Rotation–Covariant Texture Learning Using Steerable Riesz Wavelets

Abstract

Abstract-We propose a texture learning approach that exploits local organizations of scales and directions. First, linear combinations of Riesz wavelets are learned using kernel support vector machines. The resulting texture signatures are modeling optimal class-wise discriminatory properties. The visualization of the obtained signatures allows verifying the visual relevance of the learned concepts. Second, the local orientations of the signatures are optimized to maximize their responses, which is carried out analytically and can still be expressed as a linear combination of the initial steerable Riesz templates. The global process is iteratively repeated to obtain final rotationcovariant texture signatures. Rapid convergence of class-wise signatures is observed, which demonstrates that the instances are projected into a feature space that leverages the local organizations of scales and directions. Experimental evaluation reveals average classification accuracies in the range of 97% to 98% for the Outex_TC_00010, the Outex_TC_00012, and the Contrib_TC_00000 suites for even orders of the Riesz transform, and suggests high robustness to changes in images orientation and illumination. The proposed framework requires no arbitrary choices of scales and directions and is expected to perform well in a large range of computer vision applications.

Automated classification of brain tumor type in whole-slide digital pathology images using local representative tiles

“…The multi-scale nature of Riesz wavelets allows examination of the tissue at multiple spatial scales, from individual nuclei to multicellular structures. The directional components of the Riesz features can also be oriented to locally maximize the response of the first filter at the most granular scale, which has the desirable effect of normalizing all image directions among instances (Depeursinge et al, 2014). Since pathology has no universal orientation, this allows us to directly compare features from slide to slide without imposing an arbitrary directionality.…”

“…Then features were extracted from the whole tissue segmentation, from the nuclear segmentation, and from the non-nuclear regions, independently for both the hematoxylin and eosin stains. Specifically, shape, color ), Haralick texture features (Haralick et al, 1973), and second order unaligned Riesz features (Depeursinge et al, 2014) were extracted from each tile. The Riesz features correspond qualitatively to a multi-scale Hessian filter- bank (Fig.…”

“…Skeleton features for the nuclei were computed along with the other shape feature to better define nuclear morphology (Zhao and Daut, 1991). Additionally, aligned secondorder Riesz features with six dyadic scales are computed to characterize texture in the fine analysis, rather than using the unaligned features used in the coarse analysis (Depeursinge et al, 2014). Alignment of the Riesz wavelets allows for rotation invariance, and avoids imposing arbitrary directionality on the tissue analysis.…”

Design of Steerable Wavelets to Detect Multifold Junctions

“…The connection between wavelet steerability and the highorder Riesz transform is discussed in [44]. An application of steerable Riesz wavelets for texture learning was presented in [45]. Spherical harmonics, which are the 3D counterparts of circular harmonics, have also been used to represent and detect features and shapes in 3D [46], [47].…”

3D Solid Texture Classification Using Locally-Oriented Wavelet Transforms

“…Popular approaches are gray-level matrices (co-occurrence [6], run-length [7], and size-zone [8]), local binary patterns (LBP) [9], wavelets and filterbanks (Laplacian of Gaussian [10], Gabor [11], maximum-response eight [12], Riesz [13], [14]), fractals [15], and learned representations (dictionary learning [16], deep convolutional neural networks [17]). In natural images, 2D analysis also often includes visual descriptors such as color, shape, and appearance [18] that complement texture.…”