Much of the previous work in texture segmentation employs filter banks, comprising both isotropic and anisotropic filters, to capture texture statistics. For instance, researchers have used Gabor-filter responses to discriminate between different kinds of textures [124,148,149]. Gabor filters are a prominent example from the class of oriented multiscale filters [39,21]. This approach emphasizes the extraction of appropriate features for discriminating between specific textures, which is typically a nontrivial task. The proposed method, on the other hand, does not rely on using specific descriptors that work for certain kinds of textures, but is based on a more generic approach that tries to adaptively capture the core properties of a wide variety of textures.
Researchers have also investigated using more compact sets of texture features. For instance, Bigun et al. [18] use the structure tensor, which includes all derivatives upto second order, to detect local orientation. Rousson et al. [144] refine this strategy by using vector-valued anisotropic diffusion, instead of Gaussian blurring, on the feature space formed using the components of the structure tensor. This strategy requires the structure tensors to have a sufficient degree of homogeneity within regions as well as sufficient dissimilarity between regions. However, as the coming paragraphs explain, not all texture images can be distinguished using these criteria.
Other approaches use the intensity (or grayscale) histograms to distinguish between textures [87,83]. However, the grayscale intensity statistics (i.e., 1D histograms), may fail to capture the geometric structure of neighborhoods, which is critical for distinguishing textures with similar 1D histograms. The proposed method exploits higher-order image statistics, modeled nonparametrically, to adaptively capture the geometric regularity in textures.
Figure 7.1(a) shows two textures that are both irregular (in addition to having similar means and gradient-magnitudes) that would pose a challenge for structure-tensor-based approaches such as [18,144]. In Figure 7.1(b) the textures differ only in scale. Approaches based on structure tensors at a single scale would fail to distinguish such cases, as reported in [144]. Approaches solely using intensity histograms would also fail here. In Figure 7.1(c) the textures have identical histograms, identical scale, and an almost-identical set of structure-tensor matrix components. In this case, the above-mentioned approaches [18,144] would face a formidable challenge. The proposed method, on the other hand, incorporating a fundamentally-richer texture description, produces successful segmentations (depicted by white/gray outlines) for all the images in Figure 7.1.
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Recently, researchers have investigated more direct approaches towards modeling image statistics. For instance, the dynamic-texture segmentation approach by Doretto et al. [46] uses a Gauss-Markov process to model the relationships among pixels within regions and over time. However, that approach assumes a Gaussian process for image intensities, a restrictive assumption that cannot easily account for complex or subtle texture differences [46,144,39,189]. Rousson et al. [144] use nonparametric statistics for one of the channels (the image-intensity histogram) in their feature space to counter this restriction and the proposed method generalizes that strategy to the complete higher-order image statistics.