Multiscale Fractal Dimension Research Articles

Medical image retrieval based on complexity analysis

Texture is one of the most important visual attributes used in image analysis. It is used in many content-based image retrieval systems, where it allows the identification of a larger number of images from distinct origins. This paper presents a novel approach for image analysis and retrieval based on complexity analysis. The approach consists of a texture segmentation step, performed by complexity analysis through BoxCounting fractal dimension, followed by the estimation of complexity of each computed region by multiscale fractal dimension. Experiments have been performed with MRI database in both pattern recognition and image retrieval contexts. Results show the accuracy of the method and also indicate how the performance changes as the texture segmentation process is altered.

Filtered Dynamics and Fractal Dimensions for Noisy Speech Recognition

We explore methods from fractals and dynamical systems theory for robust processing and recognition of noisy speech. A speech signal is embedded in a multidimensional phase-space and is subsequently filtered exploiting aspects of its unfolded dynamics. Invariant measures (fractal dimensions) of the filtered signal are used as features in automatic speech recognition (ASR). We evaluate the new proposed features as well as the previously proposed multiscale fractal dimension via ASR experiments on the Aurora 2 database. The conducted experiments demonstrate relative improved word accuracy for the fractal features, especially at lower signal-to-noise ratio, when they are combined with the mel-frequency cepstral coefficients

A low-complexity index for fractal image indexing

Fractal signatures are an important statistical property of texture images. Most existing fractal signatures are extracted by computing an image multiscale fractal dimension. Recently, it has been very interesting to see fractal block coding being investigated for image indexing. A second kind of fractal signature is extracted from image fractal codes. This paper investigates how to reduce the complexity of fractal-code signatures based on independence between the fractal parameters of orthogonalization fractal block coding. This independence is used to construct a low-complexity index. The proposed index is compared with existing fractal-dimension signatures using a database of texture images. The results indicate that the proposed index outperforms the fractal-dimension signatures.

A graph-based approach for multiscale shape analysis

This paper presents two shape descriptors, multiscale fractal dimension and contour saliences, using a graph-based approach— the image foresting transform. It introduces a robust approach to locate contour saliences from the relation between contour and skeleton. The contour salience descriptor consists of a vector, with salience location and value along the contour, and a matching algorithm. We compare both descriptors with fractal dimension, Fourier descriptors, moment invariants, Curvature Scale Space and Beam Angle Statistics regarding to their invariance to object characteristics that belong to a same class (compact-ability) and to their ability to separate objects of distinct classes (separability).

Investigating shape and function relationship in retinal ganglion cells.

This article addresses the investigation of the relationship between neural shape and function in cat retinal ganglion cells in terms of representative morphological features. More specifically, a series of geometrical measures is extracted from two-dimensional images of these cells, and pattern recognition methods are applied in order to quantify the differentiation between the two classes (i.e., alpha, beta). The morphological measures cover several of the more meaningful geometrical features of neuronal cells, including: (a) the distribution of angles along the cell contours considering several smoothing degrees; (b) the overall interaction between the cell arborization and the surrounding space, quantified in terms of the multiscale fractal dimension; and (c) the distribution of width and extent of the dendritic processes. Several combinations of such morphological measures are assessed with respect to the separability of the classes. The obtained results indicate that the methods based on statistic relation between segment length and segment diameter, and the method of multiscale angle entropy not only successfully encapsulated a large amount of experimental data into relatively compact patterns but also marked off various ganglion cells into befit groups. On the other hand, the method of neuron classification based on fractal dimension resulted relatively less effective for class separation.