Computer-generated aesthetic patterns are widely used as design materials in various fields. The most common methods use fractals or dynamical systems as basic tools to create various patterns. To enhance aesthetics and controllability, some researchers have introduced symmetric layouts along with these tools. One popular strategy employs dynamical systems compatible with symmetries that construct functions with the desired symmetries. However, these are typically confined to simple planar symmetries. The other generates symmetrical patterns under the constraints of tilings. Although it is slightly more flexible, it is restricted to small ranges of tilings and lacks textural variations. Thus, we proposed a new approach for generating aesthetic patterns by symmetrizing quasi-regular patterns using general $k$-uniform tilings. We adopted a unified strategy to construct invariant mappings for $k$-uniform tilings that can eliminate texture seams across the tiling edges. Furthermore, we constructed three types of symmetries associated with the patterns: dihedral, rotational, and reflection symmetries. The proposed method can be easily implemented using GPU shaders and is highly efficient and suitable for complicated tiling with regular polygons. Experiments demonstrated the advantages of our method over state-of-the-art methods in terms of flexibility in controlling the generation of patterns with various parameters as well as the diversity of textures and styles.

Mixed reality technologies provide real-time and immersive experiences, which bring tremendous opportunities in entertainment, education, and enriched experiences that are not directly accessible owing to safety or cost. The research in this field has been in the spotlight in the last few years as the metaverse went viral. The recently emerging omnidirectional video streams, i.e., 360° videos, provide an affordable way to capture and present dynamic real-world scenes. In the last decade, fueled by the rapid development of artificial intelligence and computational photography technologies, the research interests in mixed reality systems using 360° videos with richer and more realistic experiences are dramatically increased to unlock the true potential of the metaverse. In this survey, we cover recent research aimed at addressing the above issues in the 360° image and video processing technologies and applications for mixed reality. The survey summarizes the contributions of the recent research and describes potential future research directions about 360° media in the field of mixed reality.