A Sub-pixel Multifractal Method for the Image Segmentation

The framework of image segmentation based on the sub-pixel multifractal measure (SPMM) is presented in this paper. A more precise singularity exponent distribution in the image can be obtained based on the SPMM. According to the singularity exponents and their statistical properties, the image can be decomposed into a series of sets with different physical characteristics automatically and easily. Moreover, the most singular manifold can be interpreted as the set from which energy is injected in the flow to the other fractal sets. The simulation results show that the SPMM has higher quality factor in the image edge detection.

[1]  Carlo H. Séquin,et al.  Interlacing in charge-coupled imaging devices , 1973 .

[2]  Antonio Turiel,et al.  Multifractal measures: definition, description, synthesis and analysis. A detailed study , 2003 .

[3]  F. Parmiggiani,et al.  An investigation of the textural characteristics associated with gray level cooccurrence matrix statistical parameters , 1995, IEEE Transactions on Geoscience and Remote Sensing.

[4]  J. Nadal,et al.  Self-Similarity Properties of Natural Images Resemble Those of Turbulent Flows , 1998, cond-mat/0107314.

[5]  Antonio Turiel,et al.  Multifractal geometry in stock market time series , 2003 .

[6]  A Turiel,et al.  Multifractal wavelet filter of natural images. , 2000, Physical review letters.

[7]  N. Decoster,et al.  A wavelet-based method for multifractal image analysis. II. Applications to synthetic multifractal rough surfaces , 2000 .

[8]  Patrick Pérez,et al.  Dense Estimation of Fluid Flows , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  N. Parga,et al.  Ju l 2 00 1 The multi-fractal structure of contrast changes in natural images : from sharp edges to textures , 2008 .

[10]  Andrea Baraldi,et al.  An investigation of the textural characteristics associated with gray level cooccurrence matrix statistical parameters , 1995, IEEE Transactions on Geoscience and Remote Sensing.

[11]  A. Arneodo,et al.  WAVELET BASED MULTIFRACTAL ANALYSIS OF ROUGH SURFACES : APPLICATION TO CLOUD MODELS AND SATELLITE DATA , 1997 .

[12]  Antonio Turiel,et al.  Numerical methods for the estimation of multifractal singularity spectra on sampled data: A comparative study , 2006, J. Comput. Phys..

[13]  Pierrick Legrand,et al.  Local regularity-based image denoising , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[14]  Antonio Turiel,et al.  Analysis and comparison of functional dependencies of multiscale textural features on monospectral infrared images , 2003, IGARSS 2003. 2003 IEEE International Geoscience and Remote Sensing Symposium. Proceedings (IEEE Cat. No.03CH37477).

[15]  Antonio Turiel,et al.  Reconstructing images from their most singular fractal manifold , 2002, IEEE Trans. Image Process..