Real-TimeTextureSynthesisbyPatch-BasedSampling基于样图的纹理合成

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Real-Time Texture Synthesis by

Patch-Based Sampling

LIN LIANG, CE LIU, YING-QING XU, BAINING GUO,

and HEUNG-YEUNG SHUM

Microsoft Research China, Beijing

We present an algorithm for synthesizing textures from an input sample. This patch-based sampling

algorithm is fast and it makes high-quality texture synthesis a real-time process. For generating

textures of the same size and comparable quality, patch-based sampling is orders of magnitude

faster than existing algorithms. The patch-based sampling algorithm works well for a wide variety

of textures ranging from regular to stochastic. By sampling patches according to a nonparametric

estimation of the local conditional MRF density function, we avoid mismatching features across

patch boundaries. We also experimented with documented cases for which pixel-based nonpara-

metric sampling algorithms cease to be effective but our algorithm continues to work well.

Categories and Subject Descriptors: I.2.10 [Artiﬁcial Intelligence]: Vision and Scene Understand-

ing—texture; I.3.3 [Computer Graphics]: Picture/Image Generation; I.4.7 [Image Processing

and Computer Vision]: Feature Measurement—texture

General Terms: Algorithms

Additional Key Words and Phrases: Texture synthesis, patch-pasted nonparametric sampling

1. INTRODUCTION

Texture synthesis has a variety of applications in computer vision, graphics, and

image processing. An important motivation for texture synthesis comes from

texture mapping. Texture images usually come from scanned photographs, and

the available photographs may be too small to cover the entire object surface.

In this situation, a simple tiling will introduce unacceptable artifacts in the

forms of visible repetition and seams. Texture synthesis solves this problem by

generating textures of the desired sizes. Other applications of texture synthesis

include various image processing tasks such as occlusion ﬁll-in and image/

video compression.

The texture synthesis problem may be stated as follows. Given an input sam-

ple texture I

, synthesize a texture I

out

that is sufﬁciently different from the

given sample texture, yet appears perceptually to be generated by the same

underlying stochastic process. In this work, we use the Markov Random Field

Authors’ address: Microsoft Research China, 5F, Beijing Sigma Center, No. 49., Zhichun Road,

Haidian District, Beijing, 100080, PRC; email: bainguo@microsoft.com.

Permission to make digital/hard copy of part or all of this work of personal or classroom use is

granted without fee provided that the copies are not made or distributed for proﬁt or commercial

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that copying is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers,

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2001 ACM 0730-0301/01/0700-0127 $5.00

ACM Transactions on Graphics, Vol. 20, No. 3, July 2001, Pages 127–150.

128

•

L. Liang et al.

(MRF) as our texture model and assume that the underlying stochastic pro-

cess is both local and stationary. We choose MRF because it is known to ac-

curately model a wide range of textures. Other successful but more special-

ized models include reaction-diffusion [Turk 1991; Witkin and Kass 1991], fre-

quency domain [Lewis 1984], and fractals [Fournier 1982; Worley 1996] (see also

Perlin [1985]).

In recent years, a number of successful texture synthesis algorithms have

been proposed in graphics and vision. Motivated by psychology studies, Heeger

and Bergen [1995] developed a pyramid-based texture synthesis algorithm

that approximately matches marginal histograms of ﬁlter responses. Zhu et al.

[1997, 1998] introduced a mathematical model called FRAME, which integrates

ﬁlters and histograms into MRF models and uses a minimax entropy princi-

ple to select feature statistics. Several texture synthesis algorithms are based

on matching joint statistics of ﬁlter responses. De Bonet’s [1997] algorithm

matches the joint histogram of a long vector of ﬁlter responses. Portilla and

Simoncelli [1999] developed an iterative projection method for matching the

correlations of certain ﬁlter responses. These methods, along with many oth-

ers in the literature [Iverson and Lonnestad 1994; Wu et al. 2000], represent

two different approaches to texture synthesis. The ﬁrst is to compute global

statistics in feature space and sample images from the texture ensemble [Zhu

et al. 2000] directly.

The second approach is to estimate the local conditional

probability density function (PDF) and synthesize pixels incrementally [Zhu

et al. 1997].

The texture synthesis algorithm we propose follows the second approach. In

their pioneer work, Zhu et al. [1997] explored this approach using the analyt-

ical FRAME model and an accurate but expensive Markov chain Monte Carlo

method. More recently, Efros and Leung [1999] demonstrated the power of

sampling from a local PDF by presenting a nonparametric sampling algorithm

that works well for a wide variety of textures ranging from regular to stochas-

tic. Efros and Leung’s algorithm, while much faster than Zhu et al. [1997],

is still too slow. Inspired by a cluster-based texture model [Popat and Picard

1993], Wei and Levoy [2000] signiﬁcantly accelerated Efros and Leung’s algo-

rithm using tree-structured vector quantization (TSVQ). However, this TSVQ-

accelerated nonparametric sampling algorithm is still not real-time. Another

problem with Efros and Leung [1999] and Wei and Levoy [2000] is that they

break down for some textures. Efros and Leung [1999] attribute the problem

of their algorithm to the fact that it is a greedy algorithm and it can “slip”

into a wrong part of the search space and start to grow “garbage.” Wei and

Levoy’s algorithm also suffers quality problems. Ashikhmin [2001] noted the

quality problems of Wei and Levoy’s algorithm on a class of textures and has

developed a special-purpose algorithm for that class. It is possible to combine

Ashikhmin’s algorithm with that of Wei and Levoy, as Hertzmann et al. [2001]

have done.

Please also see Heeger and Bergen [1995], DeBonet [1997], Portilla and Simoncelli [1999], and

Zhu et al. [2000].

ACM Transactions on Graphics, Vol. 20, No. 3, July 2001.

Patch-Based Sampling

•

129

Fig. 1. Texture synthesis example: (a) 192 × 192 input sample texture; (b) 256 × 256 texture

synthesized by patch-based sampling. The synthesis takes 0.02 seconds on a 667 MHz PC.

In this article we show that high-quality texture can be synthesized in real-

time on a midlevel PC. A key ingredient of our patch-based sampling algorithm

is a sampling scheme that uses texture patches of the sample texture as build-

ing blocks for texture synthesis. The patch-based sampling algorithm is fast.

For synthesizing textures of the same size and comparable (or better) quality,

our algorithm is orders of magnitude faster than existing texture synthesis al-

gorithms including Wei and Levoy [2000]. Figure 1 shows an example produced

by our algorithm. After spending 0.6 seconds analyzing the input sample, our

algorithm took 0.02 seconds to synthesize this texture on a 667 MHz PC. The

patch-based sampling algorithm works well for a wide variety of textures rang-

ing from regular to stochastic. We examined documented cases for which Efros

and Leung [1999], Wei and Levoy [2000], and Ashikhmin [2001] cease to be

effective and have found that our algorithm continues to produce good results.

In particular, the texture patches in our sampling scheme provide implicit con-

straints for avoiding garbage as found in some textures synthesized by Efros

and Leung [1999].

The patch-based sampling algorithm is an extension of our earlier work on

texture synthesis by random patch pasting [Xu et al. 2000]. Praun [2000] has

successfully adapted this patch-pasting algorithm for texture mapping on 3-D

surfaces. Unfortunately, these patch-pasting algorithms suffer from mismatch-

ing features across patch boundaries. The patch-based sampling algorithm, on

the other hand, avoids mismatching features across patch boundaries by sam-

pling texture patches according to the local conditional MRF density. Patch-

based sampling includes patch pasting as a special case, in which the local

PDF implies a null statistical constraint.

Patch-based sampling is amenable to acceleration and the fast speed of our al-

gorithm is partially attributable to our carefully designed acceleration scheme.

The core computation in patch-based sampling can be formulated as a search for

approximate nearest neighbors (ANN). We accelerate this search by combining

ACM Transactions on Graphics, Vol. 20, No. 3, July 2001.

130

•

L. Liang et al.

an optimized technique for general ANN search, a novel data structure called

the quadtree pyramid for ANN search of images, and principal components

analysis of the input sample texture.

The patch-based sampling algorithm is easy to use and ﬂexible. It is ap-

plicable to both unconstrained and constrained texture synthesis. Examples of

constrained texture synthesis include hole ﬁlling and tileable texture synthesis.

The patch-based sampling algorithm has an intuitive randomness parameter.

The user can utilize this parameter to interactively control the randomness of

the synthesized texture.

In concurrent work, Efros and Freeman [2001] developed a texture quilting

algorithm. For unconstrained texture synthesis, texture quilting is very similar

to patch-based sampling. There are several differences between our work and

that of Efros and Freeman [2001]. First, we accelerate patch-based sampling

and demonstrate that it can run in real-time, whereas they do not explore the

issue of speed. Second, we show how to solve constrained texture synthesis prob-

lems, which they do not address. Finally, patch-based sampling and Efros and

Freeman [2001] use different techniques to improve the transitions between

texture patches. We apply feathering [Szeliski and Shum 1997] while Efros

and Freeman use a minimum error boundary cut. Later, we compare these two

boundary treatment techniques in detail.

The rest of the article is organized as follows. In Section 2, we introduce

patch-based sampling and its applications to unconstrained and constrained

texture synthesis. In Section 3, we present our acceleration techniques. The

texture synthesis results and speed are discussed in Section 4, followed by

conclusions and suggestions for future work in Section 5.

2. PATCH-BASED SAMPLING

The patch-based sampling algorithm uses texture patches of the input sample

texture I

as the building blocks for constructing the synthesized texture I

out

In each step, we paste a patch B

of the input sample texture I

into the synthe-

sized texture I

out

. To avoid mismatching features across patch boundaries, we

carefully select B

based on the patches already pasted in I

out

, {B

, ..., B

k−1

The texture patches are pasted in the order shown in Figure 3. For simplicity,

we only use square patches of a prescribed size w

× w

2.1 Sampling Strategy

Let I

and I

be two texture patches of the same shape and size. We say that

and I

match if d(R

, R

) <δ, where d() represents the distance between

two texture patches and δ is a prescribed constant.

Assuming the Markov property, the patch-based sampling algorithm esti-

mates the local conditional MRF (FRAME or Gibbs) density p(I

| I

∂ R

)ina

nonparametric form by an empirical histogram. Deﬁne the boundary zone ∂ R

of a texture patch I

as a band of width w

along the boundary of R as shown

in Figure 2. When the texture on the boundary zone I

∂ R

is known, we would

like to estimate the conditional probability distribution of the unknown texture

patch I

. Instead of constructing a model, we directly search the input sample

ACM Transactions on Graphics, Vol. 20, No. 3, July 2001.

Patch-Based Sampling

•

131

Fig. 2. A patch-based sampling strategy. In the synthesized texture shown in (b), the hatched area

is the boundary zone. In the input sample texture shown in (a), three patches have boundary zones

matching the texture patch I

in (b) and the red patch is selected.

texture I

for all patches having the known I

∂ R

as their boundary zones. The

results of the search form an empirical histogram 9 for the texture patch I

To synthesize I

, we just pick an element from 9 at random. Mathematically,

the estimated conditional MRF density is

p(I

| I

∂ R

) =

δ(I

− I

= 1,

where I

is a patch of the input sample texture I

whose boundary zone I

∂ R

matches the boundary zone I

∂ R

and δ() is Dirac’s delta. The weight α

is a

normalized similarity scale factor.

With patch-based sampling, the statistical constraint is implicit in the bound-

ary zone ∂ R. A large boundary zone implies a strong statistical constraint. Gen-

erally speaking, a nonparametric local conditional PDF such as in Efros and

Leung [1999] and Wei and Levoy [2000] is faster to estimate than the analyt-

ical FRAME model in Zhu et al. [1997]. On the down side, the nonparametric

density estimation is subject to greater statistical ﬂuctuations, because in a

small sample texture I

there may be only a few sites that satisfy the local

statistical constraints.

2.2 Unconstrained Texture Synthesis

Now we use the patch-based sampling strategy to choose the texture patch B

the kth texture patch to be pasted into the output texture I

out

As Figure 3(a) shows, only part of the boundary zone of B

overlaps the

boundary zone of the already pasted patches {B

, ...,B

k−1

} in I

out

.Wesay

that two boundary zones match if they match in their overlapping region. In

Figure 3(a), B

has a boundary zone E

of width w

. The already pasted

patches in I

out

also have a boundary zone E

out

of width w

. According to the

patch-based sampling strategy, E

should match E

out

For the randomness of the synthesized texture I

out

, we form a set 9

con-

sisting of all texture patches of I

whose boundary zones match E

out

. Let B

(x, y)

ACM Transactions on Graphics, Vol. 20, No. 3, July 2001.

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