedded in fractal representation. BibRef

Pi, M., Li, H.,
Fractal indexing with the joint statistical properties and its application in texture image retrieval,
IET-IPR(2), No. 4, August 2008, pp. 218-230.
WWW Version. 0905
BibRef

Li, J.[Jian], Du, Q.[Qian], Sun, C.X.[Cai-Xin],
An improved box-counting method for image fractal dimension estimation,
PR(42), No. 11, November 2009, pp. 2460-2469.
Elsevier DOI Link
WWW Version. 0907
BibRef
Earlier: A1, A3, A2:
A New Box-Counting Method for Estimation of Image Fractal Dimension,
ICIP06(3029-3032). 0610

IEEE DOI Link Fractal dimension; Box-counting dimension; Fractional Brownian motion; Texture image; Remote sensing image BibRef

Ebrahimi, M.[Mehran],
A Necessary and Sufficient Contractivity Condition for the Fractal Transform Operator,
JMIV(33), No. 3, November 2009, pp. xx-yy.
Springer DOI Link 0909
BibRef

Wang, X.Y.[Xing-Yuan], Li, F.P.[Fan-Ping], Wang, S.G.[Shu-Guo],
Fractal image compression based on spatial correlation and hybrid genetic algorithm,
JVCIR(20), No. 8, November 2009, pp. 505-510,.
Elsevier DOI Link
WWW Version. 0911
Fractal image compression; Block coding; PIFS; Spatial correlation; Hybrid genetic algorithm; Simulated annealing; Neighborhood; Dyadic mutation operator BibRef

Ouahabi, A.[Abdeldjalil], Jaffard, S.[Stephane], Aouit, D.A.[Djedjiga Ait],
Wavelet based Multifractal Analysis in Fractography,
IPTA08(1-8).
IEEE DOI Link 0811
BibRef

Chauveau, J.[Julien], Rousseau, D.[David], Chapeau-Blondeau, F.[François],
Pair Correlation Integral for Fractal Characterization of Three-Dimensional Histograms from Color Images,
ICISP08(200-208).
Springer DOI Link 0807
BibRef

Koenig, E.[Emilie], Chainais, P.[Pierre],
Multifractal Analysis on the Sphere,
ICISP08(613-621).
Springer DOI Link 0807
BibRef

Backes, A.R.[André R.], Bruno, O.M.[Odemir M.],
Plant Leaf Identification Using Multi-scale Fractal Dimension,
CIAP09(143-150).
Springer DOI Link 0909
BibRef
Earlier:
A New Approach to Estimate Fractal Dimension of Texture Images,
ICISP08(136-143).
Springer DOI Link 0807
BibRef

Backes, A.R.[André R.], Bruno, O.M.[Odemir M.], Campiteli, M.G.[Mônica G.], Martinez, A.S.[Alexandre S.],
Deterministic Tourist Walks as an Image Analysis Methodology Based,
CIARP06(784-793).
Springer DOI Link 0611
Texture characterization based on scan pattern. BibRef

Dolez, B.[Benoit], Vincent, N.[Nicole],
Sample Selection in Textured Images,
ICIP07(II: 221-224).
IEEE DOI Link 0709
Texture learning based on fractals. BibRef

Varma, M.[Manik], Garg, R.[Rahul],
Locally Invariant Fractal Features for Statistical Texture Classification,
ICCV07(1-8).
IEEE DOI Link 0710
BibRef

Cao, G.[Guitao], Shi, P.F.[Peng-Fei], Hu, B.[Bing],
Texture Classification Based on the Fractal Performance of the Moment Feature Images,
ICIAR05(762-769).
Springer DOI Link 0509
BibRef

Grazzini, J., Turiel, A., Yahia, H.,
Presegmentation of High-Resolution Satellite Images with a Multifractal Reconstruction Scheme Based on an Entropy Criterium,
ICIP05(I: 649-652).
IEEE DOI Link 0512
BibRef

Pi, M.H.[Ming Hong], Basu, A., Mandal, M.K., Li, H.[Hua],
A comparison of non-orthogonal and orthogonal fractal decoding,
ICIP04(I: 505-508).
IEEE DOI Link 0505
BibRef

Zhang, P., Bui, T.D., Suen, C.Y.,
Recognition of similar objects using 2-D wavelet-fractal feature extraction,
ICPR02(II: 316-319).
IEEE DOI Link 0211
BibRef

Valdés, J.J.[Julio J.], Molina, L.C.[Luis C.], Espinosa, S.[Sergio],
Behavior Analysis of Fractal Features for Texture Description in Digital Images: an Experimental Study,
ICPR00(Vol III: 905-908).
IEEE DOI Link 0009
BibRef

Deguy, S., Debain, C., Benassi, A.,
Classification of Texture Images using Multi-scale Statistical Estimators of Fractal Parameters,
BMVC00(xx-yy).
PDF Version. 0009
BibRef

Anh, V.V., Maeda, J., Tieng, Q.M., Tsui, H.T.,
Multifractal Texture Analysis and Classification,
ICIP99(IV:445-449).
IEEE Abstract. IEEE Top Reference. BibRef 9900

Anh, V.V.[Vo V.], Maeda, J.[Junji], Ishizaka, T.[Tohru], Suzuki, Y.[Yukinori], Tieng, Q.M.[Quang M.],
Two-dimensional fractal segmentation of natural images,
CIAP97(I: 287-294).
WWW Version. 9709
BibRef

Betti, A., Barni, M., Mecocci, A.,
Using a wavelet-based fractal feature to improve texture discrimination on SAR images,
ICIP97(I: 251-254).
IEEE DOI Link 9710
BibRef

Fioravanti, S.[Stefano], Giusto, D.D.[Daniele D.],
Texture recognition by the q-th order fractal analysis,
CAIP93(283-290).
Springer DOI Link 9309
BibRef

Boulecane, H., Vincent, N., Ruffier, M., Emptoz, H.,
Control of composite material strucrure by fractal methods,
CAIP93(726-731).
Springer DOI Link 9309
BibRef

Levy Vehel, J., Mignot, P., Berroir, J.P.,
Multifractals, texture, and image analysis,
CVPR92(661-664).
IEEE Abstract. IEEE Top Reference. 0403
BibRef

Levy Vehel, J.,
Fractal probability functions-an application to image analysis,
CVPR91(378-383).
IEEE Abstract. IEEE Top Reference. 0403
BibRef

Albregtsen, F., Nielsen, B., Yogesan, K.,
Fractal dimension, only a fraction of the truth?,
ICPR92(III:733-736).
IEEE DOI Link 9208
BibRef

Chapter on 2-D Feature Analysis, Extraction and Representations, Shape, Skeletons, Texture continues in
Autoregressive Texture Models .