Synthesizing solid particle textures via a visual hull algorithm

Abstract

Numerous techniques have been proposed to successfully synthesize two-dimensional (2D) textures in terms of quality and performance. Three-dimensional (3D) or solid texture synthesis, on the other hand, remains relatively unexplored due to its higher complexity. There are several types of existing algorithms for solid texture synthesis, and among them, the outstanding work by Jagnow et al. opens a new door for solid texture synthesis of discrete particles; however, their work leaves two important issues unaddressed. First, without the help of stereology, users need to explicitly provide the 3D shapes of target particles for synthesis. Second, the locations and orientations of the 3D particles are resolved by a simulated annealing method, which is intrinsically a non-deterministic approach, and thus the optimality is not always guaranteed. To solve the shape problem, we propose a simple algorithm that applies the idea of visual hulls to approximate the shapes of 3D particles when only a 2D image is given; to solve the location and orientation problem, we design a deterministic algorithm that can place these desired 3D particles in space more properly. Additionally we also propose a method to further couple the color and size information of particles to achieve an even better resemblance to the 2D image.

Introduction

Due to the advances of technologies, modern GPUs have often surpassed CPUs in terms of graphics computing power. For example, today GPUs capable of rendering dozens of millions of smoothly-shaded triangles per second are common. Unfortunately, it is well-known that to achieve photorealism in real time, such rendering power alone is still not enough. One solution to this is to employ a clever idea to create photorealism from photorealism, which is the very spirit of texture mapping. That is, instead of creating photorealistic images from scratch, we could make use of real images to help to create the desired photorealism. However, one frequent problem encountered in texture mapping is that the source texture image often comes with a small size/low resolution. As a result, finding methods for generating a larger texture from a given smaller texture has become one of the most important problems in the field of texture synthesis.

Textures can be two-dimensional (2D), three-dimensional (3D), and four or even higher-dimensional. It is well-known that higher-dimensional texture mapping, such as 3D texture mapping, can be used to address the distortion problems that are associated with lower-dimensional texture mapping, such as 2D texture mapping. One classical example is to perform texture mapping to a sphere, where 3D texture mapping is usually preferred to its 2D counterpart. Despite the fact that there have been numerous research methodologies that can be used to successfully perform texture synthesis, in terms of quality and efficiency, most of the works concentrate on 2D texture synthesis, while 3D texture, or solid texture synthesis, receives relatively less attention. The scarcity of related papers is mainly attributed to the much higher complexity involved in solid texture synthesis. Among the existing approaches for solid texture synthesis, the synthesis of discrete particles has attracted our attention, as it is an area that so far has been even less explored. The pioneering work in this specific direction, done by Jagnow et al. [1], especially caught our eyes for its great outcome, but it still leaves two important issues that have not been fully addressed. The first issue concerns the 3D shapes of target synthesized particles. According to the paper, these shapes could be derived by applying stereology, otherwise the provision of 3D particles is required. However, as often times only one 2D image is available for texture synthesis, the application of stereology may be difficult. Instead, we propose a simple algorithm that could approximately construct the shapes of desired 3D particles through the concept of visual hull, assuming the synthesized 3D particles are isotropic, i.e., bearing similar cross sections from every viewing direction. The second issue is regarding the placement of these 3D particles. In their paper, this issue is solved by a simulated annealing approach, where all the particles were initially put into the volume, and then their locations or even orientations could be gradually adjusted to avoid collisions. Rather than using such a soft optimization technique, where the optimal solution cannot always be guaranteed, we develop a simple algorithm that could deterministically and appropriately place the particles in the output texture volume. Additionally, we have further coupled the color and size information of particles to achieve even better results than all existing approaches.

The rest of the paper is organized as the following. Section 2 reviews some of the literature related to this study. Section 3 details how we synthesize solid texture of particles. Section 4 presents the experimental results produced by our system, while Section 5 concludes our work and hints several potential future research directions.