Periodicity estimation of nearly regular textures based on discrepancy norm

Abstract

This paper proposes a novel approach to determine the texture periodicity, the texture element size and further characteristics like the area of the basin of attraction in the case of computing the similarity of a test image patch with a reference. The presented method utilizes the properties of a novel metric, the so-called discrepancy norm. Due to the Lipschitz and the monotonicity property the discrepancy norm distinguishes itself from other metrics by well-formed and stable convergence regions. Both the periodicity and the convergence regions are closely related and have an immediate impact on the performance of a subsequent template matching and evaluation step.The general form of the proposed approach relies on the generation of discrepancy norm induced similarity maps at random positions in the image. By applying standard image processing operations like watershed and blob analysis on the similarity maps a robust estimation of the characteristic periodicity can be computed. From the general approach a tailored version for orthogonal aligned textures is derived which shows robustness to noise disturbed images and is suitable for estimation on near regular textures. In an experimental set-up the estimation performance is tested on samples of standardized image databases and is compared with state-of-theart methods. Results show that the proposed method is applicable to a wide range of nearly regular textures and estimation results keeps up with current methods. When adding a hypothesis generation/selection mechanism it even outperforms the current state-or-the-art.

Grid-based matching for full-field large-area deformation measurement

“…The periodicity and regularity of the grid allows for the calculation of registration parameters under deformation. In the literature, methods for identifying the periodicity of structural textures have been proposed based on Fourier spectral analysis (FSA) [22], DIC [26], co-occurrence matrix [20], and discrepancy norm [21]. These methods have various weaknesses: FSA is not suitable for the periodicity estimation of textures of insufficient large size which lack salient peaks in the power spectrum; Cooccurrence matrix methods are unacceptably slow for large textures and sensitive to distortion [20]; Discrepancy norm is sensitive to image contrast because it relies on the difference between pixel values [23].…”