基于外观空间的纹理合成技术

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"Appearance-Space Texture Synthesis" 这篇论文介绍了一种新的纹理合成方法，它超越了传统的基于颜色邻域比较的纹理合成技术，引入了考虑非局部信息的“外观向量”（appearance vectors），如特征和辐射传递数据。这种方法显著提高了纹理合成的质量。在进行合成之前，通过降维处理这些外观向量，创建了一个新的低维、欧几里得空间——“外观空间”（appearance space）。与文本空间不同，外观空间具有较低的维度，这使得在合成过程中可以将运行时的邻域向量从5x5网格减少到仅4个位置，从而大大减少了计算复杂度。在这一统一框架下，研究者提出了几种创新技术，包括一致性各向异性合成、直接在普通图集（atlas）中进行表面纹理合成以及纹理平移（texture advection）。这些功能都能够在实时环境中实现，比以往的方法快3到4个数量级。论文中提到的“0541Appearance-Space Texture Synthesis”可能是论文的一个特定标识或编号，作者Sylvain Lefebvre和Hugues Hoppe来自于微软研究院。图1展示了将示例（exemplar）转换为8维外观空间（E'）的过程，这个转换提升了合成质量并开启了新的实时功能。在“Abstract”部分，作者进一步强调了他们的方法不仅改善了合成效果，而且允许在不牺牲速度的情况下实现新功能。他们指出，即使在复制、发布或分发作品时，只要不用于商业优势且包含版权声明，个人或课堂使用是被许可的。但对其他非ACM所有版权的作品，需要遵守相应的版权规定。这篇论文的核心贡献在于提出了一种新的纹理合成策略，它利用了更丰富的信息源和低维度空间来提高效率和质量，同时实现了多种高级纹理合成技术的实时应用。这对于游戏开发、图像处理、虚拟现实等领域具有重要的实际应用价值。

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Appearance-Space Texture Synthesis

Sylvain Lefebvre Hugues Hoppe

Microsoft Research

Exemplar E Transformed

′



Isometric synthesis Anisometric synthesis Synthesis in atlas domain Textured surface Radiance-transfer syn.

Figure 1: Transforming an exemplar into an 8D appearance space

′



improves synthesis quality and enables new real-time functionalities.

Abstract

Exemplar

Color space

′

Appearance space

′



dim. red.

Transforme

exemplar

texture synthesis

[]ES

appearance

vectors

Synthesized

coo

ates

Synthesized

texture

Figure 2: Overview of synthesis using exemplar transformation.

The traditional approach in texture synthesis is to compare color

neighborhoods with those of an exemplar. We show that quality

is greatly improved if pointwise colors are replaced by appearance

vectors that incorporate nonlocal information such as feature and

radiance-transfer data. We perform dimensionality reduction on

these vectors prior to synthesis, to create a new appearance-space

exemplar. Unlike a texton space, our appearance space is low-

dimensional and Euclidean. Synthesis in this information-rich

space lets us reduce runtime neighborhood vectors from 5×5 grids

to just 4 locations. Building on this unifying framework, we

introduce novel techniques for coherent anisometric synthesis,

surface texture synthesis directly in an ordinary atlas, and texture

advection. Remarkably, we achieve all these functionalities in

real-time, or 3 to 4 orders of magnitude faster than prior work.

Keywords: exemplar-based synthesis, surface textures, feature-based

synthesis, anisometric synthesis, dimensionality reduction, RTT synthesis.

1. Introduction

We describe a new framework for exemplar-based texture synthe-

sis (Figure 1). Our main idea is to transform an exemplar image E

from the traditional space of pixel colors to a space of appearance

vectors, and then perform synthesis in this transformed space

(Figure 2). Specifically, we compute a high-dimensional appear-

ance vector at each pixel to form an appearance-space image E′,

and map E′ onto a low-dimensional transformed exemplar

′



using principal component analysis (PCA) or nonlinear dimen-

sionality reduction. Using

′



as the exemplar, we synthesize an

image S of exemplar coordinates. Finally, we return E[S] which

accesses the original exemplar, rather than

[]ES

′



The idea of exemplar transformation is simple, but has broad

implications. As we shall see, it improves synthesis quality and

enables new functionalities while maintaining fast performance.

Several prior synthesis schemes use appearance vectors. Heeger

and Bergen [1995], De Bonet [1997], and Portilla and Simoncelli

[2000] evaluate steerable filters on image pyramids. Malik et al

[1999] use multiscale Gaussian derivative filters, and apply

clustering to form discrete textons. Tong et al [2002] and Magda

and Kriegman [2003] synthesize texture by examining inter-

texton distances. However, textons have two drawbacks: the

clustering introduces discretization errors, and the distance metric

requires costly access to a large inner-product matrix. In contrast,

our approach defines an appearance space that is continuous, low-

dimensional, and has a trivial Euclidean metric.

The appearance vector at an image pixel should capture the local

structure of the texture, so that each pixel of the transformed

exemplar

′



provides an information-rich encoding for effective

synthesis (Section 3). We form the appearance vector using:

• Neighborhood information, to encode not just pointwise attrib-

utes but local spatial patterns including gradients.

• Feature information, to faithfully recover structural texture

elements not captured by local L

error.

• Radiance transfer, to synthesize material with consistent meso-

scale self-shadowing properties.

Because exemplar transformation is a preprocess, incorporating

the neighborhood, feature, and radiance-transfer information has

little cost. Moreover, the dimensionality reduction encodes all the

information concisely using exemplar-adapted basis functions,

rather than generic steerable filters.

In addition we present the following contributions:

• We show that exemplar transformation permits parallel pixel-

based synthesis using a runtime neighborhood vector of just 4

spatial points (Section 4), whereas prior schemes require at least

5×5 neighborhoods (and often larger for complex textures).

• We design a scheme for high-quality anisometric synthesis.

The key idea is to maintain texture coherence by only accessing

immediate pixel neighbors, and to transform their synthesized

coordinates according to a desired Jacobian field (Section 5).

• We create surface texture by performing anisometric synthesis

directly in the parametric domain of an ordinary texture atlas.

Because our synthesis algorithm accesses only immediate pixel

neighbors, we can jump across atlas charts using an indirection

map to form seamless texture. Prior state-of-the-art schemes

541

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