MathSciDoc: An Archive for Mathematician ∫

In this paper, we present a novel pairwise-force smoothed particle hydrodynamics (PF-SPH) model to allow modeling of various interactions at interfaces in real time. Realistic capture of interactions at interfaces is a challenging problem for SPH-based simulations, especially for scenarios involving multiple interactions at different interfaces. Our PF-SPH model can readily handle multiple kinds of interactions simultaneously in a single simulation; its basis is to use a larger support radius than that used in standard SPH. We adopt a novel anisotropic filtering term to further improve the performance of interaction forces. The proposed model is stable; furthermore, it avoids the particle clustering problem which commonly occurs at the free surface. We show how our model can be used to capture various interactions. We also consider the close connection between droplets and bubbles, and show how to animate bubbles rising in liquid as well as bubbles in air. Our method is versatile, physically plausible and easy-to-implement. Examples are provided to demonstrate the capabilities and effectiveness of our approach.

We present the first computational tool to help ordinary users create transforming pop-up books. In each transforming pop-up, when the user pulls a tab, an initial flat 2D pattern, i.e. a 2D shape with a superimposed picture, such as an airplane, turns into a new 2D pattern, such as a robot, standing up from the page. Given the two 2D patterns, our approach automatically computes a 3D pop-up mechanism that transforms one pattern into the other; it also outputs a design blueprint, allowing the user to easily make the final model. We also present a theoretical analysis of basic transformation mechanisms; combining these basic mechanisms allows more flexibility of final designs. Using our approach, inexperienced users can create models in a short time; previously, even experienced artists often took weeks to manually create them. We demonstrate our method on a variety of real world examples.

Personal videos often contain visual distractors, which are objects that are accidentally captured that can distract viewers from focusing on the main subjects. We propose a method to automatically detect and localize these distractors through learning from a manually labeled dataset. To achieve spatially and temporally coherent detection, we propose extracting features at the Temporal-Superpixel (TSP) level using a traditional SVM-based learning framework. We also experiment with end-to-end learning using Convolutional Neural Networks (CNNs), which achieves slightly higher performance than other methods. The classification result is further refined in a post-processing step based on graph-cut optimization. Experimental results show that our method achieves an accuracy of 81% and a recall of 86%. We demonstrate several ways of removing the detected distractors to improve the video quality, including video hole filling; video frame replacement; and camera path re-planning. The user study results show that our method can significantly improve the aesthetic quality of videos.

We introduce a unified particle framework which integrates the phase-field method with multi-material simulation to allow modeling of both liquids and solids, as well as phase transitions between them. A simple elastoplastic model is used to capture the behavior of various kinds of solids, including deformable bodies, granular materials, and cohesive soils. States of matter or phases, particularly liquids and solids, are modeled using the non-conservative Allen-Cahn equation. In contrast, materials—made of different substances—are advected by the conservative Cahn-Hilliard equation. The distributions of phases and materials are represented by a phase variable and a concentration variable, respectively, allowing us to represent commonly observed fluid-solid interactions. Our multi-phase, multi-material system is governed by a unified Helmholtz free energy density. This framework provides the first method in computer graphics capable of modeling a continuous interface between phases. It is versatile and can be readily used in many scenarios that are challenging to simulate. Examples are provided to demonstrate the capabilities and effectiveness of this approach.

Sharp edges are important shape features and their extraction has been extensively studied both on point clouds and surfaces. We consider the problem of extracting sharp edges from a sparse set of colour-and-depth (RGB-D) images. The noise-ridden depth measurements are challenging for existing feature extraction methods that work solely in the geometric domain (e.g. points or meshes). By utilizing both colour and depth information, we propose a novel feature extraction method that produces much cleaner and more coherent feature lines. We make two technical contributions. First, we show that intensity edges can augment the depth map to improve normal estimation and feature localization from a single RGB-D image. Second, we designed a novel algorithm for consolidating feature points obtained from multiple RGB-D images. By utilizing normals and ridge/valley types associated with the feature points, our algorithm is effective in suppressing noise without smearing nearby features.