Texture Classification Using Fractal Dimension and Lacunarity (original) (raw)
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TEXTURAL IMAGES REPRESENTATION USING FRACTAL GEOMETRY MEASURES
Fractal functions are good choice for modeling natural textured surfaces and they have long been recognized as important features in classifying images because the fractal dimension for a surface correlates nearly perfectly with the perception of roughness in many situations. The use of new set of fractal features to identify visual texture is explored in this paper. We have adopted a set of two fractal features (i.e. fractal dimension and lacunarity) for describing different visual textures. A modified differential box counting approach for estimating these two fractal features from image surfaces is proposed. Also, a focus on these two fractal features (parameters), with their accuracy and robustness were evaluated. The problem of textural images description was presented. The research conducted a testing procedure to evaluate the degree of sensitivity against the textural attributes (i.e. softness, feature size and power). The results have shown satisfactory results, which can justify the usage of fractal features as textural discriminating criteria. Keywords- Fractal, Textural, Lacunarity etc
Fractal functions are good choice for modeling natural textured surfaces and they have long been recognized as important features in classifying images because the fractal dimension for a surface correlates nearly perfectly with the perception of roughness in many situations. The use of new set of fractal features to identify visual texture is explored in this paper. We have adopted a set of two fractal features (i.e. fractal dimension and lacunarity) for describing different visual textures. A modified differential box counting approach for estimating these two fractal features from image surfaces is proposed. Also, a focus on these two fractal features (parameters), with their accuracy and robustness were evaluated. The problem of textural images description was presented. The research conducted a testing procedure to evaluate the degree of sensitivity against the textural attributes (i.e. softness, feature size and power). The results have shown satisfactory results, which can justify the usage of fractal features as textural discriminating criteria.
An improved fuzzy fractal dimension for texture analysis
2015
In the real life, a lot of phenomena cannot be described by the traditional geometry; fractals are one of these objects. It serves to give a suitable description for these objects. Texture analysis plays an important role in image processing. Fractal dimension is utilized in texture segmentation and classification and prove to be an interesting parameter to characterize image roughness and extract image feature. In some complex and irregular scenes, it becomes not effective for feature extracting and classification. Therefore, a more general approach known as fuzzy fractal dimension can be used to model such types of scenes effectively. A new fuzzy fractal dimension method is proposed in this paper, it is verified by the experiment on a set of nature texture images to show its efficiency and accuracy, a satisfactory result is found. It also offers promising performance when it is tested among some types of noises to show a good robustness to them.
Color texture analysis based on fractal descriptors
Pattern Recognition, 2012
Color texture classification is an important step in image segmentation and recognition. The color information is especially important in textures of natural scenes, such as leaves surfaces, terrains models, etc. In this paper, we propose a novel approach based on the fractal dimension for color texture analysis. The proposed approach investigates the complexity in R, G and B color channels to characterize a texture sample. We also propose to study all channels in combination, taking into consideration the correlations between them. Both these approaches use the volumetric version of the Bouligand-Minkowski Fractal Dimension method. The results show a advantage of the proposed method over other color texture analysis methods.
An efficient approach to estimate fractal dimension of textural images
Pattern Recognition, 1992
Fractal dimension is an interesting parameter to characterize roughness in an image. It can be used in texture segmentation, estimation of three-dimensional (3D) shape and other information. A new method is proposed to estimate fractal dimension in a two-dimensional (2D) image which can readily be extended to a 3D image as well. The method has been compared with other existing methods to show that our method is both efficient and accurate.
Locally Invariant Fractal Features for Statistical Texture Classification
2007 IEEE 11th International Conference on Computer Vision, 2007
We address the problem of developing discriminative, yet invariant, features for texture classification. Texture variations due to changes in scale are amongst the hardest to handle. One of the most successful methods of dealing with such variations is based on choosing interest points and selecting their characteristic scales [Lazebnik et al. PAMI 2005]. However, selecting a characteristic scale can be unstable for many textures. Furthermore, the reliance on an interest point detector and the inability to evaluate features densely can be serious limitations. Fractals present a mathematically well founded alternative to dealing with the problem of scale. However, they have not become popular as texture features due to their lack of discriminative power. This is primarily because: (a) fractal based classification methods have avoided statistical characterisations of textures (which is essential for accurate analysis) by using global features; and (b) fractal dimension features are unable to distinguish between key texture primitives such as edges, corners and uniform regions. In this paper, we overcome these drawbacks and develop local fractal features that are evaluated densely. The features are robust as they do not depend on choosing interest points or characteristic scales. Furthermore, it is shown that the local fractal dimension is invariant to local bi-Lipschitz transformations whereas its extension is able to correctly distinguish between fundamental texture primitives. Textures are characterised statistically by modelling the full joint PDF of these features. This allows us to develop a texture classification framework which is discriminative, robust and achieves state-of-the-art performance as compared to affine invariant and fractal based methods.
Fractal Features Classification for Texture Image Using Neural Network and Mathematical Morphology
This work proposes a new method for unsupervised texture image classification, which is based on both Kohonen maps and mathematical morphology. Various features obtained from the fractal dimension computed using differential box counting method, are extracted from the texture images and then applied and projected into a Kohonen map. This map is represented by the underlying probability density function (pdf) estimated, by a non-parametric technique in the n-dimensional space, from the weight vectors resulting of the learning process. Under the assumption that each modal region of the underlying pdf corresponds to a one homogenous region in the texture image, the second step of the process understanding consists to an extraction, in the Kohonen map, of the modal regions of the pdf as connected components without using any thresholding procedure. That is done by making concepts of morphological watershed transformations suitable for modal domains detection. The observations falling in the so localised homogenous region in the image are considered as prototypes and are then used in the clustering procedure by means of an assignment rule.
Local fractal and multifractal features for volumic texture characterization
Pattern Recognition, 2011
For texture analysis, several features such as co-occurrence matrices, Gabor filters and the wavelet transform are used. Recently, fractal geometry appeared to be an effective feature to analyze texture. But it is often restricted to 2D images, while 3D information can be very important especially in medical image processing. Moreover applications are limited to the use of fractal dimension. This study focuses on the benefits of fractal geometry in a classification method based on volumic texture analysis. The proposed methods make use of fractal and multifractal features for a 3D texture analysis of a voxel neighborhood. They are validated with synthetic data before being applied on real images. Their efficiencies are proved by comparison to some other texture features in supervised classification processes (AdaBoost and support vector machine classifiers).
Fractal Features Classification for Texture Image Using Neural Network and Mathematical Morphology T
This work proposes a new method for unsupervised texture image classification, which is based on both Kohonen maps and mathematical morphology. Various features obtained from the fractal dimension computed using differential box counting method, are extracted from the texture images and then applied and projected into a Kohonen map. This map is represented by the underlying probability density function (pdf) estimated, by a non-parametric technique in the n-dimensional space, from the weight vectors resulting of the learning process. Under the assumption that each modal region of the underlying pdf corresponds to a one homogenous region in the texture image, the second step of the process understanding consists to an extraction, in the Kohonen map, of the modal regions of the pdf as connected components without using any thresholding procedure. That is done by making concepts of morphological watershed transformations suitable for modal domains detection. The observations falling in...
International Journal of Image, Graphics and Signal Processing, 2016
Fractal analysis is currently in full swing in particular in the medical field because of the fractal nature of natural phenomena (vascular system, nervous system, bones, breast tissue ...). For this, many algorithms for estimating the fractal dimension have emerged. Most of them are based on the principle of box counting. In this work we propose a new method for calculating fractal attributes based on contrast homogeneity and energy that have been extracted from gray level co-occurrence matrix. As application we are investigated in the characterization and classification of mammographic images with SuportVectorMachine classifier. We considered in particular images with tumor masses and architectural disorder to compare with normal ones. We calculate, for comparison the fractal dimension obtained by a reference method (triangular prism) and perform a classification similar to the previous. Results obtained with new algorithm are better than reference method (classification rate is 0.91 vs 0.65). Hence new fractal attributes are relevant.