Shape analysis using fractal dimension: a curvature based approach

The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from a shape by applying a multi-scale approach to the calculus of the fractal dimension. The fractal dimension is estimated by applying the curvature scale-space technique to the original shape. By applying a multi-scale transform to the calculus, we obtain a set of descriptors which is capable of describing the shape under investigation with high precision. We validate the computed descriptors in a classification process. The results demonstrate that the novel technique provides highly reliable descriptors, confirming the efficiency of the proposed method.

[1]  André Ricardo Backes,et al.  A comparative study on multiscale fractal dimension descriptors , 2012, Pattern Recognit. Lett..

[2]  G. Smith,et al.  Numerical Solution of Partial Differential Equations: Finite Difference Methods , 1978 .

[3]  Mats Carlin,et al.  Measuring the complexity of non-fractal shapes by a fractal method , 2000, Pattern Recognit. Lett..

[4]  André Ricardo Backes,et al.  A Novel Approach to Estimate Fractal Dimension from Closed Curves , 2009, CAIP.

[5]  David E. Booth,et al.  Applied Multivariate Analysis , 2003, Technometrics.

[6]  B. Mandelbrot.  Fractal Geometry of Nature , 1984 .

[7]  Fatos T. Yarman-Vural,et al.  BAS: a perceptual shape descriptor based on the beam angle statistics , 2003, Pattern Recognit. Lett..

[8]  Luciano da Fontoura Costa,et al.  Shape Analysis and Classification: Theory and Practice , 2000 .

[9]  O. Bruno,et al.  Leaf shape analysis using the multiscale Minkowski fractal dimension, a new morphometric method: a study with Passiflora (Passifloraceae) , 2005 .

[10]  L Billeci,et al.  Assessment and comparison of neural morphology through metrical feature extraction and analysis in neuron and neuron–glia cultures , 2009, Journal of biological physics.

[11]  Paul Wintz,et al.  Digital image processing (2nd ed.) , 1987 .

[12]  Sadegh Abbasi,et al.  Matching shapes with self-intersections:application to leaf classification , 2004, IEEE Transactions on Image Processing.

[13]  C. Tricot.  Curves and Fractal Dimension , 1994 .

[14]  B. Everitt,et al.  Applied Multivariate Data Analysis: Everitt/Applied Multivariate Data Analysis , 2001 .

[15]  Luciano da Fontoura Costa,et al.  A graph-based approach for multiscale shape analysis , 2004, Pattern Recognit..

[16]  Sven Loncaric,et al.  A survey of shape analysis techniques , 1998, Pattern Recognit..

[17]  Farzin Mokhtarian,et al.  A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Andrew P. Witkin,et al.  Scale-space filtering: A new approach to multi-scale description , 1984, ICASSP.

[19]  G. Song,et al.  Fractal research on AFM images of polycrystalline aluminum surface with adsorption film of SDS inhibitor , 2009 .

[20]  Odemir Martinez Bruno,et al.  Fractal dimension applied to plant identification , 2008, Inf. Sci..

[21]  Luciano da Fontoura Costa,et al.  2D Euclidean distance transform algorithms: A comparative survey , 2008, CSUR.

[22]  André Ricardo Backes,et al.  Medical image retrieval based on complexity analysis , 2010, Machine Vision and Applications.

[23]  N. Lam,et al.  Multi-Scale Fractal Analysis of Image Texture and Pattern , 1999 .

[24]  Pavel Pudil,et al.  Introduction to Statistical Pattern Recognition , 2006 .

[25]  Keinosuke Fukunaga,et al.  Introduction to statistical pattern recognition (2nd ed.) , 1990 .