2013 13th International Conference on Computer-Aided Design and Computer Graphics

Stego-Marbling-Texture
Jiayi Xu
Hangzhou Dianzi University, China
Email: xujiay@hdu.edu.cn

Aubrey Jaffer
Digilant, USA
Email: agj@alum.mit.edu

Xiaoyang Mao (Corresponding Author)
University of Yamanashi, Japan
Email: mao@yamanashi.ac.jp

Shufang Lu
State Key Lab of CAD&CG,
Zhejiang University, China
Email: lushufang@cad.zju.edu.cn

Xiaogang Jin
State Key Lab of CAD&CG,
Zhejiang University, China
Email: jin@cad.zju.edu.cn

Li Li
Hangzhou Dianzi University, China
Email: lili2008@hdu.edu.cn

Masahiro Toyoura
University of Yamanashi, Japan
Email: mtoyoura@yamanashi.ac.jp

Abstract—We present stego-marbling-texture, a new andunique texture design method which allows users to deliver
personalized messages with beautiful marbling textures. Our
approach is inspired by the success of the recent work onmodeling traditional marbling operations as mathematical
functions. The encrypter transforms an input image or a text
message into an intricate marbling pattern using marbling
operations deﬁned as reversible functions, and the decrypter
recovers the input image or message through reversing theprocess of marbling operations. When applying marbling
operations, the parameters of operations are automaticallyrecorded, encrypted, and then invisibly embedded into themarbling pattern to create a stego-marbling-texture. In thisway, the decrypter can be implemented as a stand along
software, enabling the receiver to extract the hidden message
from the stego-marbling-texture without requiring any extra
information from the sender. To ensure that the message isunnoticeably and beautifully covered by the marbling texture,
we propose a new technique for automatically creating a
background which is harmonious with the input message basedon a set of visual perception cues.

convey additional information. The technique is comprisedof an encrypter and a decrypter. The encrypter is realized as
an interactive marbling texture design system which allows
a user to take a message or an image as the input and turnit into a desired marbling pattern by successively applying
reversible mathematical marbling functions. The parametersof the functions are automatically recorded, encrypted, andinvisibly embedded into the resulting marbling pattern tocreate a stego-marbling-texture. The decrypter extracts themarbling parameters from the stego-marbling-texture andthen reveals the hidden message by applying the reverse of
the marbling functions.
One large advantage of marbling is that only a few basic
operations are sufﬁcient to design a beautiful piece of art
and even novice users can easily create an intricate andmysterious pattern by compounding the basic operation
steps. By representing each operation as the parametersof the mathematical formula, our technique succeeded in
encoding the sequence of marbling operations as a compact
bit string which can be embedded into the marbling patternitself. In this way, any marbling textures, freely created bya user can be used for conveying private messages. Since
the stego-marbling-textures consist of all the information
required for retrieving the hidden messages, the decrypter
can be implemented and distributed independently of theinteractive marbling texture design system. For example, we
can make the decrypter as a part of an image browser or acell phone application.
Figure 1(a) shows an example of using stego-marblingtexture for decorating an e-card. One can artistically transform a photograph or a private message into a stego-marblingtexture and share it with intimate friends only. The receiverof the e-card can enjoy watching the animation in which
the private message appears gradually when the decrypter
executes the reverse marbling operations successively. Fig-

Keywords-Texture design; Marbling texture; Steganography;
Information hiding; Visual perception;

I. I NTRODUCTION
Marbling is a traditional art of making patterns by manipulating the colors ﬂoating on liquid. Through centuries,
marbling patterns have been widely used for decorating
various products such as book cover, stationery, wallpaper,
wrapping paper, fabric, picture frames, and so on. This
traditional art is revitalized recently with modern computational technologies. A series of research works [1] [2] havebeen conducted to simulate the pattern formation process
on computers and several digital marbling systems havebeen developed allowing users to create fascinating marblingtextures interactively. Inspired by the latest research work on
mathematical marbling [2], this paper proposes a novel technique for creating value-added marbling textures which can
978-1-4799-2576-6/13 $31.00 © 2013 IEEE
DOI 10.1109/CADGraphics.2013.38

236

Figure 1: Stego-marbling-textures and the process to reveal the hidden messages. (a) An e-card; (b) Decorated virtual
objects.

visible only to authenticated receivers when necessary.

ure 1(b) shows an example of using stego-marbling-texture
for decorating virtual objects in 3D rendered scenes. By
making the decrypter as a part of a renderer, we can produce
fascinating animations from a single stego-marbling-texture.
The proposed technique can also be viewed as a uniquedata hiding technique with which messages are invisibly inwrought in beautiful marbling patterns. Unlike the majorityof the information embedding algorithms that may pose
various limits on the hidden message or may require theuse of visually unpleasing cover images, our technique canembed any image or hand writing message in its originalform into a beautiful marbling texture.
To be more speciﬁc, our work offers the following contributions:

II. R ELATED W ORK
Traditional marbling design involves tedious manual steps. Being able to relieve users from physical constraints
and tough manual steps, computer marbling systems havebeen attracting large attentions in the past decade. Typicalcomputer marbling texture design systems follow the ﬂuid
dynamic theory. Mao et al. [1] ﬁrst succeeded in modelingmarbling texture design process as a 2D computational
ﬂuid dynamic problem. Akgun [3] presented a design toolfor creating the Turkish style marbling and improved the
speed problem by reducing the image size. Acar et al. [4]proposed to use a multi-scale ﬂuid solver to model highturbulent marbling patterns. Jin et al. [5] extended Mao’s
work and ﬁrst succeeded in achieving real-time performanceby implementing the solver on GPU. Xu et al. [6] succeeded in generating more realistic marbling textures byusing complex high-order advection schemes to alleviatedissipation. Zhao et al. [7] employed an accurate yet fast
third-order unsplit semi-Lagragian constrained interpolation
proﬁle method to further reduce numerical dissipation withimproved stability. Recently, instead of physical simulation,
Lu et al. [2] used mathematical formulae to efﬁciently
describe the marbling operations. In addition to the advantage of being computationally efﬁcient and completely
dissipation free, the mathematical-formula-based approachalso implied the possibility of deﬁning reversible marbling
operations. Our technique reﬁnes and extends Lu et al’s
formulae to deﬁne a set of reversible marbling operations.
A user can turn a private message into a beautiful marblingtexture by combining those operations in different order, andWe present the novel idea of stego-marbling-texture,
which is useful not only as an unique texture synthesis
technique but also an effective information embedding
technique.
• We reﬁne and extend Lu’s work [2] by deﬁning a
set of marbling operations as reversible mathematical
functions. Even novice users can generate intricate patterns freely by combining these very basic operations
in different order. The resulting marbling texture canbe used for various decorating purposes.
• We propose an automatic background generation
method based on perceptual measures to make the embedded message less noticeable and retain harmonious
in the resulting texture.
• We propose a new data encoding and embedding technique to invisibly hide the operation parameters into
the resulting marbling texture, covering any message
with his/own preferred marbling patterns and making it•

237

contains hidden objects in a line drawing background image.
Mitra et al. [14] proposed a technique to generate images
consisting of 3D objects which are difﬁcult to be detectedby computer vision techniques but can be recognized byhumans. Papas et al. [15] designed real-world magic lenses
to warp source images into several hidden images viewed
from prescribed orientations. Chu et al. [16] created camouﬂage images by replacing the texture details of hidden
ﬁgures with the surrounding background and made sure an
appropriate amount of visual clues are remained. Tong etal. [17] proposed a method to generate hidden images by ﬁrst
detecting edge features of a hidden object, and then ﬁnding asuitable embedding place in the background scene using anenergy optimizing process. Du et al. [18] utilized the contour
completion property of human perception to generate digitalcamouﬂage images. All the above mentioned techniques aim
to hide objects in background images by fooling the humanrecognition process. Although the hidden objects are lessnoticeable, they are still recognizable by any observers. In
case of stego-marbling-texture, however, we can make thehidden message retrievable only to authenticated receivers
when necessary.

the message can be recovered when necessary by reversing
the operations.
Our technique can also be used as an effective steganography technology, which aims to conceal a message inside some media that will not arouse suspicion [8]. The
use of steganography technologies can be dated back tothousands years ago. One famous method of the traditional
steganography technique is to write a message with invisible
secret ink, such as lemon juice. When the ink is heated, themessage appears magically. Our technique mimics such effects digitally. By processing a stego-marbling-texture with adecrypter installed computer, the embedded private message
appears gradually when the reverse of marbling operations isapplied. The major components of a steganography system
include the cover message, secret message, stego key, andembedding algorithm. Although many digital media, suchas text and video can be used as cover massages in recent
technologies, image remains to be most popularly used [8].
Watermarking can also be viewed as a kind of steganography technology with the image to be protected being thecover image and the watermark being the message to beembedded. Compared to existing image based steganography
techniques, our technique has two advantages: ﬁrst, it candirectly hide an arbitrary image, such as the image of a hand
written message or photograph in its original form, while
the majority of the existing steganography technologies needto encode a secret message as bit strings or impose some
restraint on it to embed an image directly. For example, aclassic technique to embed an image into another one isto substitute the lower signiﬁcant bits of the cover image
with the secret image [9] [10], which may largely suppress
the dynamic range of both images. Second, our techniqueuses a multi-layered encryption scheme which makes it more
difﬁcult to detect the embedded message. The secret message is ﬁrst hidden by invisibly in-wrought into a marbling
pattern. Then the parameters of marbling operations are
encoded into an encrypted bit string and embedded into themarbling pattern to create a stego-marbling-texture using
a steganography technique. We use RSA algorithm [11]to encrypt the parameters and extended FPcode [12] forembedding the marbling parameters. Typical steganographyalgorithms, such as those based on LSB [9] [10], usuallycannot resist from the image degradation caused by printing
or capturing. Since we want to apply the stego-marblingtexture for decorating real products found in our daily life in
the future, such defection has to be taken into consideration.
FPcode uses the relative average intensity of adjacent blocks
in the cover image to embed a bit string, therefore it is lesssensitive to the change of illumination conditions and thedegradation caused by printing.
Information embedding is an attention attracting topic also
for computer graphics community. Several works have been
published on creating artistic work with hidden information.
Yoon et al. [13] presented a hidden-picture puzzle which

III. S YSTEM OVERVIEW
The proposed technique consists of 2 components: a realtime marbling design system for creating a stego-marblingtexture from a given message, and a decrypter which can be
distributed separately for the retrieval of the hidden message.
Figure 2 and Figure 3 depict the overall procedure forthe stego-marbling-texture generation and hidden message
retrieval, respectively. As shown in Figure 2, to create astego-marbling-texture, ﬁrst a background harmonious with
the input message in color and texture is automaticallycreated. Then, the user is allowed to perform the marbling
operations interactively until a desired pattern has beenobtained. The operations together with their parameters areautomatically recorded and encoded into a bit string. Finally,
the bit string is embedded into the marbling pattern tocreate the ﬁnal stego-marbling-texture. To retrieve the hidden
message, as shown in Figure 3, the embedded bit string isﬁrst extracted from the stego-marbling-texture and decoded
to obtain the parameters of marbling operations. Then thereverse of those operations are applied to the stego-marblingtexture to reveal the hidden message.
We introduce perceptual measures based on color, curviness,orientation, and frequency to guide the generation of a background with which the message becomes less noticeable in
the resulting stego-marbling-texture. Although as the default,
the system can automatically create such a background, theuser is also allowed to change the background as he/she
likes. In addition to a text message, the input message canalso be a full size image, such as a memorial photograph.
In such a case, marbling operations can be applied to thephotograph directly without using an additional background.

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Figure 4: Embed data with a random chosen background.

Figure 2: Stego-marbling-texture generating steps.
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Figure 3: Hidden message retrieval steps.

Figure 5: Embed data using our method.

The details about the deﬁnition of reversible marbling operations, the generation of background, and the encryption
and decryption algorithms will be given in Sect. IV, Sect. V,
and Sect. VI, respectively.

1) Determining the dominant colors: To achieve theharmony in color, we detect i most dominant colors in the
input message and use them for designing the background.
We construct a color histogram by recording the per-pixel
colors of the input message and select i tallest bins. i is thesmaller one of p and c, where p is a user given constant andc is the total number of colors in the input message.
2) Measuring the curviness: We employ Hough line
detector to measure the curviness of visual elements in the
input message. We compute the percentage of straight lines
in the detected lines. If straight lines are in the majority,elements like sticks and stripes are used for background.
Otherwise, elements like cycles, rings, ellipses, and arcs arechosen.
3) Measuring the orientation: We use the following
Gabor ﬁlter to measure the orientation.
u2 +v 2uπG(u, v) = e 2δ2 cos(2π
+ ),
(1)
2λ
2

IV. R EVERSIBLE MARBLING OPERATIONS
A. Generating backgroundA stego-marbling-texture should satisfy the following two
requirements:• It should be as beautiful as conventional marblingtextures.
• The hidden message should be as unnoticeable aspossible.
The ﬁrst step of marbling texture design is to paint the background with dye colors. In the traditional way, droplets andstripes are usually used. To create a stego-marbling-texture
satisfying the above requirements, special considerations are
required for the background. For example, if we simply
use a randomly chosen stripe pattern as the background,the hidden message becomes noticeable as an artifact whichruins the marbling pattern itself (Figure 4). Figure 5 showsa result using a background automatically created with theproposed technique, where the message has been artfully
hidden into the marbling pattern. Comparing Figure 4 to
Figure 5, we can ﬁnd that a key point to create a successfulstego-marbling-texture is to make the message harmonious
to the background. Based on such consideration, we propose an automatic background generating method based on
several perceptual measures of visual cues. Currently, four
visual cues are considered: color, curviness, orientation, andelement size.
More speciﬁcally, dye colors are determined by the maincolors from the input message. The type and size of background elements are determined by the strokes detected in
the input message. Then, droplets are randomly scatteredon the background. The background generation process isﬁnished when the overall percentage of colorful pixels isroughly the same as that in the input message. The diagramof design process is shown in Figure 6.

u = x cos(θ) + y sin(θ),
v = x sin(−θ) + y cos(θ).

(2)

Here λ and θ are the parameters for controlling the frequency
and orientation, respectively. We compute the power of theﬁlter response for k different frequencies and n orientations(k and n are given by the user). For each frequency, theorientation with the largest power is selected. As a result,
we have k dominant orientations. When generating thebackground, dye elements are rotated to these orientations.
4) Measuring the element size: We adopt two different
methods to determine the size of droplets. When using
stick, arc, and ring elements, we use the Gabor ﬁlter tomeasure the element size in the input message. We test kfrequencies and n evenly spaced orientations in the same
way as measuring the orientation. For each frequency, we
add power of all directions together. The inverse of thefrequency with maximum power should be close to halfof the dominant element size. Therefore, we adopt λ ofEquation 1 as the expected average size of elements forthe background. When round shaped elements should be239

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(a) Tine-line pattern(b) Sinusoidal pattern(c) Tangent pattern(d) Skew pattern(e) Circular patternFigure 7: Basic operations in our current implementation.

s deﬁnes the space between two tines.
We deﬁne a new reverse function as follows: if My = 0,
Equation 4 is used; otherwise, Equation 5 is used.
⎧x⎨ x = x − M
My = xαλMy,(4)⎩ y = y − |x Nx −Nx Mx y −Ax Nx −Ay Ny |+λused, we compute the bounding box of each element in themessage and use them to deﬁne the size of droplets.
B. Reversible marbling operations
We reﬁne the deﬁnitions of mathematical formulations
used by Lu [2], and ensure tine-line, sinusoidal wavy, andcircular marbling patterns to be reversible. In addition, we
propose new skew, and tangent-like wavy patterns. Users
may compose several manipulation steps to create a complex
and beautiful marbling result of their own style. The effectsof currently provided basic operations are demonstrated in
Figure 7.
1) Tine-line pattern: This function mimics the effect a
comb running straight across the image in x or y direction.
According to [2]’s deﬁnition (Figure 8(a)), point P (x, y) ismapped to point P  (x , y  ) according to equation:αλP = P +M,(3)d+λwhere d = |P −(A+f mod(d/s)s)N | calculates the distance
between point P and L (f mod is the modulo function), and



My

αλMx
My 
|y  Ny −Ny Mx
x −Ax Nx −Ay Ny |+λM
y = y  − Mxy = y 


x=x −

.

(5)

2) Sinusoidal wavy pattern: In order to get a reversible
mapping, this pattern is restricted to be sinusoidal shaped
wavy in x or y direction. Readers may refer [2] to get
implementation details.
3) Tangent wavy pattern: This function transforms partof the image into tangent curves. Only deformation in x or y
direction is allowed. In case of deformation in x direction,
x coordinate is mapped to x while keeping y coordinate
unchanged:x = x + min(β tan(αy), t),

240

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Figure 8: (a) Tine-line operation. (b) Circular operation.
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Figure 9: Structure of encrypted bit string.
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Figure 11: Embedding algorithm.

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Figure 10: Code structure for tine-line operations.

where α is the wavelength, and the maximum amount of
displacement is clamped to t.
4) Skew pattern: Combining this pattern with the sinusoidal wavy pattern or the tangent wavy pattern can realize
wavy curves at any direction. In case of deformation in x
direction, x coordinate is mapped to x while keeping ycoordinate unchanged:x = x + αy(a) Original image (b) FPcode method

A. Encoding of operations
The encoding step is realized using RSA algorithm [11].
As shown in Figure 9, information to be embedded into
marbling textures is encoded as a bit string composed of
2 parts: the public key, and the ciphertext. The ciphertext
is composed of marbling operations that encrypted by the
public key. More speciﬁcally, each parameter is encrypted
according to public key and then concatenated to form theciphertext. Since each operation has different parameters, anon-ﬁxed length coding structure is used to keep the code
as compact as possible. The coding of marbling operations
starts with the number of operations, followed by the parameters of each operation. To balance the security and capacity
consumed, 32 bits are used to represent the public key incurrent implementation. In Figure 10, we show the structureof the tine-line operation.

(7)

where α controls the amount of movement.
5) Circular pattern: We modify circular pattern proposedby [2] by introducing γ and new deﬁnition of d. To mimic
concentric cycles (Figure 8(b)), point P is mapped to P according to equation:cos θ − sin θ,(8)P = C + (P − C)
sin θ
cos θ
l
θ = |P −C|γ ,d = |f mod(|P − C|/s) − r|,(c) Our method

Figure 12: Comparison of visual quality between existing
method and ours.

(9)

where γ controls the attenuation, and s deﬁnes the space
between two tines.
By replacing −θ with θ, we get the backward transformationof point P from point P  .

B. Embedding of bit strings
To embed the bit string into a marbling pattern, we employ
FPcode proposed by Genta et al. [12]. FPcode aims toprovide an easy link between ofﬂine materials and online
information by embedding the URL information into theofﬂine materials. A user can access the online information
simply by capturing the ofﬂine materials with a decrypter
installed cellphone. Represented by QR-code, these kinds oftechnology, called media bridge [19], have been attracting
more and more attentions recently with the popularizationof the mobile-device-based Internet access. While the mainconcern of conventional steganography techniques is how
to make the algorithm robust against various attacks, amain technical issue of media bridge techniques is how toraise the success rate of decoding under various capturing
environments. Recently more media bridge technologies [20]V. E MBEDDING AND EXTRACTION ALGORITHMS
When creating a marbling pattern, the parameters of theoperations applied are automatically recorded and encoded
into a bit string. Then, a steganography technique is employed to embed the bit string into the marbling pattern tocreate a stego-marbling-texture. To retrieve the hidden message, the bit string is ﬁrst extracted from the stego-marblingtexture and decoded to get the operation parameters withwhich inverse operations can be performed to reveal thehidden message. In this session, we describe the details on
the encoding of operations, embedding of bit strings and theextraction of embedded bit strings.

241

(a) Color histogram.

(b) Gabor ﬁlter with different orientations.

(c) Gabor ﬁlter with different frequencies.

Figure 13: Feature detection of text message.

2) Compare the sum of yellow values between the adjacent block pairs (such as Block00 and Block01,
Block12 and Block13).
3) If the difference is smaller than f , thena) if the left block is smaller than the right block(such as Block12 and Block13), we get  0 ;b) if the left block is larger than the right block(such as Block00 and Block01), we get  1 .
From the ﬁrst 32 bits of extracted bit string, we get the
public key. Using both the transmitted public key and one’s
own private key in hand, we decrypt the type of operations
and their parameters. Finally, the reverse of those operations
are applied in a reverse order to reveal the hidden message.

based on steganography or watermarking algorithms havebeen developed. We adopt Genta et al.’s technique for taking
its advantage of having a relatively large embedding capacityand being robust against color distortion caused by scanning,
printing or the illumination conditions of capturing.
To ensure a high success rate of decoding from a printed
media, Genta et al.’s technique embeds one bit using therelative average intensity of two adjacent blocks. As shownin Figure 11, the original image is divided into m×m blocks.
The pixels of two adjacent blocks are modiﬁed so that theleft one has a lower average value than the right one for
embedding  0 , and higher than the right one for embedding 
1 . They suggest using the yellow channel of the image forthe embedding since human eyes are less sensitive to thechange in the yellow channel. We found, however, a naive
implementation of Genta et al.’s technique can introduce
noticeable artifacts in the resulting stego-marbling-texture.
An example of such artifacts is indicated in Figure 12(b).
It is caused by over changing the relative average value
between two blocks across edges. We solve this problem bylimiting the amount of color change from the original image
and skipping those block pairs which exceed the limit. Suchblock pairs can be identiﬁed by computing the difference of
average values between the two blocks.
We actually compare the sum of yellow values between
the block pairs. Constants m and f are user-controllable
parameters. Increasing m can enlarge the embedding capacity, but small blocks would need larger changes forindividual pixels to produce a difference of sum between
block pairs, which is signiﬁcant enough for embedding abit. f is also a parameter which trades image quality withembedding capacity. A small f identiﬁes more block pairs
as not suitable for embedding. The best values of m and fshould be application dependent.

VI. R ESULTS AND DISCUSSION
We have implemented our stego-marbling-texture design
system and decrypter on a computer with 2.93GHz Intel
Core 2 Due CPU and NVIDIA Geforce GTS 250 GPU.
The background generation algorithm is implemented using
OpenCV. The remaining part of our system is implemented
using GLSL shaders on GPU.
In Figure 13, we present a detailed explanation of the featuredetection process by taking Figure 4 as an example. Firstly,
we analyze the main colors components (Figure 13(a)).
Then, we ﬁnd 82% of the detected stroke is straight using
the Hough line detector, so sticks are used as the painting
element. To decide the width and orientation of sticks,
we use a Gabor ﬁlter with 6 orientations and 5 different
frequencies. In Figure 13(b), we ﬁxed the orientation, andtested 5 different frequencies. The response reaches strongest
when λ is 3. So we deﬁne the width of sticks to be 3 ± σ,
where σ is a randomly deﬁned small scalar. In Figure 13(c),we ﬁxed λ as 3, and tested 6 orientations. The the mainorientation is 30 degrees. Figure 1(a) shows an e-card ofstego-marbling-texture style. In Figure 1(b), stego-marblingtexture is used to decorate a virtual cup in 3D renderedscene.

C. Retrieval of hidden message
Taking Figure 11 as an example, the extraction of the bit
string from the stego-marbling-texture can be realized withthe following 3 steps:
1) Extract the yellow channel from the stego-marblingtexture and divide it into m ∗ m blocks.

VII. C ONCLUSIONS AND FUTURE WORK
We have proposed a novel technique for creating marblingtextures with the additional value of being able to convey

242

private messages. Users may enjoy the fun of interactive
marbling texture creation. The resulting stego-marblingtexture can be used for sharing private messages among
authenticated friends. Under the beautiful marbling pattern,large capacity of personalized messages can be hidden andrecovered in a fascinating way.
In our current version, hidden messages can only be retrieved
when the stego-marbling-texture is delivered as a digital
image. For the decoding from a printed stego-marblingtexture, the captured images need to be pre-processed forcorrecting the geometric distortions. Recently, many rotationand scaling resistant techniques have been developed forembedding information in printed materials without using
visible registration markers [21] [22]. We are now working
on incorporating these technologies into stegano-marblingtexture.

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ACKNOWLEDGMENT
This research was supported by the Natural Science
Foundation of Zhejiang Province, China (No. Q12F020007),the Zhejiang Provincial Education Department, China (No.
Y201121352), the Major Science and Technology Innovation Team of Zhejiang Province, China (No. 2010R50040),
the National Key Technology Research and Development
Program of the Ministry of Science and Technology ofChina (No. 2012BAH91F03), the National Natural Science
Foundation of China (No. 61370218 ).
The authors like to thank Mr. Dongliang Chen for his help
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