Edge-preserving image filtering is an essential task in computational photography and imaging. In this paper, we propose a simple yet effective global edge-preserving filter based on soft clustering, and we propose a novel soft clustering algorithm based on a restricted Gaussian mixture model. Given specified parameters, the soft clustering process is firstly performed on the image to derive the partition matrix, from which the affinity matrix is then constructed for filtering. The filtering output is calculated as the weighted average of the pixels in the local window, so the proposed filter could suppress the intensity shift artifacts that impede most global filters. Besides, the weights in the proposed filter are derived by clustering, which properly separates dissimilar pixels, so the proposed filter could handle the halo artifacts that haunt many local filters. Moreover, our filter provides flexible control over the amount of smoothing that is deficient in the deep learning-based filters. Besides the efficacy in smoothing, the proposed filter naturally has low computational complexity. Qualitative and quantitative results suggest that the proposed filter benefits various applications, including edge-preserving smoothing, image enhancing, flash/non-flash fusion, HDR tone mapping, and dehazing.

Origami has provided a potential way to construct 3D curved structures by folding flat sheet materials without cutting or stretching. As a traditional origami, waterbomb tessellation is widely studied from aspects of science and engineering. However, users cannot easily utilize this kind of origami to fit curved target surfaces because the underlying geometric constraints limit the design space. In this study, we propose computational design methods for approximating cylindrical and axisymmetric curved surfaces based on waterbomb tessellations. With consideration of symmetry and periodic repetition, a single strip of the waterbomb tessellation is first modeled and then longitudinally and circumferentially replicated to construct cylindrical and axisymmetric waterbomb tessellations, respectively. To fulfill flat-foldability, an optimization process is introduced for minimizing flat-foldable residuals iteratively and then a regulation process of the crease pattern is applied for further reducing such residuals. In addition, we demonstrate waterbomb-derivative tessellations with quad-paddings to expand the design variations. Furthermore, rigid-folding sequences and several physically engineered origami pieces are presented. The proposed methods can be utilized to facilitate the design of origami-inspired structures for various engineering design purposes, such as foldable shelters, tubular structures, metamaterials, and so on.