Analysis of Texture Anisotropy Based on Some Gaussian Fields with Spectral Density. In: Bergounioux M, editor. Mathematical Image Processing. Berlin: Springer Berlin Heidelberg; 2011. pp. 59-73. [DOI: 10.1007/978-3-642-19604-1_3]

Directional fractal signature methods for trabecular bone texture in hand radiographs: data from the Osteoarthritis Initiative

PURPOSE

To develop directional fractal signature methods for the analysis of trabecular bone (TB) texture in hand radiographs. Problems associated with the small size of hand bones and the orientation of fingers were addressed.

METHODS

An augmented variance orientation transform (AVOT) and a quadrant rotating grid (QRG) methods were developed. The methods calculate fractal signatures (FSs) in different directions. Unlike other methods they have the search region adjusted according to the size of bone region of interest (ROI) to be analyzed and they produce FSs defined with respect to any chosen reference direction, i.e., they work for arbitrary orientation of fingers. Five parameters at scales ranging from 2 to 14 pixels (depending on image size and method) were derived from rose plots of Hurst coefficients, i.e., FS in dominating roughness (FSSta), vertical (FSV) and horizontal (FSH) directions, aspect ratio (StrS), and direction signatures (StdS), respectively. The accuracy in measuring surface roughness and isotropy/anisotropy was evaluated using 3600 isotropic and 800 anisotropic fractal surface images of sizes between 20 × 20 and 64 × 64 pixels. The isotropic surfaces had FDs ranging from 2.1 to 2.9 in steps of 0.1, and the anisotropic surfaces had two dominating directions of 30° and 120°. The methods were used to find differences in hand TB textures between 20 matched pairs of subjects with (cases: approximate Kellgren-Lawrence (KL) grade ≥ 2) and without (controls: approximate KL grade <2) radiographic hand osteoarthritis (OA). The OA Initiative public database was used and 20 × 20 pixel bone ROIs were selected on 5th distal and middle phalanges. The performance of the AVOT and QRG methods was compared against a variance orientation transform (VOT) method developed earlier [M. Wolski, P. Podsiadlo, and G. W. Stachowiak, "Directional fractal signature analysis of trabecular bone: evaluation of different methods to detect early osteoarthritis in knee radiographs," Proc. Inst. Mech. Eng., Part H 223, 211-236 (2009)].

RESULTS

The AVOT method correctly quantified the isotropic and anisotropic surfaces for all image sizes and scales. Values of FSSta were significantly different (P < 0.05) between the isotropic surfaces. Using the VOT and QRG methods no differences were found at large scales for the isotropic surfaces that are smaller than 64 × 64 and 48 × 48 pixels, respectively, and at some scales for the anisotropic surfaces with size 48 × 48 pixels. Compared to controls, using the AVOT and QRG methods the authors found that OA TB textures were less rough (P < 0.05) in the dominating and horizontal directions (i.e., lower FSSta and FSH), rougher in the vertical direction (i.e., higher FSV) and less anisotropic (i.e., higher StrS) than controls. No differences were found using the VOT method.

CONCLUSIONS

The AVOT method is well suited for the analysis of bone texture in hand radiographs and it could be potentially useful for early detection and prediction of hand OA.

Self-similar anisotropic texture analysis: the hyperbolic wavelet transform contribution

Textures in images can often be well modeled using self-similar processes while they may simultaneously display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of Gaussian anisotropic selfsimilar processes. It will be first shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2D-discrete wavelet transform with the hyperbolic wavelet transform, which permits the use of different dilation factors along the horizontal and vertical axes. Defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized; this discrepancy defines a rotation angle. Second, we show that this rotation angle can be jointly estimated. Third, a nonparametric bootstrap based procedure is described, which provides confidence intervals in addition to the estimates themselves and enables us to construct an isotropy test procedure, which can be applied to a single texture image. Fourth, the robustness and versatility of the proposed analysis are illustrated by being applied to a large variety of different isotropic and anisotropic self-similar fields. As an illustration, we show that a true anisotropy built-in self-similarity can be disentangled from an isotropic self-similarity to which an anisotropic trend has been superimposed.