Poly-Spline Finite Element Method
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can sometimes be computed between nearly-isometric meshes, the more general case of meshes with diverse geometries remains challenging. We propose a novel approach for direct map computation between triangle meshes without mapping to an intermediate domain, which optimizes for the harmonicity and reversibility of the forward and backward maps. Our method is general both in the information it can receive as input, e.g. point landmarks, a dense map or a functional map, and in the diversity of the geometries to which it can be applied. We demonstrate that our maps exhibit lower conformal distortion than the state-of-the-art, while succeeding in correctly mapping key features of the input shapes.
With the popularity of immersive display systems that fill the viewers field of view (FOV) entirely, demand for wide FOV content has increased. A video extrapolation technique based on reuse of existing videos is one of the most efficient ways to produce wide FOV content. Extrapolating a video poses a great challenge, however, due to the insufficient amount of cues and information that can be leveraged for the estimation of the extended region. This paper introduces a novel framework that allows the extrapolation of an input video and consequently converts a conventional content into one with wide FOV. The key idea of the proposed approach is to integrate the information from all frames in the input video into each frame. Utilizing the information from all frames is crucial because it is very difficult to achieve the goal with a 2D transformation based approach when parallax caused by camera motion is apparent. Warping guided by scene-space information matches the viewpoints between the different frames. The matched frames are blended to create extended views. Various experiments demonstrate that the results of the proposed method are more visually plausible than those produced using state-of-the-art techniques.
We propose a new algorithm for color transfer between images that have perceptually similar semantic structures. We aim to achieve a more accurate color transfer that leverages semantically-meaningful dense correspondence between images. To accomplish this, our algorithm uses neural representations for matching. Additionally, the color transfer should be spatially-variant and globally coherent. Therefore, our algorithm optimizes a local linear model for color transfer satisfying both local and global constraints. Our proposed approach jointly optimizes matching and color transfer, adopting a coarse-to-fine strategy. The proposed method can be successfully extended from "one-to-one" to "one-to-many" color transfers. The latter further addresses the problem of mismatching elements of the input image. We validate our proposed method by testing it on a large variety of image content.
Advances in multimaterial 3D printing have the potential to reproduce various visual appearance attributes of an object in addition to its shape. Since many existing 3D file formats encode color and translucency by RGBA textures mapped to 3D shapes, RGBA information is particularly important for practical applications. In contrast to color (encoded by RGB), translucency (encoded by A) is neither linked to any measurable physical nor perceptual quantity and is, therefore, open for interpretation. In this paper, we propose a rigorous definition for A suitable for graphical 3D printing which links both optical material properties and perceptual uniformity for human observers. By deriving our definition from the absorption and scattering coefficients of virtual reference materials with an isotropic phase function, we achieve two important properties. First, a simple adjustment of A is possible, which preserves the translucency appearance if an object is rescaled for printing. Second, determining A for a real material can be achieved by minimizing a distance function between light transport measurements of this material (conducted by commercial spectrophotometers) and simulated measurements of the reference materials. Finally, we derive from visual experiments an embedding of A into a nearly perceptually-uniform scale of translucency for the reference materials.
Imaging objects obscured by occluders is a significant challenge for many applications. A camera that could ``see around corners'' could help improve navigation and mapping capabilities of autonomous vehicles or make search and rescue missions more effective. Time-resolved single-photon imaging systems have recently been demonstrated to record optical information of a scene that can lead to an estimation of the shape and reflectance of objects hidden from the line of sight of a camera. However, existing non-line-of-sight (NLOS) reconstruction algorithms have been constrained in the types of light transport effects they model for the hidden scene parts. We introduce a factored NLOS light transport representation that accounts for partial occlusions and surface normals. Based on this model, we develop a factorization approach for inverse time-resolved light transport and demonstrate high-fidelity NLOS reconstructions for challenging scenes both in simulation and with an experimental NLOS imaging system.