Textile surface inspection by using translation invariant wavelet transform

It is known that texture can be modeled better using both deterministic and random components. The Wavelet transform, which can be computed efficiently, is a well-known multi-resolution analysis method. However, when it is applied to texture analysis, the Wavelet transform has the problem that the transformed result of the deterministic component of the texture is no longer translation invariant. In this paper, we will constitute 2D RI-Spline Wavelets, which consist of a pair of symmetric and anti-symmetric bi-orthogonal spline wavelets. Using the 2-D RI-Spline wavelets, which can be considered to be one variation of Complex wavelets, we can obtain translation invariance. Then, we apply the translation invariant 2-D RI-Spline wavelets to the automated inspection of textile surfaces. In our approach, first to remove textile textures from textile surfaces we use the 2-D RI-Spline wavelets. Once the textural information is removed from textile surfaces, the remaining inspection process becomes a tractable problem, which we can handle using a standard statistical method. The experimental results show that our inspection method is effective for real textile surfaces.