Fundamental Techniques for Blind Digital Watermarking CS 591: Forensics & Security (Fall 2011) Daniel C. Cannon For: Professor Fernando P´ erez-Gonz´ ales Dept. of Electrical & Computer Engineering December 9, 2011 University of New Mexico Introduction Blind digital watermarking encompasses a variety of techniques for embedding information in a digital signal that only a receiver with knowledge of a secret key, and no knowledge of the original host signal, can detect [3, 1]. While different applications of blind digital watermarking impose different design constraints, most techniques attempt to optimize the trade-offs between three opposing objectives: [5] 1. Bandwidth. The size of the message that can be embedded must be sufficiently large. 2. Robustness. The watermark must survive deliberate and unintentional attacks, such as compression and rescaling of an image. 3. Imperceptibility. It must not be apparent to a casual viewer that the signal has been altered, nor should the presence of a watermark be otherwise detectable without knowledge of a secret key. In this report, I will present and analyze two popular classes of techniques for embedding and decoding watermarks in digital images: spread-spectrum watermarking and quantization-based watermarking. In Section 1, I will define spread-spectrum watermarking and discuss a simple scheme for applying spread- spectrum watermarking to embed information in the pixel domain of an image. In Section 2, I will present an alternative spread-spectrum scheme that embeds information in the discrete cosine transform (DCT) domain of an image. In Section 3, I will describe dither modulation [2], a form of quantization index modulation (QIM), and show that this approach can achieve far greater bandwidths, and with greater robustness to interference, than spread-spectrum techniques. Finally, in Section 4, I will apply dither modulation in the DCT domain and characterize its performance.
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Fundamental Techniques for Blind Digital WatermarkingCS 591: Forensics & Security (Fall 2011)
Daniel C. Cannon For: Professor Fernando Perez-GonzalesDept. of Electrical & Computer Engineering
December 9, 2011 University of New Mexico
Introduction
Blind digital watermarking encompasses a variety of techniques for embedding information in a digital
signal that only a receiver with knowledge of a secret key, and no knowledge of the original host signal, can
detect [3, 1]. While different applications of blind digital watermarking impose different design constraints,
most techniques attempt to optimize the trade-offs between three opposing objectives: [5]
1. Bandwidth. The size of the message that can be embedded must be sufficiently large.
2. Robustness. The watermark must survive deliberate and unintentional attacks, such as compression
and rescaling of an image.
3. Imperceptibility. It must not be apparent to a casual viewer that the signal has been altered, nor
should the presence of a watermark be otherwise detectable without knowledge of a secret key.
In this report, I will present and analyze two popular classes of techniques for embedding and decoding
watermarks in digital images: spread-spectrum watermarking and quantization-based watermarking. In
Section 1, I will define spread-spectrum watermarking and discuss a simple scheme for applying spread-
spectrum watermarking to embed information in the pixel domain of an image. In Section 2, I will present an
alternative spread-spectrum scheme that embeds information in the discrete cosine transform (DCT) domain
of an image. In Section 3, I will describe dither modulation [2], a form of quantization index modulation
(QIM), and show that this approach can achieve far greater bandwidths, and with greater robustness to
interference, than spread-spectrum techniques. Finally, in Section 4, I will apply dither modulation in the
DCT domain and characterize its performance.
FUNDAMENTAL TECHNIQUES FOR BLIND DIGITAL WATERMARKING CANNON
1 Additive Spread-Spectrum Watermarking in the Pixel Domain
1.1 Overview
While some of the earliest techniques for data hiding, such as quantize-and-replace schemes [2], were ca-
pable of high message bandwidths, practical applications of digital watermarking, such as identifying the
copyright holder of an image, generally require a minimal amount of embedded data [1], but with high ro-
bustness and low perceptibility. Additive spread-spectrum techniques [6] attempt to address this challenge
by redundantly embedding information about the value of a single bit in multiple locations in the signal,
thus sacrificing bandwidth for robustness.
Conceptually, additive spread-spectrum embedding involves adding a small amount of noise to each
pixel (or other coefficient) of an image. While the added noise appears to be uncorrelated white noise, it
can be partitioned by a pseudorandom interleaver into sets corresponding to each bit of a message, and each
noise term in the set constitutes, effectively, a vote about the true value of the bit.
More concretely, we assume that the sender and the receiver of the message are privy to a secret key k.
Using this secret key, we pseudorandomly partition the coefficients of the image Z into non-overlapping sets
Si, with each set corresponding to a bit bi ∈ {−1,+1} of our message, and we generate a pseudorandom
matrix B of the same dimensionality as our image where ∀x ∈ B : x ∈ {−1,+1}. We can then use this
matrix B and a perceptual mask A (see Section 1.2) to define a modulation matrix,
Φi[m,n] =
A[m,n]B[m,n], (m,n) ∈ Si
0, otherwise.
(1)
Once the modulation matrices for each bit bi of the message are computed, the watermark can be
computed as
W[m,n] =
l∑i=1
biΦi[m,n] (2)
and our new, watermarked image is simply the sum of the original image and the watermark,
Z′ = Z + W. (3)
While the embedding of a spread spectrum watermark is relatively straightforward, the method for
recovering the embedded message from a watermarked, and possibly attacked, image Z′ is far less obvious
under the assumption that the receiver has no knowledge of the original signal.
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FUNDAMENTAL TECHNIQUES FOR BLIND DIGITAL WATERMARKING CANNON
Consider first the inner product of the image Z′ with a modulation matrix Φi,
ρi = 〈Z′,Φi〉 (4)
=∑m
∑n
(Z[m,n] + biΦi[m,n]) Φi[m,n] (5)
= bi∑m
∑n
(Φi[m,n])2 +∑m
∑n
Z[m,n]Φi[m,n] (6)
= bi∑m
∑n
(Φi[m,n])2 + 〈Z,Φi〉. (7)
We recognize that Eqn. 7 is the sum of an information term and a noise term, 〈Z,Φi〉. That is, while
we cannot compute Φi exactly, we can closely estimate it, and we know that the information term will be
positive if bi = +1 and negative if bi = −1. More importantly, while we do not have knowledge of Z, we
do know that E(Φi) ≈ 0, and so expect that the noise term should be comparatively small. Thus, we expect
that
ρi ≈ bi∑m
∑n
(Φi[m,n])2 . (8)
We therefore begin by computing the modulation matrices Φ′i for the image Z′. We can then compute
the mean value of the inner product of Z′ with each Φ′i,
µ = E(〈Z′,Φ′i〉
)(9)
=1
l
l∑i=1
〈Z′,Φ′i〉 (10)
yielding an approximate measure of the expected value of the noise term. If we then compute the sum of the
squared values of each Φ′i,
νi =∑m
∑n
(Φ′i[m,n]
)2. (11)
we can then obtain an estimated reconstruction of the original message, given by
ri =
−1, |〈Z′,Φ′i〉 − µ− νi| < |〈Z′,Φ′i〉 − µ+ νi|
+1, otherwise.
(12)
1.2 Computation of the Perceptual Mask
Because the human visual system is most sensitive to disruptions in smooth regions of images, an ideal
perceptual mask should concentrate alterations in regions of the image that are already noisy. One simple
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FUNDAMENTAL TECHNIQUES FOR BLIND DIGITAL WATERMARKING CANNON