Seamless tiling of quasi-periodic textures via an optimal cyclic shift on a discrete torus
Вантажиться...
Дата
2026
Автори
Назва журналу
Номер ISSN
Назва тому
Видавець
Хмельницький національний університет
Анотація
In practical computer vision and computer graphics pipelines, it
is often necessary to repeatedly replicate a single texture sample to
construct a large canvas, background, or regular covering. When the
mosaic is not strictly periodic, visible seams appear at the boundaries
during repetition, disrupting the perceptual continuity of the texture and
often manifesting as a regular grid of artifacts. Such seams not only
degrade visual quality but can also alter local gradients and spectral
components, which is critical for subsequent processing stages. Common
seamless stitching methods increase computational complexity, introduce
additional hyperparameters, and modify the local image statistics, which is
undesirable in reproducible pipelines and in tasks where the invariance of
pixel values is essential. The goal of this work is to propose a simple,
reproducible, and computationally efficient method for seam reduction in
quasiperiodic textures by selecting an optimal cyclic shift of the pattern that
minimizes the energy of mismatch between opposite boundaries. The tile
is modeled as a function on the discrete torus ℤ𝑀 × ℤ𝑁. A cyclic shift group
𝐺 = ℤ𝑀 × ℤ𝑁 is introduced, acting as a permutation of pixels. For each shift
𝜏𝑎,𝑏
, the boundary seam energy 𝐸(𝜏𝑎,𝑏
𝐼) is computed in a band of width 𝑤
for opposite boundary pairs, and the minimizing shift is selected. When
needed, the evaluation is accelerated via cyclic correlations and FFT.
Experiments on synthetic and real textures show that the optimal cyclic
shift significantly reduces seam energy and the visual prominence of
boundaries during tiling without modifying pixel values. For strictly periodic
tiles, the method does not degrade the result. The proposed approach is a
lightweight baseline tool for seamless tiling: it does not perform stitching
but selects the best cut of the torus. The method is easy to integrate into
production pipelines and can be used as a preprocessing step before further
processing
Опис
Ключові слова
seamless tiling, quasi-periodic textures, optimal cyclic shift, discrete torus, minimization of boundary artifacts, periodic boundary conditions, FFT-based optimization
Бібліографічний опис
Bedratiuk A. Seamless tiling of quasi-periodic textures via an optimal cyclic shift on a discrete torus // Computer Systems and Information Technologies. 2026. No. 1. P. 16-27.