Fractal Dimension of Color Fractal Images

Transilvania University, Bras¸ov 500036, România.
IEEE Transactions on Image Processing (Impact Factor: 3.63). 01/2011; 20(1):227-35. DOI: 10.1109/TIP.2010.2059032
Source: PubMed


Fractal dimension is a very useful metric for the analysis of the images with self-similar content, such as textures. For its computation there exist several approaches, the probabilistic algorithm being accepted as the most elegant approach. However, all the existing methods are defined for 1-D signals or binary images, with extension to grayscale images. Our purpose is to propose a color version of the probabilistic algorithm for the computation of the fractal dimension. To validate this new approach, we also propose an extension of the existing algorithm for the generation of probabilistic fractals, in order to obtain color fractal images. Then we show the results of our experiments and conclude this paper.

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    • "Fractal dimension is an important indicator which is used to measure signals irregularity and explore the complexity of things. At present, it has been widely applied in image analysis [10], vibration signal fault diagnosis [11], and dynamics analysis [12]. Onedimensional fractal dimension, box-counting dimension [13], can be sufficient for the description of the features of a simple signal. "
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    ABSTRACT: In low SNR condition, it is difficult to identify the radio transient characteristics of the signals. To solve this problem, a new recognition algorithm based on multifractal dimension characteristics is proposed. In fractal theory, multifractal dimension is the most sophisticated characterize that can describe the similar characteristics of the signals. Therefore, multifractal dimension is used in this paper to extract the subtle features of different impulse noise signals, in order to achieve the purpose of the classification and identification of the radiation source.
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    • "However, the proposed method needs more than 3 colour channels to be accurate and the computational resources it requires are very high. An extension to the above-mentioned mass distribution method in colour space has been done recently in an unpublished work of Ivanovici and Richard [12]. For a certain square of size ε in the x − y plane, they count the number of data elements (pixels) that fall inside a 3-D cube of size ε centered in the current pixel. "
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    ABSTRACT: The box counting method for fractal dimension estimation had not been applied to large or colour images thus far due to the processing time required. In this letter we present a fast, easy to implement and very easily expandable to any number of dimensions variation, the box merging method. It is applied here in RGB images which are considered as sets in 5-D space.
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    ABSTRACT: Vision is a complex process that integrates multiple aspects of an image: spatial frequencies, topology and colour. Unfortunately, so far, all these elements were independently took into consideration for the development of image and video quality metrics, therefore we propose an approach that blends together all of them. Our approach allows for the analysis of the complexity of colour images in the RGB colour space, based on the probabilistic algorithm for calculating the fractal dimension and lacunarity. Given that all the existing fractal approaches are defined only for gray-scale images, we extend them to the colour domain. We show how these two colour fractal features capture the multiple aspects that characterize the degradation of the video signal, based on the hypothesis that the quality degradation perceived by the user is directly proportional to the modification of the fractal complexity. We claim that the two colour fractal measures can objectively assess the quality of the video signal and they can be used as metrics for the user-perceived video quality degradation and we validated them through experimental results obtained for an MPEG-4 video streaming application; finally, the results are compared against the ones given by unanimously-accepted metrics and subjective tests.
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