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 tessellations have shown the potential to be utilized for approximating curved target surfaces by folding a set of elemental units. As those units are in partially folded states, the origami approximation captures the outline of the target while demonstrating a corrugated surface. In this paper, we focus on the cylindrical surface and propose a method for constructing its discrete version via square or rectangular units with crease patterns inspired by the waterbomb tessellation. We unify the unit size through optimization to realize cost-efficient constructions. Three-dimensional curved structures are deployed by folding collinear creases between adjacent rows of units and the other creases in each row are remained unfolded. The deployed structure can still be folded to a compact state by folding all creases. To flexibly approximate the outline of the target surface, we analyse relationships between the width and height of the rectangular unit and utilize variations of the waterbomb tessellation to control the region of the origami structure when fully folded. The proposed method provides a novel solution to the so-called inverse-origami-design problem for generating foldable cylindrical surfaces using unfolded waterbomb origami units.

Three-dimensional (3D) origami, which can generate a structure through folding a crease pattern on a flat sheet of paper, has received considerable attention in art, mathematics, and engineering. With consideration of symmetry, the user can efficiently generate a rational crease pattern and make the fabricated shape stable. In this paper, we focus on a category of axisymmetric origami consisting of triangular facets and edit the origami in 3D space for expanding its variations. However, it is difficult to retain the developability, which requires the sum of the angles around each interior vertex needing to equal 360 degrees, for designing origami. Intersections occur between crease lines when such a value is larger than 360 degrees. On the other hand, blank spaces (unfolded areas) emerge in the crease pattern when the value is less than 360 degrees. The former case is difficult to generate a realizable shape due to the crease lines are intersected with each other. For the latter case, however, blank spaces can be filled with crease lines and become a part of the origami through tucking. Here, we propose a computational method to add flaps or tucks on the 3D shape, which contains non-developable interior vertices, for achieving the resulting origami. Finally, on the application side, we describe a load-bearing experiment on a stool shape-like origami to demonstrate the potential usage.