DCT domain: | DWT domain: |
The mark is a Gaussian sequence of pseudo-random real numbers matching the number of selected coefficients.
Image decomposition
The authors do not specify how to decompose the image, however,
it seems plausible to perform at least 5
decomposition steps.
Watermark embedding
The watermark is added to significant coefficients
in significant subbands.
The search for these locations is based on the design principles of the
multi-threshold wavelet coder (MTWC)
, namely successive subband quantization (SSQ) and bit-plane coding.
The algorithm selects coefficients whose magnitude is larger than a current subband threshold.
The algorithm starts with the most significant subband (with the highest initial threshold and proceeds until enough coefficients are selected. A coefficient is selected only once for embedding, however, a subband may be visited multiple times. Only detail subbands are considered for watermark casting, the approximation subband is not selected.
Discussion
In one of the later papers
, the authors focus more on security aspects and propose to use a key-dependent
coefficient skipping scheme to achieve non-invertibility and, optionally,
a key-dependent transform structure in order to conceal the embedding locations.
By weighting the wavelet coefficients according to their perceptual importance via the selection thresholds the resulting image distortion can be constrained to an acceptable fidelity loss. Values for the subband weighting factor can be found in the work of Barni.
Su extends this scheme for image labeling and region of interest (ROI) watermarking applications. A binary ROI map is constructed for each resolution level to select the region to be watermarked. To this end, the spatial ROI mask has to be scaled to fit the multi-resolution subbands of the wavelet transform domain.
A variation of the algorithm has been proposed that allows blind detection. Since the original image is not available during the watermark extraction step, the original coefficients have to be modeled and estimated. Therefore, the blind embedding and extraction algorithms rely on truncating (quantizing) selected coefficients to well-defined values.
Analysis of the blind detection method shows that the detection performance is four times weaker compared with the non-blind scheme for identical values of alpha (same acceptable distortion). Since the coefficient selection algorithm depends on the correct order of significant subbands which is determined by the subband's maximum coefficien t magnitude, the watermark detection scheme can be easily foiled by manipulating the subband's maximum coefficient. The authors show that tweaking the subband's maximum coefficient add only little distortion to the image.
The watermark is a sequence of binary values.
Image decomposition
The authors propose using the Daubechies family of orthogonal
wavelet filters to derive a multi-resolution representation of the image
data.
A decomposition level of 3 or 4
is used in the experiments.
Watermark embedding
The algorithm pseudo-randomly selects locations in
the detail subbands.
For each bit to embed, a coefficient triple
is selected, each coefficient from a different subband, but at the same spatial position.
The selected coefficient triple is sorted in ascending coefficient magnitude order. Then the median coefficient is quantized to represent the information of a single watermark bit. The median coefficient is set to the nearest reconstruction point that represents the current watermark information.
The bin width parameter controls the quantization step size. Coarser quantization will lead to more robust watermark embedding, however, this will also introduce more distortion.
Discussion
In order to improve robustness, an extension of the above scheme has been published later:
A known reference watermark is embedded together with the secret watermark
in an interlaced way.
It is assumed that both watermarks, i.e.
the reference and the secret mark, undergo the same type and amount of
distortion due to attack or image processing.
Thus, by analyzing the error of the known reference watermark, one can
estimate the error on the secret watermark.
This allows to apply different weights to the recovered watermark information.
Furthermore, the watermark is redundantly embedded to improve robustness.
The authors claim that by embedding the watermark in a different domain than the one used for image compression, the robustness can be improved -- at least the watermarking and compression systems should use different perceptual models.
The mark is a Gaussian sequence of pseudo-random real numbers.
Image decomposition
The authors propose using a 2-level decomposition and the
Haar wavelet filter.
Watermark embedding
The watermark is embedded in large coefficients of
the high and middle frequency bands (detail subbands).
The LL subband does not carry any watermark information.
Embedding is done using the additive embedding formula f'(m,n) = f(m,n) + a * f(m,n)^b * wi where a is the embedding strength and b indicates the amplification of large coefficients.
Watermark extraction
Extraction is done using the inverse embedding formula.
Discussion
The authors discuss the advantage of a multi-resolution representation.
The detection process can benefit from the hierarchical decomposition and
save unnecessary computations if the watermark can already be detected
in an early stage of the decomposition.
Since large coefficients in the detail subbands generally indicate edges, this algorithms places most watermark energy in areas containing edges and texture.
The authors claim that the DWT has advantages over the DCT after rescaling attacks. The DCT coefficients of the rescaled image are shifted in two directions from the locations of the original image. Due to the localization of the DWT, not only in the time but also in the frequency domain, the correlation does not suffer as much as in the DCT case.
The mark is a Gaussian sequence of pseudo-random real numbers, length 32*32 = 1024.
Image decomposition
The host image is decomposed to obtain a multi-resolution
approximation image of size 32 * 32.
Watermark embedding
The watermark is embedded into the approximation image using an additive embedding formula.
The authors state that the DC component of the approximation image is not manipulated since the mean coefficient value is subtracted.
Discussion
Nicchiotti
improves the above scheme with ideas from Nikolaidis's work to achieve non-invertibility.
The watermark is a sequence of binary values.
Image decomposition
The host image is decomposed to obtain a low-frequency approximati
on representation.
Watermark embedding
The watermark is embedded solely in the approximation (LL subband)
of the host image.
Each time, the coefficient triple of a non-overlapping 3x1
sliding window is selected and manipulated.
First, the coefficients of the local sliding window are sorted in ascending order according to their magnitude. Next, the median of the coefficient triple is modified to become a multiple of a window-adaptive quantizer in order to represent one bit of watermark information.
Watermark extraction
The watermark extraction algorithm works without the original
image.
The median of the sliding window is determined and quantized to obtain
a reconstruction point.
The bit value associated with that reconstructed point is
assigned to extracted watermark sequence.
Discussion
Although the schemes is proposed for image authentication application
, however, contrary to the authors' claims, its robustness makes it also
suitable for other purposes such as copyright protection.
We found that the robustness is mainly determined by the number of decompositio
n steps .
Very good robustness can be achieved employing e.g.
a five-level wavelet decomposition using Daubechies-7/9 bi-orthogonal filters.
The authors discuss employing the above algorithm in the EZW and SPIHT coding schemes.
Not only binary embedding, but also m-ary signaling is proposed and compared with an analytical capacity bound. The authors found that multi-bit engraving can improve the capacity.
The mark is a Gaussian sequence of pseudo-random real numbers. The length of the watermark sequence equals the number of detail coefficients.
Image decomposition
The authors suggest a four-level wavelet decomposition.
Watermark embedding
All high-pass subband coefficients are selected, sparing
only the LL subband.
Embedding is done using an additive embedding formula.
The watermark sequence at different resolution levels is nested,
Watermark extraction
The peak correlation over all resolution levels is used to detect the presence
or absence of the watermark.
Discussion
Because of its simple structure, the algorithm can be easily
incorporated in video watermarking application based on a 3-D wavelet transform.
The watermark is a Gaussian sequence of pseudo-random real numbers matching size of the detail subbands.
Although the watermark is added only to a few selected significant coefficients , using an image size watermark fixes the locations that are manipulated. Hence, there is no dependence on the order of significant coefficients during correlation.
Image decomposition
The wavelet transform is a three-level decomposition with
Daubechies-8 filters.
Watermark embedding
The equation used for watermark casting in selected significant
coefficients is similar to Piva's: f'(m,n) = f(m,n) + a * |f(m,n)| * wi
Discussion
The author state that visual masking is done implicitly due to
the time-frequency localization property of the DWT.
Since the detail subbands where the watermark is added contain typically
edge information, the signature's energy is concentrated in the edge areas
of the image.
This makes the watermark invisible because the human eye is less sensitive
to texture and edge information.
The watermark is a sequence of binary values matching the number of zerotrees found in the host image.
Image decomposition
The authors propose a 3-level decomposition using 5/3 symmetric
short kernel filters (SSKF) or Daubechies-16 filters.
Wavelet coefficients are classified as significant or insignificant using the notion of zerotrees. The zerotree structure has been first described by Lewis and successfully incorporated in image compression schemes by Shapiro.
If a coefficient and all of its descendants (i.e. the coefficients corresponding to the same spatial location but at a finer scale of the same orientation) are insignificant then the set of these insignificant wavelet coefficients is called zerotree.
A coefficient at the coarse scale is called parent while all four coefficients at the finer resolution level are called children. A wavelet coefficient is called zerotree root if it is not the descendant of a previously found zerotree root.
The proposed watermarking scheme comes in two flavors, one based on manipulating significant (method A) and the other one based on manipulating insignificant coefficients (method B).
Watermark embedding
The embedding strategy for method A sets all coefficients of zerotree to -m to signal a 0 message bit and to m to signal a 1 message bit.
Method B casts the watermark symbol on a selected coefficient via quantization.
Watermark extraction
The watermark extraction algorithms of method A computes the
average coefficient value, M, for the coefficients belonging to zerotree and checks if M if greater or less than zero to determine the message bit, 1 or 0, resp.
Method B extracts the watermark symbol from a significant coefficient by quantizing the magnitude and setting the message bit to match the respective quantization bin.
Discussion
Although the authors claim that method A of the algorithm can
extract the embedded information without the original host image (blind
extraction), the scheme uses the positions of zerotree roots to guide the
extraction algorithms.
Therefore, the algorithm should be actually called semi-blind.
Without this guidance, the proposed algorithm looses synchronization easily
because it depends on insignificant coefficients only.
The watermark is a Gaussian sequence of pseudo-random real numbers.
Image decomposition
The proposed method uses bi-orthogonal filters to decompose the original image into 3 levels.