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Re: [WM]: Advantages of Wavelet watermarking
this is wat i have understood and learnt from other group members....
http://www.geocities.com/gwatermarker
(my site on watermarking)
**********************************DCT*********************************
Characteristic of DCT Coefficients
1. Magnitude of DC component of an 8x8 block DCT
coefficient is
proportional to the average grey level of the corresponding block [Huang et al. 2000].
2. Provides excellent signal approximation with few
coefficients.
3. Frequency components are ordered in a sequential
order, starting
with low frequency, mid frequency and high frequency components. Proper components can be selected based on this.
4. If most of the high frequency coefficients that are
zero then it
represents a smooth blocks [Jellinek 2000].
5. If the low frequency AC coefficients have large
absolute values
they normally refer to an edge blocks [Jellinek 2000].
6. It is faster and can be implemented in O (n log n)
operations
Coefficient Selection Criteria
1. Coefficients which have large perceptual capacity
should be
selected because they allow stronger watermarks to be embedded and result in least perceptual distortion [Huang et al.
2000].
2. Those coefficients should be selected which are
least changed by
common image processing attacks like low-pass filtering, noise addition etc [Huang et al. 2000].
3. Low frequency AC components (or high value
coefficients) satisfy
the above criteria and are selected in most watermarking algorithms.
4. Common image processing operation affects the high
frequency
components and hence it's not a good choice for watermarking.
5. DC component can also be used because the magnitude
of DC
component is much larger than the AC component which means they have a very high perceptual capacity. Secondly DC components are
less affected by common image processing attacks unlike AC component which are very sensitive to such attacks [Huang et al. 2000].
Embedding in the transform domain by modifying the DCT coefficients offer many advantages including robustness against unintentional
image processing attacks like brightness and contrast adjustment, gamma correction, filtering, blurring etc. It also shows
resistance against compression. However most of the DCT based approaches do not completely address the issue of geometric attacks
like cropping.
Nevertheless this
approach is much more robust compared to spatial domain approach.
As mentioned earlier using the transform domain for embedding watermarks offers many advantages including robustness against
unintentional and unintentional attacks. Most of the DCT watermarking algorithms show robustness against compression. This is
achieved by understanding and incorporating JPEG compression mechanism into watermark embedder. Another advantage of using DCT for
watermarking is the extensive study of human visual system in this domain which has resulted in the standard JPEG quantization
table. So watermarking can be more adaptive to HVS in this domain. However most of the DCT based approaches do not completely
address the issue of geometric attacks like cropping and scaling. Nevertheless this approach is much more robust compared to spatial
domain approach.
************************************
DWT***********************************
Characteristics of DWT
1. The wavelet decomposition decomposes the image into
three
spatial directions i.e. horizontal, vertical and diagonal. Hence wavelets reflect the anisotropic properties of HVS more precisely
[Voloshynovskiy et al. 2000].
2. Multi-resolution nature: Because of its
multi-resolution nature
they are suitable for applications which require scalability and tolerable degradation. Hence it allows for progressive transmission
of images
3. The larger the magnitude of the wavelet coefficient
the more
significant it is.
4. Watermark detection at lower resolutions is
computationally
effective because at every successive resolution level there are few frequency bands involved.
5. Multiresolution watermarking is robust against
downsampling
operation by a power of two in either space or time domain [Zhu 1999].
6. High resolution subbands helps to easily locate
edge and
textures patterns in an image.
7. Wavelet Transform is computationally efficient and
can be
implemented by using simple filter convolution.
8. Robustness: It is more robust against transmission
and decoding
errors.
9. Magnitude of DWT coefficients is larger in the
lowest bands (LL)
at each level of decomposition [Tao and Eskicioglu 2004].
10. Magnitude of DWT coefficients is smaller for other
bands (HH,
LH, HL).
Coefficient Selection Criteria
1. According to Cox et al. and Huang et al. (2000)
watermark should
be embedded in the DC and the low frequency AC coefficients in the DCT domain due to their large perceptual capacity. Similar
strategy can be applied to DWT as well by embedding in the LL4 subband.
2. Embedding watermark in the higher level subbands
increases the
robustness of the watermark however the image visual fidelity may be lost which can be measured by PSNR.
3. Embedding the watermark in lower level subbands
increases the
image's visual fidelity or makes it perceptually invisible however reduces its robustness.
Figure: Multiresolution Image Decomposition using DWT
4. With DWT the edges and texture can be easily
identified in the
high frequency bands like HH, LH, and HL. The large coefficients in these bands normally indicate edges in the image [Xia et al.
1997].
5. Low frequency components have larger perceptual
capacity
compared to high frequency components because they have large magnitudes and can be used to embed stronger watermarks without
introducing any visible artifacts. This can also be related to Weber's law which states that "contrast ratio threshold is
proportional to the amplitude of the background signal". In watermarking the watermark could be considered as a weak signal which is
embedded in stronger signal i.e.
the image. If the contrast ratio of the embedded signal is lower than the threshold there won't be any perceptual distortion [Kang
et al.
2003].
6. Low level bands have higher magnitude and we can
use a larger
scaling factor to embed a more robust watermark.
However other three
bands have smaller magnitudes and hence we can use a low scaling factor to embed a comparatively weaker watermark [Tao and
Eskicioglu 2004].
Advantages of DWT over DCT
1. Wavelet coded image is a multi-resolution
description of image.
Hence an image can be shown at different level of resolution and can be sequentially processed from low resolution to high
resolution.
2. Wavelet transform understands the HVS more closely
than the DCT.
3. No blocking artifacts: Visual artifacts introduced
by wavelet
coded images are less evident compared to DCT because wavelet transform doesn't decompose the image into blocks for processing. At
high compression ratios blocking artifacts are noticeable in DCT however in wavelet coded images it's much clearer.
4. DFT and DCT are full frame transform and hence any
change in the
transform coefficients affects the entire image except if DCT is implemented using a block based approach. However DWT has spatial
frequency locality which means if signal is embedded it will affect the image locally [Lee and Lee 2005]. Hence a wavelet transform
provides both frequency and spatial description for an image.
5. When the image is not distorted to a great extent
cross
correlation with the whole image is not required. It can be achieved by the Multiresolution character of the image and hence we can
save a lot of computational power [Xia et al. 1997].
6. Sometimes embedding in the HL and LH subband is
resistant to
histogram equalization and gamma correction attacks [Ganic and Eskicioglu 2004].
Disadvantages of DWT over DCT
1. Computational complexity of DWT is more compared to
DCT [Xiong
et al. 1999]. As Feig (1990) pointed out it only takes
54
multiplications to compute DCT for a block of 8x8, unlike wavelet calculation depends upon the length of the filter used, which is
at least 1 multiplication per coefficient.
reason for the use of DCT domain in watermarking is the availability of Human Visual System models using DCT.
That helps in
perceptually adaptive watermarking to increase the robustness of the watermark.
--- Water Mark <watermarking24@hotmail.com> wrote:
> Dear watermarkers,
>
> I am currently looking at the advantages of one embedding domain
> over another. I was wondering what people thought the advantages of
> each was. I know the wavelet is common due to the standarisation of
> the JPEG2000 standard and thus is seen as relatively robust to JPEG
> compression. DCT was common becuase JPEG and MPEG used it. Was there
> any other advantages of it over the DFT for example? Do you think
> wavelet domain is the way forward?
>
> Michael
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