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71-493: The Digital Watermarking Alliance is a group of like-minded companies that share a common interest in furthering the adoption of digital watermarking . The mission of the Digital Watermarking Alliance is: The Digital Watermarking Alliance is made up of 12 companies that all have an established presence in the digital watermarking technology and solutions market. Member companies include: As of January 2018,

142-476: A binary codeword c k {\displaystyle c_{k}} . An important consideration is the number of bits used for each codeword, denoted here by l e n g t h ( c k ) {\displaystyle \mathrm {length} (c_{k})} . As a result, the design of an M {\displaystyle M} -level quantizer and an associated set of codewords for communicating its index values requires finding

213-452: A classification of the different techniques according to their intent, the way they express the watermark, the cover type, granularity level, and verifiability was published in 2010 by Halder et al. in the Journal of Universal Computer Science . Quantization (signal processing) Quantization , in mathematics and digital signal processing , is the process of mapping input values from

284-430: A dead-zone quantizer is given by where r k {\displaystyle r_{k}} is a reconstruction offset value in the range of 0 to 1 as a fraction of the step size. Ordinarily, 0 ≤ r k ≤ 1 2 {\displaystyle 0\leq r_{k}\leq {\tfrac {1}{2}}} when quantizing input data with a typical probability density function (PDF) that

355-485: A finite set of discrete values. Most commonly, these discrete values are represented as fixed-point words. Though any number of quantization levels is possible, common word-lengths are 8-bit (256 levels), 16-bit (65,536 levels) and 24-bit (16.8 million levels). Quantizing a sequence of numbers produces a sequence of quantization errors which is sometimes modeled as an additive random signal called quantization noise because of its stochastic behavior. The more levels

426-547: A large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements . Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error )

497-409: A mid-riser or mid-tread quantizer may not actually be a uniform quantizer – i.e., the size of the quantizer's classification intervals may not all be the same, or the spacing between its possible output values may not all be the same. The distinguishing characteristic of a mid-riser quantizer is that it has a classification threshold value that is exactly zero, and the distinguishing characteristic of

568-411: A mid-riser uniform quantizer is given by: where the classification rule is given by and the reconstruction rule is Note that mid-riser uniform quantizers do not have a zero output value – their minimum output magnitude is half the step size. In contrast, mid-tread quantizers do have a zero output level. For some applications, having a zero output signal representation may be a necessity. In general,

639-422: A mid-tread quantizer is that is it has a reconstruction value that is exactly zero. A dead-zone quantizer is a type of mid-tread quantizer with symmetric behavior around 0. The region around the zero output value of such a quantizer is referred to as the dead zone or deadband . The dead zone can sometimes serve the same purpose as a noise gate or squelch function. Especially for compression applications,

710-407: A percentage of the full signal range, changes by a factor of 2 for each 1-bit change in the number of quantization bits. The potential signal-to-quantization-noise power ratio therefore changes by 4, or 10 ⋅ log 10 ⁡ ( 4 ) {\displaystyle \scriptstyle 10\cdot \log _{10}(4)} , approximately 6 dB per bit. At lower amplitudes

781-480: A quantization step size equal to some value Δ {\displaystyle \Delta } can be expressed as where the notation ⌊   ⌋ {\displaystyle \lfloor \ \rfloor } denotes the floor function . Alternatively, the same quantizer may be expressed in terms of the ceiling function , as (The notation ⌈   ⌉ {\displaystyle \lceil \ \rceil } denotes

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852-452: A quantizer uses, the lower is its quantization noise power. Rate–distortion optimized quantization is encountered in source coding for lossy data compression algorithms, where the purpose is to manage distortion within the limits of the bit rate supported by a communication channel or storage medium. The analysis of quantization in this context involves studying the amount of data (typically measured in digits or bits or bit rate ) that

923-417: A rather general way. For example, vector quantization is the application of quantization to multi-dimensional (vector-valued) input data. An analog-to-digital converter (ADC) can be modeled as two processes: sampling and quantization. Sampling converts a time-varying voltage signal into a discrete-time signal , a sequence of real numbers. Quantization replaces each real number with an approximation from

994-413: A selected set of design constraints such as the bit rate R {\displaystyle R} and distortion D {\displaystyle D} . Assuming that an information source S {\displaystyle S} produces random variables X {\displaystyle X} with an associated PDF f ( x ) {\displaystyle f(x)} ,

1065-410: A watermark designer or for end-users, therefore, different evaluation strategies exist. Often used by a watermark designer is the evaluation of single properties to show, for example, an improvement. Mostly, end-users are not interested in detailed information. They want to know if a given digital watermarking algorithm may be used for their application scenario, and if so, which parameter sets seems to be

1136-458: A wide range of applications, such as: The information to be embedded in a signal is called a digital watermark, although in some contexts the phrase digital watermark means the difference between the watermarked signal and the cover signal. The signal where the watermark is to be embedded is called the host signal. A watermarking system is usually divided into three distinct steps, embedding, attack, and detection. In embedding, an algorithm accepts

1207-604: Is a many-to-few mapping, it is an inherently non-linear and irreversible process (i.e., because the same output value is shared by multiple input values, it is impossible, in general, to recover the exact input value when given only the output value). The set of possible input values may be infinitely large, and may possibly be continuous and therefore uncountable (such as the set of all real numbers, or all real numbers within some limited range). The set of possible output values may be finite or countably infinite . The input and output sets involved in quantization can be defined in

1278-564: Is assumed that distortion is measured by mean squared error, the distortion D , is given by: A key observation is that rate R {\displaystyle R} depends on the decision boundaries { b k } k = 1 M − 1 {\displaystyle \{b_{k}\}_{k=1}^{M-1}} and the codeword lengths { l e n g t h ( c k ) } k = 1 M {\displaystyle \{\mathrm {length} (c_{k})\}_{k=1}^{M}} , whereas

1349-536: Is called fragile if it fails to be detectable after the slightest modification. Fragile watermarks are commonly used for tamper detection (integrity proof). Modifications to an original work that clearly are noticeable, commonly are not referred to as watermarks, but as generalized barcodes . A digital watermark is called semi-fragile if it resists benign transformations, but fails detection after malignant transformations. Semi-fragile watermarks commonly are used to detect malignant transformations. A digital watermark

1420-586: Is called imperceptible if the watermarked content is perceptually equivalent to the original, unwatermarked content. In general, it is easy to create either robust watermarks or imperceptible watermarks, but the creation of both robust and imperceptible watermarks has proven to be quite challenging. Robust imperceptible watermarks have been proposed as a tool for the protection of digital content, for example as an embedded no-copy-allowed flag in professional video content. Digital watermarking techniques may be classified in several ways. A digital watermark

1491-400: Is called robust if it resists a designated class of transformations. Robust watermarks may be used in copy protection applications to carry copy and no access control information. A digital watermark is called imperceptible if the original cover signal and the marked signal are perceptually indistinguishable. A digital watermark is called perceptible if its presence in the marked signal

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1562-500: Is known. This technique reportedly has been used to detect the source of illegally copied movies. The term digital watermark was coined by Andrew Tirkel and Charles Osborne in December 1992. The first successful embedding and extraction of a steganographic spread spectrum watermark was demonstrated in 1993 by Andrew Tirkel, Gerard Rankin, Ron Van Schyndel, Charles Osborne, and others. Watermarks are identification marks produced during

1633-409: Is not always a valid assumption. Quantization error (for quantizers defined as described here) is deterministically related to the signal and not entirely independent of it. Thus, periodic signals can create periodic quantization noise. And in some cases it can even cause limit cycles to appear in digital signal processing systems. One way to ensure effective independence of the quantization error from

1704-425: Is noticeable (e.g. digital on-screen graphics like a network logo, content bug, codes, opaque images). On videos and images, some are made transparent/translucent for convenience for consumers due to the fact that they block portion of the view; therefore degrading it. This should not be confused with perceptual , that is, watermarking which uses the limitations of human perception to be imperceptible. The length of

1775-412: Is referred to as quantization error . A device or algorithmic function that performs quantization is called a quantizer . An analog-to-digital converter is an example of a quantizer. For example, rounding a real number x {\displaystyle x} to the nearest integer value forms a very basic type of quantizer – a uniform one. A typical ( mid-tread ) uniform quantizer with

1846-579: Is symmetric around zero and reaches its peak value at zero (such as a Gaussian , Laplacian , or generalized Gaussian PDF). Although r k {\displaystyle r_{k}} may depend on k {\displaystyle k} in general, and can be chosen to fulfill the optimality condition described below, it is often simply set to a constant, such as 1 2 {\displaystyle {\tfrac {1}{2}}} . (Note that in this definition, y 0 = 0 {\displaystyle y_{0}=0} due to

1917-411: Is used to quantize, the quantization error has a mean of zero and the root mean square (RMS) value is the standard deviation of this distribution, given by 1 12 L S B   ≈   0.289 L S B {\displaystyle \scriptstyle {\frac {1}{\sqrt {12}}}\mathrm {LSB} \ \approx \ 0.289\,\mathrm {LSB} } . When truncation

1988-407: Is used to represent the output of the quantizer, and studying the loss of precision that is introduced by the quantization process (which is referred to as the distortion ). Most uniform quantizers for signed input data can be classified as being of one of two types: mid-riser and mid-tread . The terminology is based on what happens in the region around the value 0, and uses the analogy of viewing

2059-452: Is used, the error has a non-zero mean of 1 2 L S B {\displaystyle \scriptstyle {\frac {1}{2}}\mathrm {LSB} } and the RMS value is 1 3 L S B {\displaystyle \scriptstyle {\frac {1}{\sqrt {3}}}\mathrm {LSB} } . Although rounding yields less RMS error than truncation, the difference is only due to

2130-413: Is useful for the design and analysis of quantization behavior, and it illustrates how the quantized data can be communicated over a communication channel – a source encoder can perform the forward quantization stage and send the index information through a communication channel, and a decoder can perform the reconstruction stage to produce the output approximation of the original input data. In general,

2201-657: The Lagrange multiplier λ {\displaystyle \lambda } is a non-negative constant that establishes the appropriate balance between rate and distortion. Solving the unconstrained problem is equivalent to finding a point on the convex hull of the family of solutions to an equivalent constrained formulation of the problem. However, finding a solution – especially a closed-form solution – to any of these three problem formulations can be difficult. Solutions that do not require multi-dimensional iterative optimization techniques have been published for only three PDFs:

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2272-516: The Digital Watermarking Alliance have 6 companies as its members. Digital watermarking Like traditional physical watermarks , digital watermarks are often only perceptible under certain conditions, e.g. after using some algorithm. If a digital watermark distorts the carrier signal in a way that it becomes easily perceivable, it may be considered less effective depending on its purpose. Traditional watermarks may be applied to visible media (like images or video), whereas in digital watermarking,

2343-439: The appropriate balance is the use of automatic gain control (AGC). However, in some quantizer designs, the concepts of granular error and overload error may not apply (e.g., for a quantizer with a limited range of input data or with a countably infinite set of selectable output values). A scalar quantizer, which performs a quantization operation, can ordinarily be decomposed into two stages: These two stages together comprise

2414-571: The best. Epson and Kodak have produced cameras with security features such as the Epson PhotoPC 3000Z and the Kodak DC-290. Both cameras added irremovable features to the pictures which distorted the original image, making them unacceptable for some applications such as forensic evidence in court. According to Blythe and Fridrich, "[n]either camera can provide an undisputable proof of the image origin or its author". A secure digital camera (SDC)

2485-399: The carrier signal. Instead, if integrity has to be ensured, a fragile watermark would be applied. Both steganography and digital watermarking employ steganographic techniques to embed data covertly in noisy signals. While steganography aims for imperceptibility to human senses, digital watermarking tries to control the robustness as top priority. Since a digital copy of data is the same as

2556-638: The ceiling function). The essential property of a quantizer is having a countable-set of possible output-values members smaller than the set of possible input values. The members of the set of output values may have integer, rational, or real values. For simple rounding to the nearest integer, the step size Δ {\displaystyle \Delta } is equal to 1. With Δ = 1 {\displaystyle \Delta =1} or with Δ {\displaystyle \Delta } equal to any other integer value, this quantizer has real-valued inputs and integer-valued outputs. When

2627-402: The data (in which resolution is diminished), cropping an image or video, or intentionally adding noise. Detection (often called extraction) is an algorithm that is applied to the attacked signal to attempt to extract the watermark from it. If the signal was unmodified during transmission, then the watermark still is present and it may be extracted. In robust digital watermarking applications,

2698-443: The dead-zone may be given a different width than that for the other steps. For an otherwise-uniform quantizer, the dead-zone width can be set to any value w {\displaystyle w} by using the forward quantization rule where the function sgn {\displaystyle \operatorname {sgn} } ( ) is the sign function (also known as the signum function). The general reconstruction rule for such

2769-407: The dead-zone quantizer is also a uniform quantizer, since the central dead-zone of this quantizer has the same width as all of its other steps, and all of its reconstruction values are equally spaced as well. A common assumption for the analysis of quantization error is that it affects a signal processing system in a similar manner to that of additive white noise – having negligible correlation with

2840-571: The definition of the sgn {\displaystyle \operatorname {sgn} } ( ) function, so r 0 {\displaystyle r_{0}} has no effect.) A very commonly used special case (e.g., the scheme typically used in financial accounting and elementary mathematics) is to set w = Δ {\displaystyle w=\Delta } and r k = 1 2 {\displaystyle r_{k}={\tfrac {1}{2}}} for all k {\displaystyle k} . In this case,

2911-416: The digital watermark and replacing the image data that had been overwritten. Digital watermarking for relational databases has emerged as a candidate solution to provide copyright protection, tamper detection, traitor tracing, and maintaining integrity of relational data. Many watermarking techniques have been proposed in the literature to address these purposes. A survey of the current state-of-the-art and

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2982-435: The distortion D {\displaystyle D} depends on the decision boundaries { b k } k = 1 M − 1 {\displaystyle \{b_{k}\}_{k=1}^{M-1}} and the reconstruction levels { y k } k = 1 M {\displaystyle \{y_{k}\}_{k=1}^{M}} . After defining these two performance metrics for

3053-455: The distortion. Quantization noise is a model of quantization error introduced by quantization in the ADC. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The noise is non-linear and signal-dependent. It can be modelled in several different ways. In an ideal ADC, where the quantization error is uniformly distributed between −1/2 LSB and +1/2 LSB, and

3124-427: The embedded message determines two different main classes of digital watermarking schemes: A digital watermarking method is referred to as spread-spectrum if the marked signal is obtained by an additive modification. Spread-spectrum watermarks are known to be modestly robust, but also to have a low information capacity due to host interference . A digital watermarking method is said to be of quantization type if

3195-426: The exact amplitude of the signal. The calculations are relative to full-scale input. For smaller signals, the relative quantization distortion can be very large. To circumvent this issue, analog companding can be used, but this can introduce distortion. Often the design of a quantizer involves supporting only a limited range of possible output values and performing clipping to limit the output to this range whenever

3266-643: The extraction algorithm should be able to produce the watermark correctly, even if the modifications were strong. In fragile digital watermarking, the extraction algorithm should fail if any change is made to the signal. A digital watermark is called robust with respect to transformations if the embedded information may be detected reliably from the marked signal, even if degraded by any number of transformations. Typical image degradations are JPEG compression, rotation, cropping, additive noise, and quantization . For video content, temporal modifications and MPEG compression often are added to this list. A digital watermark

3337-412: The forward quantization stage may use any function that maps the input data to the integer space of the quantization index data, and the inverse quantization stage can conceptually (or literally) be a table look-up operation to map each quantization index to a corresponding reconstruction value. This two-stage decomposition applies equally well to vector as well as scalar quantizers. Because quantization

3408-506: The host and the data to be embedded, and produces a watermarked signal. Then the watermarked digital signal is transmitted or stored, usually transmitted to another person. If this person makes a modification, this is called an attack . While the modification may not be malicious, the term attack arises from copyright protection application, where third parties may attempt to remove the digital watermark through modification. There are many possible modifications, for example, lossy compression of

3479-428: The input exceeds the supported range. The error introduced by this clipping is referred to as overload distortion. Within the extreme limits of the supported range, the amount of spacing between the selectable output values of a quantizer is referred to as its granularity , and the error introduced by this spacing is referred to as granular distortion. It is common for the design of a quantizer to involve determining

3550-461: The input signal is a full-amplitude sine wave the distribution of the signal is no longer uniform, and the corresponding equation is instead Here, the quantization noise is once again assumed to be uniformly distributed. When the input signal has a high amplitude and a wide frequency spectrum this is the case. In this case a 16-bit ADC has a maximum signal-to-noise ratio of 98.09 dB. The 1.761 difference in signal-to-noise only occurs due to

3621-487: The input-output function of the quantizer as a stairway . Mid-tread quantizers have a zero-valued reconstruction level (corresponding to a tread of a stairway), while mid-riser quantizers have a zero-valued classification threshold (corresponding to a riser of a stairway). Mid-tread quantization involves rounding. The formulas for mid-tread uniform quantization are provided in the previous section. Mid-riser quantization involves truncation. The input-output formula for

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3692-489: The marked signal is obtained by quantization. Quantization watermarks suffer from low robustness, but have a high information capacity due to rejection of host interference. A digital watermarking method is referred to as amplitude modulation if the marked signal is embedded by additive modification which is similar to spread spectrum method, but is particularly embedded in the spatial domain. The evaluation of digital watermarking schemes may provide detailed information for

3763-415: The mathematical operation of y = Q ( x ) {\displaystyle y=Q(x)} . Entropy coding techniques can be applied to communicate the quantization indices from a source encoder that performs the classification stage to a decoder that performs the reconstruction stage. One way to do this is to associate each quantization index k {\displaystyle k} with

3834-403: The original, digital watermarking is a passive protection tool. It just marks data, but does not degrade it or control access to the data. One application of digital watermarking is source tracking . A watermark is embedded into a digital signal at each point of distribution. If a copy of the work is found later, then the watermark may be retrieved from the copy and the source of the distribution

3905-472: The paper-making process. The first watermarks appeared in Italy during the 13th century, but their use rapidly spread across Europe. They were used as a means to identify the paper maker or the trade guild that manufactured the paper. The marks often were created by a wire sewn onto the paper mold. Watermarks continue to be used today as manufacturer's marks and to prevent forgery. Digital watermarking may be used for

3976-399: The probability p k {\displaystyle p_{k}} that the random variable falls within a particular quantization interval I k {\displaystyle I_{k}} is given by: The resulting bit rate R {\displaystyle R} , in units of average bits per quantized value, for this quantizer can be derived as follows: If it

4047-415: The proper balance between granular distortion and overload distortion. For a given supported number of possible output values, reducing the average granular distortion may involve increasing the average overload distortion, and vice versa. A technique for controlling the amplitude of the signal (or, equivalently, the quantization step size Δ {\displaystyle \Delta } ) to achieve

4118-449: The quantization error becomes dependent on the input signal, resulting in distortion. This distortion is created after the anti-aliasing filter, and if these distortions are above 1/2 the sample rate they will alias back into the band of interest. In order to make the quantization error independent of the input signal, the signal is dithered by adding noise to the signal. This slightly reduces signal to noise ratio, but can completely eliminate

4189-405: The quantization step size (Δ) is small relative to the variation in the signal being quantized, it is relatively simple to show that the mean squared error produced by such a rounding operation will be approximately Δ 2 / 12 {\displaystyle \Delta ^{2}/12} . Mean squared error is also called the quantization noise power . Adding one bit to

4260-441: The quantizer halves the value of Δ, which reduces the noise power by the factor ⁠ 1 / 4 ⁠ . In terms of decibels , the noise power change is 10 ⋅ log 10 ⁡ ( 1 / 4 )   ≈   − 6   d B . {\displaystyle \scriptstyle 10\cdot \log _{10}(1/4)\ \approx \ -6\ \mathrm {dB} .} Because

4331-427: The quantizer, a typical rate–distortion formulation for a quantizer design problem can be expressed in one of two ways: Often the solution to these problems can be equivalently (or approximately) expressed and solved by converting the formulation to the unconstrained problem min { D + λ ⋅ R } {\displaystyle \min \left\{D+\lambda \cdot R\right\}} where

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4402-424: The reconstruction stage maps the index k {\displaystyle k} to the reconstruction value y k {\displaystyle y_{k}} that is the output approximation of the input value. For the example uniform quantizer described above, the forward quantization stage can be expressed as and the reconstruction stage for this example quantizer is simply This decomposition

4473-412: The set of possible output values of a quantizer is countable, any quantizer can be decomposed into two distinct stages, which can be referred to as the classification stage (or forward quantization stage) and the reconstruction stage (or inverse quantization stage), where the classification stage maps the input value to an integer quantization index k {\displaystyle k} and

4544-454: The signal and an approximately flat power spectral density . The additive noise model is commonly used for the analysis of quantization error effects in digital filtering systems, and it can be very useful in such analysis. It has been shown to be a valid model in cases of high-resolution quantization (small Δ {\displaystyle \Delta } relative to the signal strength) with smooth PDFs. Additive noise behavior

4615-399: The signal being a full-scale sine wave instead of a triangle or sawtooth. For complex signals in high-resolution ADCs this is an accurate model. For low-resolution ADCs, low-level signals in high-resolution ADCs, and for simple waveforms the quantization noise is not uniformly distributed, making this model inaccurate. In these cases the quantization noise distribution is strongly affected by

4686-480: The signal has a uniform distribution covering all quantization levels, the Signal-to-quantization-noise ratio (SQNR) can be calculated from where Q is the number of quantization bits. The most common test signals that fulfill this are full amplitude triangle waves and sawtooth waves . For example, a 16-bit ADC has a maximum signal-to-quantization-noise ratio of 6.02 × 16 = 96.3 dB. When

4757-487: The signal may be audio, pictures, video, texts or 3D models. A signal may carry several different watermarks at the same time. Unlike metadata that is added to the carrier signal, a digital watermark does not change the size of the carrier signal. The needed properties of a digital watermark depend on the use case in which it is applied. For marking media files with copyright information, a digital watermark has to be rather robust against modifications that can be applied to

4828-444: The source signal is to perform dithered quantization (sometimes with noise shaping ), which involves adding random (or pseudo-random ) noise to the signal prior to quantization. In the typical case, the original signal is much larger than one least significant bit (LSB). When this is the case, the quantization error is not significantly correlated with the signal, and has an approximately uniform distribution . When rounding

4899-500: The static (DC) term of 1 2 L S B {\displaystyle \scriptstyle {\frac {1}{2}}\mathrm {LSB} } . The RMS values of the AC error are exactly the same in both cases, so there is no special advantage of rounding over truncation in situations where the DC term of the error can be ignored (such as in AC coupled systems). In either case, the standard deviation, as

4970-419: The values of { b k } k = 1 M − 1 {\displaystyle \{b_{k}\}_{k=1}^{M-1}} , { c k } k = 1 M {\displaystyle \{c_{k}\}_{k=1}^{M}} and { y k } k = 1 M {\displaystyle \{y_{k}\}_{k=1}^{M}} which optimally satisfy

5041-498: Was proposed by Saraju Mohanty, et al. in 2003 and published in January 2004. This was not the first time this was proposed. Blythe and Fridrich also have worked on SDC in 2004 for a digital camera that would use lossless watermarking to embed a biometric identifier together with a cryptographic hash . Reversible data hiding is a technique which enables images to be authenticated and then restored to their original form by removing

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