This work presents a novel descriptor for texture images based on fractal geometry and its application to image analysis. The descriptors are provided by estimating the triangular prism fractal dimension under different scales with a weight exponential parameter, followed by dimensionality reduction using Karhunen-Lo e ve transform. The efficiency of the proposed descriptors is tested on two well-known texture data sets, that is, Brodatz and Vistex, both for classification and image retrieval. The novel method is also tested concerning invariances in situations when the textures are rotated or affected by Gaussian noise. The obtained results outperform other classical and state-of-the-art descriptors in the literature and demonstrate the power of the triangular descriptors in these tasks, suggesting their use in practical applications of image analysis based on texture features.
During the last decades, another branch of methods that have presented interesting results in texture analysis, especially on natural images, are those based on fractal geometry, particularly multifractals @cite_35 , multiscale fractal dimension @cite_34 and fractal descriptors @cite_27 . In this context, this work proposes the study and application of fractal descriptors based on the estimative of the fractal dimension using a tessellation of triangular prisms @cite_13 .
@cite_35 @cite_27 @cite_34 @cite_13
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Based on multifractal analysis in wavelet pyramids of texture images, a new texture descriptor is proposed in this paper that implicitly combines information from both spatial and frequency domains. Beyond the traditional wavelet transform, a multi-oriented wavelet leader pyramid is used in our approach that robustly encodes the multi-scale information of texture edgels. Moreover, the resulting texture model shows empirically a strong power law relationship for nature textures, which can be characterized well by multifractal analysis. Combined with a statistics on affine invariant local patches, our proposed texture descriptor is robust to scale and rotation changes, more general geometrical transforms and illumination variations. In addition, the proposed texture descriptor is computationally efficient since it does not require many expensive processing steps, e.g., texton generation and cross-bin comparisons, which are often used by existing methods. As an application, the proposed descriptor is applied to texture classification and the experimental results on several public texture datasets verified the accuracy and efficiency of our descriptor. The large-scale images and videos are one kind of the main source of big data. Dynamic texture (DT) is essential for understanding the video sequences with spatio-temporal similarities. This paper presents a powerful tool called dynamic fractal analysis to DT description and classification, which integrates rich description of DT with strong robustness to environmental changes. The proposed dynamic fractal spectrum (DFS) for DT sequences is composed of two components. The first one is a volumetric dynamic fractal spectrum component (V-DFS) that captures the stochastic self-similarities of DT sequences by treating them as 3D volumes; the second one is a multi-slice dynamic fractal spectrum component (S-DFS) that encodes fractal structures of repetitive DT patterns on 2D slices along different views of the 3D volume. To fully exploit various types of dynamic patterns in DT, five measurements of DT pixels are collected for the analysis on DT sequences from different perspectives. We evaluated our method on four publicly available benchmark datasets. All the experimental results have demonstrated the excellent performance of our method in comparison with state-of-the-art approaches. HighlightsThe dynamic multi-fractal analysis is developed for DT description.Our method is very discriminative and robust to environmental changes.A computational acceleration scheme is provided for the proposed descriptor.Our method exhibits excellent performance on four benchmark datasets. Recent developments in analysis methods on the non-linear and non-stationary data have received large attention by the image analysts. In 1998, Huang introduced the empirical mode decomposition (EMD) in signal processing. The EMD approach, fully unsupervised, proved reliable monodimensional (seismic and biomedical) signals. The main contribution of our approach is to apply the EMD to texture extraction and image filtering, which are widely recognized as a difficult and challenging computer vision problem. We developed an algorithm based on bidimensional empirical mode decomposition (BEMD) to extract features at multiple scales or spatial frequencies. These features, called intrinsic mode functions, are extracted by a sifting process. The bidimensional sifting process is realized using morphological operators to detect regional maxima and thanks to radial basis function for surface interpolation. The performance of the texture extraction algorithms, using BEMD method, is demonstrated in the experiment with both synthetic and natural images. 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 [ 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.