robust motion watermarking based on multiresolution analysismrl.snu.ac.kr/papers/eg2000.pdf ·...

EUROGRAPHICS 2000 / M. Gross and F.R.A. Hopgood(Guest Editors)

Volume 19(2000), Number 3

Robust Motion Watermarking based onMultiresolution Analysis

Tae-hoon Kim, Jehee Lee, and Sung yong Shin

Department of Computer Science, Korea Advanced Institute of Science and Technology,373-1 Kusung-dong Yusung-gu, Taejon, Republic of Korea

e-mail: [email protected], [email protected], and [email protected]

AbstractDigital watermarking is one of commonly used solutions for copyright protection. A watermark should be imper-ceptible and robust to various attacks. In this paper, we address watermarking for motion data. Our watermarkingscheme is based on two well-known ideas, so called multiresolution representation and spread spectrum. We em-bed a watermark into a motion signal by perturbing large detail coefficients of its multiresolution representation,and extract the watermark by analyzing perturbation of coefficients from a suspected signal. For more effectivewatermark extraction, we align suspected motion data to the original using dynamic time warping. Our schemehas merits of spread spectrum such as the resilience to common signal processing as well as the robustness to timewarping.

1. Introduction

The advent of motion capture systems offers a convenientmeans of acquiring realistic motion data, that is, capturinglive motion of a real actor. Due to the success of this tech-nology, realistic and highly detailed motion data are rapidlyspreading in computer animation. Archives of motion clipsare also commercially available. The proliferation of motiondata gives rise to demand on copyright protection for thosedata. One of widespread approaches for copyright protec-tion is digital watermarking, that is, embedding an owner-ship information into data. For this purpose, the embeddedinformation, called a watermark, is an imperceptible iden-tification code that permanently remains in the data unlessthey are extremely degraded.

The process of publishing watermarked data and provingownership claim is as follows: Suppose that one creates orig-inal data and embeds a watermark into them, and then pub-lishes the watermarked data while keeping the original andthe embedded watermark in secret. The published data maybe altered by an attacker, and then published as if they werethe attacker’s original work. Finding such suspected data,the author compares it with the original to extract the water-mark that may remain in the suspected. Finally, the authoranalyzes the similarity between inserted and extracted wa-

termarks. If the similarity is high enough to claim an owner-ship, the author can prove that the suspected data are illegalcopy of his (or her) work.

A common approach to embed a watermark is due tospread spectrum31, 32, which is a mechanism transmitting asignal over a much larger bandwidth than normally required.Such an approach enjoys various benefits from nice prop-erties such as jam resistance (JR), low probability of inter-cept (LPI), and so on. The property of JR provides a degreeof resistance to interference and jamming. The LPI prop-erty provides a means of decreasing the probability of inter-cept by an adversary. Spread spectrum-based watermarkingtransforms a signal to that in the frequency domain, and thenembeds a random watermark generated from a secret key.The watermark, embedded with this scheme, is undetectableand robust to various attacks due to the favorable propertiesof spread spectrum.

The motion data of an articulated figure consists of a bun-dle of motion signals. Every signal represents a sequenceof sampled values each of which corresponds to either theposition or the orientation of a part of the figure, called alink or segment. Unlike the position of a 3-dimensional ob-ject, its orientation cannot be expressed by a vector in a3-dimensional space without yielding any singularity. The

c© The Eurographics Association and Blackwell Publishers 2000. Published by BlackwellPublishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA02148, USA.

Tae-hoon Kim, Jehee Lee, and Sung yong Shin / Robust Motion Watermarking based onMultiresolution Analysis

non-singular representations, such as rotation matrices andunit quaternions, form aLie group which cause a compli-cation in obtaining frequency information from the motiondata. Thus, digital watermarking for motion data requires ex-tra efforts for handling orientation data.

In this paper, we present a new scheme of embeddingwatermarks into a motion signal based on the multiresolu-tion representation proposed by Lee28. This representationof a motion consists of a coarse base signal and a hierar-chy of motion displacement maps. Displacement mapping isoriginally invented for warping a canned motion while pre-serving its detail characteristics5, 44. In the context of mul-tiresolution analysis, the hierarchy of displacement maps isused for adding details sequentially to the base signal to re-produce the original motion encoded in the representation.The displacement maps are computed by two basic opera-tions: reduction and expansion. The expansion is commonlyachieved by a subdivision scheme that can be consideredas up-sampling followed by smoothing. The reduction isa reverse operation, that is, smoothing followed by down-sampling. The generalized version of interpolatory subdivi-sion schemes and smoothing filters are used to process mo-tion signals that include orientations as well as positions.

The remainder of the paper is organized as follows. Aftera brief review of watermarking and multiresolution repre-sentations, we present a multiresolution structure for repre-senting a motion and describe in detail how to construct itin section 3. In section 4, we discuss a motion watermarkingscheme based on the multiresolution representation. In sec-tion 5, we provide experimental results. Finally, we concludethis paper in section 6.

2. Related Work

In this section, we describe previous works about water-marking and multiresolution representations.

2.1. Watermarking Methods

Digital watermarking is one of commonly used solutions forcopyright protection although it may also be used for otherpurposes such as data authentication, fingerprinting, and se-cret data hiding as well. Watermarking schemes are classi-fied into forensic watermarking7, 8, 34, 36, 37 and blind detec-tion methods20, 43. The former requires original data, and thelatter needs only a secret key for detection. The forensic wa-termarking is more robust than the blind detection method,while the blind detection is more suitable to product moni-toring in network distribution or broadcasting43. In this pa-per, we focus on the forensic watermarking scheme for copy-right protection.

There are several watermarking methods proposed forvarious media such as image, audio, video, and 3D geomet-ric models. The early watermarking methods include mod-ifying the least significant bit of the data40, embedding a

secret information that resembles quantization noiseinto adithered image42, and etc. The reader is referred to Benderel al.1 and Coxet al.8 for excellent surveys of the early ap-proaches.

Watermarking schemes achieved more imperceptibilityand robustness by transforming the data using multires-olution analysis34, Fourier transform36, or discrete cosinetransform7, 8. These transform-domain-based approachescan embed a watermark into wide portion of the data with-out incurring noticeable visual artifacts. To prevent a wa-termark from being removed without extreme degradationof the data, the watermark is also embedded globally intothe most perceptually significant portions of the data by an-alyzing frequency domain. Ruanaidhet al.36, 37 modified thephase values of Fourier coefficients to convey information.Coxet al.7, 8 used a spread-spectrum method for informationembedding to achieve more robustness. Praunet al.34 ad-dressed robust 3D mesh watermarking by generalizing thespread-spectrum approach for arbitrary triangular meshes.

In the other schemes, the human visual system or the hu-man auditory system was used to generate a more effec-tive watermark. Boneyet al.4 generated a watermark by ap-proximating the frequency masking characteristics of the hu-man auditory system. Podilchuk and Zeng33 employed vi-sual models to determine image dependent upper bounds onwatermark insertion, and increased robustness to commonimage modification.

2.2. Multiresolution Representations

Multiresolution representations are enormously popular incomputer graphics applications such as curve and surfaceediting6, 14, 16, 25, 30, 39, polygonal mesh editing19, 24, 26, 45, im-age editing2, image querying23, texture analysis and syn-thesis 3, 21, video editing and viewing15, image and sur-face compression10, 11, global illumination 18, and varia-tional modeling17.

Multiresolution representations have been used for mo-tion editing and synthesis as well. Liuet al.29 employed hier-archical wavelets with adaptive refinement to provide a sig-nificant speedup for spacetime optimization. Bruderlin andWilliams5 used a digital filterbank technique to store motiondata as a hierarchy of detail levels, where each level rep-resents a different band of spatial frequencies. Through theuse of the hierarchy, the motion data can be modified interac-tively by amplifying/attenuating particular frequency bandsand a new motion can be generated by blending two existingmotions band-wisely.

3. Multiresolution Analysis

We employ the multiresolution representation of Lee28, thatcan be constructed through two basic operations: reductionand expansion (see Figure 1).

c© The Eurographics Association and Blackwell Publishers 2000.


-1.0

0.0

1.0

Figure 2: Multiresolution analysis for a live-captured signal. The four curves represent the change of w-, x-, y-, and z-components, respectively, of a unit quaternion with respect to time. (from left to right) Original signal,M (3),M (2),M (1),M (0)

Reduction Expansion

M ( )n

M ( )n-1

D( )n−1

Figure 1: Wiring diagram of the multiresolution analysis

3.1. Displacement Mapping

The configuration of an articulated figure is specified byits joint configurations in addition to the position and ori-entation of the root segment. For uniformity, we assumethat the configuration of each joint can be specified by a 3-dimensional rigid transformation. Then, we can describe theDOFs at every body segment as a pair of a vector inR3 anda unit quaternion inS3.

Themotion datafor an articulated figure comprise a bun-dle of motion signals. Each signal consists of a sequence offrames,{(pi ,qi) ∈R3×S3}, that correspond to the positionand orientation of a body segment. Each frame(pi ,qi) spec-ifies a rigid transformationT(pi ,qi) that maps a point inR3 toanother:

T(pi ,qi)(u) = qiuq−1i +pi , (1)

whereu = (x,y,z) ∈ R3 is considered as a purely imagi-nary quaternion(0,x,y,z). Given two motion signalsM ={(pi ,qi)∈R3×S3} andM ′ = {(p′i ,q′i )∈R3×S3}, the mo-tion displacementD = {(ui ,vi) ∈ R3×R3} between themmeasured in a local (body-fixed) coordinate system givesrise to a transformation,T(p′

i ,q′i ) = T(pi ,qi)◦T(ui ,exp(vi)), called

a motion displacement mapping. We compactly representthis equation byM ′ = M ⊕D or D = M ′M , where

(p′i ,q′i ) = (pi ,qi)⊕ (ui ,vi)

= (qiuiq−1i +pi ,qi exp(vi)).

(2)

Here, exp(v) denotes a 3-dimensional rotation about the axisv‖v‖ ∈ R3 by angle1

2‖v‖ ∈ R.

3.2. Multiresolution Representation

The multiresolution representation for a motion signalM is defined by a series of successively refined signalsM (0),M (1), · · · ,M (N−1) in addition to a series of displace-ment mapsD(0),D(1), · · · ,D(N−1). The construction algo-rithm starts with the original motionM = M (N) to com-pute a coarser and smoother signalM (N−1) by reduction,that is, applying a smoothing filter and then removing everyother frames to down-sample the signal. One common wayto blur signals is through a diffusion process that leads toa local update rulepi ← pi − λL jpi , whereλ is a diffusioncoefficient andL is a discrete Laplacian operator. For exam-ple, adopting the second Laplacian operatorL2, we have aspatial mask(− 1

16, 416, 10

16, 416,− 1

16) for smoothingpi ’s, andthis mask can also be used for smoothing an orientation sig-nal qi ’s by employing a scheme of Lee28. Given a mask(a−k, ...,a0, ...,ak), we smooth a sequence of motion frames,{(pi ,qi)} as follows:

p′i = a−kpi−k + · · ·+a0pi + · · ·+akpi+k (3)

q′i = qi exp

( k−1

∑m=−k

bm log(q−1i+mqi+m+1)

), (4)

where

bm =

{∑k

j=m+1 a j , if 0 ≤m≤ k−1,

∑mj=−k−a j , if −k≤m< 0.

The expansion ofM (N−1) interpolates the missing infor-mation through interpolatory subdivision. We use a four-point interpolatory scheme12, 13 that maps a sequence ofmotion frames,M (n−1) = {(pn−1

i ,qn−1i )}, to a refined

sequence,M (n) = {(pni ,q

ni )}, where the even numbered

frames(pn2i ,q

n2i) at level n are the frames(pn−1

i ,qn−1i ) at

leveln−1, and the odd numbered frames are newly insertedbetween old frames. The subdivision scheme is defined witha subdivision mask(− 1

16, 916, 9

16,− 116) that can be general-

ized for orientation data using Equation (4).

Then, the difference betweenM (N) and M (N−1) is ex-pressed as a displacement mapD(N−1) as follows:

D(N−1) = M (N)SM (N−1), (5)



coarse base signal coarse base signal

displacement maps

original motion signal watermarked motion signal

altered displacement maps

(a)

(b) (c)

(d)

1v

2v

3v

1′v

2′v

3′v

Figure 3: Overview of our watermarking scheme. Only the orientation component of a motion signal is illustrated. (a) Thequaternion signal,q1,q2, . . . ,qn of an original signal. (b) The multiresolution representation of the original signal. A coefficientof each displacement map is parameterized by a 3D vector. The displacement maps in the figure show only the first componentsof those vectors. (c) The multiresolution representation of the watermarked signal. (d) The orientation components of thewatermarked signal (see Figure 4) scaled up by a factor of 100.

whereS is an expansion operator. Cascading these oper-ations until there remains a sufficiently small number offrames in the motion signal, we can construct the multires-olution representation that consists of the coarse base signalM (0) and a series of displacement maps. The original signalcan be reconstructed by cascading expansion and displace-ment mapping starting from the base signal, that is,

M (n) = SM (n−1)⊕D(n−1) (6)

for 1 ≤ n ≤ N. The original motion must have(k2n + 1)frames to construct a hierarchy ofn levels with its base sig-nal of (k+ 1) frames. If the original motion has less than(k2n +1) frames, then we append extra frames at the end ofthe signal by duplicating the last frame.

4. Motion Watermarking

For robustness, we adopt a well-known scheme of spreadspectrum, that is, embedding a watermark into a wide rangeof frames in a motion signal. In order to support this scheme,we need a systematic way of identifying the perceptually sig-nificant frames scattered over the entire signal. Our multires-olution representation facilitates the scheme due to its capa-bility to manipulate the motion signal at different levels ofdetails. In other words, the multiresolution representation ofa motion signal consists of a base signal together with detailcoefficients that form a coarse-to-fine hierarchy of motiondisplacement maps. Each map represents a different detailof the motion. We embed a watermark into the motion by

perturbing its detail coefficients. The perturbation of a detailcoefficient at a coarse resolution alters a large portion of themotion, while that of a coefficient at a fine resolution affectsa small portion. The effect of perturbation reveals a sym-metric oscillatory pattern as shown in Figure 4. The size ofthe pattern depends on the resolution of a displacement mapwhich contains the coefficient to modify. This pattern has apeak value at its center position and rapidly vanishes at bothboundaries.

Only the owner of a motion knows the magnitude of alter-ation for the motion signal due to watermarking, and an at-tacker may know at best the possible alteration range of mag-nitude. To completely eliminate a watermark, the attacker isexpected to modify the published motion signal as large aspossible within this range. Having a different magnitude ofa motion signal from the original, the modified one containsnoticeable visible defects.

There is a trade-off between the robustness and the imper-ceptibility of watermarking. A large perturbation is robustbut easy to perceive, while a small perturbation is impercep-tible but easy to attack. To achieve robustness, it is a commonpractice to insert a watermark into perceptually significantregions of the signal8, 34. Therefore, we embed a watermarkinto a motion signal by perturbing its large coefficients. Tomake the watermark imperceptible, we perturb each coeffi-cient with sufficiently small magnitude.

The overview of watermarking is illustrated in Figure 3.In particular, this figure shows how a motion signal is per-



Figure 4: The perturbation signal: the first components ofperturbation applied to three coefficients of the displacementmaps.

turbed for watermarking. An original signal is decomposedinto a base motion signal and displacement maps. We se-lect m largest coefficients {(u1,v1), (u2,v2), . . . , (um,vm)}from the displacement maps. They are altered to {(u′1,v

′1),

(u′2,v′2), . . . ,(u′m,v′m)} by watermarking. Reconstructing the

motion signal using these altered displacement maps makesthe watermarked signal. The difference between the signalin Figure 3-(a) and that in Figure 3-(d) is shown in figure 4as a sequence of vectors, log(q−1

1 q′1), . . . , log(q−1n q′n). The

magnitude of perturbation is exaggerated for effective expla-nation.

4.1. Watermarking

Our watermarking scheme consists of following steps: wa-termark insertion into the original signal, and watermark ex-traction from the suspected signal, and similarity check be-tween inserted and extracted watermarks.

Watermark generation. Prior to inserting watermark intoa motion signal, we first generate a watermarkw ={w1, . . . ,wm}, where wi ∈ R. Each wi is sampled inde-pendently from a normal distribution with zero mean andunit variance. To make the watermarking scheme be non-invertible, we apply a cryptographic hash function, MD538

to the original motion signal concatenated with the owner’skey, and then seed a random number generator with thehashed value9. Given them largest coefficients for water-marking, each element of the watermark is used to perturbone of those coefficients.

Watermark insertion and extraction. We insertw into theoriginal signalM in order to obtain a watermarked oneM ′.After selecting them largest coefficients, we scale each ofthe coefficients usingw. Let D(l) be the displacement mapat level l of the multiresolution representation ofM , and(ui ,vi) the i-th largest coefficient of the displacement maps,{D(0),D(1), ...,D(N−1)}, whereN−1 is the maximum level

of hierarchy for the displacement maps. We compute the per-turbed displacement vector(u′i ,v

′i ) for i = 1, ...,mas follows:

(u′i ,v′i ) = (1+αwi)(ui ,vi), (7)

where α is a user-provided scaling parameter. Thisperturbation gives the new displacement maps

{D′(0),D′(1)

, ...,D′(N−1)}. We construct the watermarkedsignal M ′ from these displacement maps by successivelyadding them to the base signal. As long as the selecteddisplacement vector is not a zero vector, the insertionprocess is invertible.

Watermark extraction is the inverse of watermark inser-tion in some sense. From the suspected motionM∗, we buildits multiresolution representation and extract the watermarkw∗ by computingw that minimize the following functionf (w):

f (w) = ‖(u∗i ,v∗i )− (1+αw)(ui ,vi)‖2, (8)

whereα, (ui ,vi), (u∗i ,v∗i ) is the same as defined in Equation(7). This function is minimized at

w =(u∗i ,v∗i ) · (ui ,vi)−‖(ui ,vi)‖2

α‖(ui ,vi)‖2, (9)

which becomes the extracted watermarkw∗i .

Analysis of similarity. A watermarking scheme must min-imize the false-positive probability, that is, the probabilityof incorrectly asserting that the data is watermarked. Thefalse-negative probability is the probability of failing to de-tect watermarked data. Ideally, it is desired to minimizeboth false-positive and false-negative probabilities, simulta-neously. However, we have a trade-off between them; en-forcing low false-negative probability often leads to highfalse-positive probability to yield the weak fidelity of anownership claim. Therefore, like other well-known water-marking schemes7, 8, 34, we focus on decreasing the false-positive probability.

We compare the inserted and extracted watermarks statis-tically. At this point, we remove outliers, that is, elementsof which differences from the mean value are greater than agiven threshold. Then, as in Praunet al.34, we compute linearcorrelation between watermarks:

ρ = ∑i (w∗i −w∗)(wi −w)√

∑i (w∗i −w∗)2×∑i (wi −w)2

, (10)

wherewi andw∗i are an element of the original watermark

and that of the extracted watermark after discarding outliers,respectively. In addition,w and w∗ are the average of theelements inw and that of the elements inw∗, respectively.Finally, we compute thefalse-positiveprobability using Stu-dent’st-test35.



M

*M

1 2 3 4 5 6 7 8 9 11

1

2

3

4

5

6

7

8

9

*M

1 2 3 4 5 6 7 8 9 10 11M

10

10

11

Figure 5: Representation of signal resampling.

4.2. Motion Signal Aligning

A suspected signal may be cropped or non-uniformly scaledalong the time axis. Therefore, before inspecting the water-mark, we optionally align the suspected signal to the orig-inal. Let M∗ andM be the suspected and original signals,respectively. That is,

M∗ = {(p∗1,q∗1),(p∗2,q∗2), ...,(p∗l ,q∗l )},M = {(p1,q1),(p2,q2), ...,(pn,qn)}.

(11)

Resampling. Suppose that the suspected signalM∗ is non-uniformly scaled along the time axis. Then, we resam-ple M∗ to align with M using the dynamic time warpingscheme5, 22, 41. Let G be al × n rectangular grid, where thecolumn indices correspond to the frame numbers ofM andthe row indices do to those ofM∗ (see Figure 5). Thus, agrid point (i, j) represents an ordered pair of frames, thatis, thei-th frame ofM∗ and thej-th frame ofM . With thisgrid, the resampling problem is reduced to constructing apath on the gridG from (1,1) to (l ,n). At each grid point,the path is allowed to move horizontally, vertically, or diago-nally. To minimize the total difference betweenM andM∗, adynamic programming technique is employed. LettingMi, jbe the minimum difference between the subsignal ofM∗ upto thei-th frame and that ofM up to thej-th frame, we have

Mi, j = min(Mi−1, j−1,Mi−1, j ,Mi, j−1)+di, j , (12)

wheredi, j = ‖(p∗i ,q∗i ) (p j ,q j )‖, that is, the difference be-tween thei-th frame ofM∗ and thej-th frame ofM . In ad-dition, M1,1 = d1,1 andMi, j =∞ for i < 1, j < 1, i > l , orj > n. Clearly,Ml ,n can be obtained inO(ln) time, and thuswe can optimally resampleM∗ in the same time bound.

Registration. Now, suppose thatM∗ is a cropped versionof M . Then, the frames in the cropped portion ofM doesnot correspond to any frame ofM∗. Therefore, we resampleM∗ to register withM and fill the missing portions ofM∗

using their corresponding portions ofM . We examine everyportion ofM , that is, the subsequence of consecutive framesof M to find an optimal portion that minimizes its differencefrom M∗, using the dynamic time warping. Since there are

Table 1: Watermark detection results for four motion data,DataA: Fly Spin Kick, DataB: Back Flip, DataC: BroadJump, and DataD: Blown Back

Attack DataA DataB DataC DataD

1. No attack 10−99 10−99 10−99 10−99

2. Noise 0.2% 10−18 10−17 10−52 10−26

3. Noise 0.7% 10−9 10−6 10−21 10−16

4. Cropping 10−35 10−22 10−14 10−9

5. Smoothing 1 10−24 10−9 10−15 10−11

6. Smoothing 2 10−7 10−5 10−5 10−12

7. Simplifying 1 10−35 10−35 10−35 10−35

8. Simplifying 2 10−27 10−38 10−27 10−17

9. Simplifying 3 10−15 10−28 10−32 10−15

10. Time warping 1 10−8 10−27 10−13 10−24

11. Time warping 2 10−10 10−3 10−30 10−36

12. Enhancement 10−4 10−4 10−12 10−4

13. Attenuation 10−7 10−5 10−14 10−15

14. 2nd watermark 10−73 10−80 10−74 10−76

n(n−1)2 possible portions ofM , and the difference between

each of them andM∗ can be computed inO(nl) time, wecan registerM∗ with M in O(n3l) time.

5. Experimental Results

In this section, we conduct some experiments to show theeffectiveness of our watermarking scheme. We use four mo-tion clips,Fly Spin Kick, Back Flip, Broad Jump, andBlownBack as shown in Figure 6. Since watermarking dependson random numbers, we perform experiments five times foreach motion clip using different watermarks and present themedian of false-positive probabilities as their estimation. Weuse 10−4 as the scaling parameterα for pelvis and 10−2 forthe others. Those scaling parameters are determined experi-mentally to provide robustness while still keeping impercep-tibility. The length of a watermark for a motion signal canbe adjusted to the characteristics of the signal. In our exper-iments, the length is chosen to be 20 for all motion clips.To extract the watermark from a distorted signal, we use 2.5times of its variance as the threshold to remove outliers inthe extracted watermark.

Table 1 summarizes our experimental results for a varietyof attacks on four motion clips. Each entry shows the estima-tion of the false-positive probability for an attack on a mo-tion signal corresponds to the head of trajectory in a motionclip. A row has four entries showing experimental results forthe attack given in the leftmost entry. Figure 7 exhibits themotion data corresponding to selected table entries writtenin bold face. The figures in the first row show the originalmotion data.



(a)

(b)

(c)

(d)

Figure 6: Four original unwatermarked motion data. (a) Fly Spin Kick. (b) Back Flip. (c) Broad Jump. (d) Blown Back.

No attack. The first row shows the results for watermarkedsignals without any attack. Their estimated false-positiveprobabilities are almost but not exactly zero due to preci-sion errors. The distortion due to precision errors is similarto that caused by a small perturbation.

Noise. Rows 2 and 3 address the cases of 0.2% and 0.7%white noise attacks, respectively. Here, each percentage rep-resents the ratio between the largest amplitude of noise andthe largest rotation angle in the motion signal. The noise isadded to the signal.

Cropping. Row 4 demonstrates the ability of our schemefor cropped signal. Though the portion of a watermark in acropped portion is eliminated completely, its remaining por-tion can be detected with little obstruction.

Smoothing. Rows 5 and 6 present the results after applyinga smoothing filter three times. We use the averaging filter ofunit radius for row 5:

HA(qi) =qi−1 +qi +qi+1

‖qi−1 +qi +qi+1‖. (13)

For row 6, we use the spatial filter of Lee28:

HS(qi) = qi exp

(λ24

(ωi−2−3ωi−1 +3ωi −ωi+1))

,

(14)whereωi is a rotation vector from thei-th frame to the(i +1)-th frame andλ is a damping factor that controls the rateof convergence. We set a damping factorλ to 1.0. Since thesmoothing filters change fine details of motion signals, ourscheme is resilient to this attack.

Simplifying. We test our watermarking scheme for a sim-plified signal whose fine levels of their multiresolution rep-resentation are eliminated. Rows 7, 8, and 9 show the resultsfor a signal with level 0 eliminated, levels 0 and 1 eliminated,and levels 0, 1 and 2 eliminated, respectively. This attackmay destroy parts of a watermark. However, our scheme candetect the remaining parts of the watermark embedded intothe coarser levels.

Time warping. Rows 10 and 11 address an attack due totime warping. The attack of uniform scaling with a factor of0.5 is presented in row 10, and that of non-uniform scalingis shown in row 11. Since the watermark is spread widelyin the motion signal, our scheme is robust for this type ofattack.

Enhancement and Attenuation. Rows 12 and 13 show theresults for the enhanced and attenuated versions, respec-tively. For row 12, we multiply a constant factor of 1.5 toeach of the detail coefficients at the coarsest level and itsnext finer level to enhance motion data. For row 13, we usea constant factor of 0.6 for attenuation. Each of these attacksalters parts of the embedded watermark as in the simplify-ing attack. Therefore, we can similarly detect the remainingwatermark.

2nd watermarking. The resilience under a second water-marking is shown in row 14. We insert a watermark to thewatermarked signal. This watermark is different from thatfor the original signal. Such an attack resembles that ofadding noise to the displacement vectors of the signal.

For each of experiments, its false-positive probability issufficiently low to support the robustness of our scheme.



50-1

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50 100-1

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100 200-1

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DataA:Fly Spin Kick DataB:Back Flip DataC:Broad Jump DataD:Blown Back

50-1

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100 200-1

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(1A): watermarked DataA (1B): watermarked DataB (1C): watermarked DataC (1D): watermarked DataD

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50 100 100 200-1

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(2A): Noise 0.2% (4B): Cropping (7C): Simplifying 1 (6D): Smoothing 2

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(3A): Noise 0.7% (12B): Enhancement (8C): Simplifying 2 (10D): Time warping 1

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(14A): 2nd watermark (13B): Attenuation (9C): Simplifying 3 (11D): Time warping 2

Figure 7: Original and watermarked motion signals (top two rows), and various attacks

6. Conclusion

In this paper, we have presented a practical method for em-bedding a watermark into a motion signal. The key ideaof our scheme is to combine two novel ideas: multiresolu-tion representation and spread spectrum. For robustness, weadopt the idea of spread spectrum, that is, embedding a wa-termark into a wide range of frames. This idea is instanti-ated through the multiresolution representation of a motionsignal, by identifying the perceptually significant frames ofthe signal to embed a watermark. Experimental results showthat our scheme is robust to various signal processing oper-ations or motion editing such as enhancement, attenuation,and time warping. In the future, we would like to improveour motion watermarking scheme to be resilient to morecomplex motion editing27 such as non-uniform scaling alongthe amplitude axis.

7. Acknowledgements

This work was supported by NRL (National Research Lab-oratory) project of KISTEP (Korea Institute of Science &Technology Evaluation and Planning).

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