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    Dither: Dither: Visual Noise in Computer Vision
    Dither: Dither: Visual Noise in Computer Vision
    Dither: Dither: Visual Noise in Computer Vision
    Ebook143 pages1 hourComputer Vision

    Dither: Dither: Visual Noise in Computer Vision

    By Fouad Sabry

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    About this ebook

    What is Dither


    Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images. Dither is routinely used in processing of both digital audio and video data, and is often one of the last stages of mastering audio to a CD.


    How you will benefit


    (I) Insights, and validations about the following topics:


    Chapter 1: Dither


    Chapter 2: Analog-to-digital converter


    Chapter 3: Dynamic range


    Chapter 4: Signal-to-noise ratio


    Chapter 5: Halftone


    Chapter 6: Comparison of analog and digital recording


    Chapter 7: Compression artifact


    Chapter 8: Sampling (signal processing)


    Chapter 9: Quantization (signal processing)


    Chapter 10: Grayscale


    (II) Answering the public top questions about dither.


    (III) Real world examples for the usage of dither in many fields.


    Who this book is for


    Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Dither.

    LanguageEnglish
    PublisherOne Billion Knowledgeable
    Release dateMay 4, 2024
    Dither: Dither: Visual Noise in Computer Vision

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      Book preview

      Dither - Fouad Sabry

      Chapter 1: Dither

      Dither is a deliberate sort of noise used to randomize quantization mistake, hence preventing large-scale patterns such as color banding in photographs. Dither is commonly employed in the processing of digital audio and video data, and is frequently one of the final steps in mastering audio for a CD.

      Commonly, dither is used to transform a grayscale image to black-and-white such that the density of black dots in the resultant image approximates the average gray level of the original image.

      …[O]ne of the earliest [applications] of dither came in World War II.

      Bombers utilized mechanical computers for navigation and calculating bomb trajectory.

      Curiously, These computers (boxes containing hundreds of gears and cogs) performed more precisely on board the airplane, and less solidly established.

      Engineers noticed that the aircraft's vibration minimized the mistake caused by sticky moving parts.

      Instead of moving in quick jerks, you should move smoothly, They moved with greater consistency.

      Miniature vibrating motors were included into the computers, The term dither was derived from the Middle English verb didderen, which means to shake. Today, When a mechanical meter is tapped to improve its accuracy, You're using dither, Modern dictionaries define dither as a profoundly anxious state of mind, confused, or agitated condition.

      In minuscule amounts, Dither effectively makes a digital system more analog in the positive meaning of the word.

      — Ken Pohlmann, Principles of Digital Audio

      Shortly after World War II, the term dither was published in literature on analog computation and hydraulically driven weaponry.

      Dither is applied in numerous fields that include digital processing and analysis. These applications include digital audio, digital video, digital photography, seismology, radar, and weather forecasting systems that require digital signal processing.

      Quantification produces mistake. If this inaccuracy is associated with the signal, then the outcome may be cyclical or predictable. In some domains, particularly those in which the receptor is sensitive to such distortions, cyclical mistakes result in unwanted artifacts. Introducing dither in these areas transforms the error into random noise. The audio industry is a prime illustration of this. The human ear acts similarly to a Fourier transform in that it detects distinct frequencies.

      In an analog system, the signal is continuous, whereas in a PCM digital system, the signal's amplitude is confined to one of a fixed set of values or numbers. This method is known as quantization. Each coded value is a discrete step; if a signal is quantized without dither, there will be quantization distortion associated with the original input signal... In order to prevent this, the signal is dithered, a procedure that mathematically eliminates harmonics and other highly undesirable distortions and replaces them with a constant, fixed level of noise.

      During the production process, a larger number of bits are often used to represent each sample; this must be reduced to 16 bits in order to create a compact disc.

      There are numerous ways to accomplish this. One can, for instance, discard the extra bits; this is known as truncation. Additionally, one can round surplus bits to the nearest value. Each of these strategies, however, produces faults that are predictable and calculable. Dithering substitutes these inaccuracies with a continuous, fixed level of noise.

      6-bit truncation audio sample examples

      16-bit sinusoid

      reduced to six bits

      reduced to 6 bits

      Having trouble playing these files? See media support.

      Take, for instance, a waveform with the following values::

      1 2 3 4 5 6 7 8

      If the waveform is diminished by 20%, then the following values result::

      0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4

      If these values are shortened, the resulting data are as follows::

      0 1 2 3 4 4 5 6

      If these values are rounded instead, the following data result::

      1 2 2 3 4 5 6 6

      The technique of decreasing the amplitude of any original waveform by 20 percent results in consistent mistakes. Consider a sine wave that, for a portion, meets the aforementioned parameters. As shown in the above example, every time the sine wave's value reached 3.2, the shortened result would be wrong by 0.2. Whenever the value of the sine wave reached 4.0, there would be no error because the shortened result would be off by 0.0, as illustrated previously. Throughout the cycle of the sine wave, the magnitude of the error varies regularly and repeatedly. This mistake specifically reveals itself as distortion. What the ear perceives as distortion is the additional information at discrete frequencies resulting from a recurring quantization error.

      A potential approach would be to round the two-digit number (for example, 4.8) in either direction. It could be rounded to five one time and then to four the next. This would make the long-term average 4.5 rather than 4, bringing the value closer to its true value over time. However, this still results in determinable (though more intricate) error. Every other time the value 4.8 is encountered, the result is a 0.2-percent error, and the other times, the error is 0.8. This still results in a quantified, repeated error.

      An alternative option would be to round 4.8 so that four out of five times it is rounded up to 5, and the fifth time it is rounded down to 4. Long term, this would average out to exactly 4.8. Unfortunately, it still results in recurring and predictable faults, and these flaws continue to show as audible distortion.

      This results in the solution of dithering. Instead of rounding up or down in a predictable, repetitive fashion, it is possible to round up or down randomly. If a series of random numbers between 0.0 and 0.9 (e.g., 0.6, 0.1, 0.3, 0.6, 0.9, etc.) are created and added to 4.8, two out of ten times the result will truncate back to 4 (if 0.0 or 0.1 are added to 4.8), and eight out of ten times the result will truncate to 5. Each condition has a 20% probability of being rounded to 4 and an 80% chance of being rounded to 5. The long-term average of these results is 4.8, and their quantization error is random noise. This noise is less obnoxious to the ear than the measurable distortion produced by other solutions.

      Prior to quantization or re-quantization, dither is introduced to decouple quantization noise from the input signal and prevent nonlinear behavior (distortion). Quantization with a lower bit depth necessitates more dither. The technique still results in distortion, but the distortion is random, therefore the resulting noise is essentially decorrelated from the desired signal.

      Lipshitz and Vanderkooi demonstrated in a seminal study published in the AES Journal that different noise types with distinct probability density functions (PDFs) react differently when employed as dither signals, Dither can be utilized to break up periodic limit cycles, a typical issue with digital filters. Typically, random noise is less annoying than the harmonic tones produced by limit cycles.

      Function of rectangular probability density (RPDF) Any value within the defined range has the same likelihood of occuring within dither noise.

      Function of triangular probability density (TPDF) Dither noise has a triangle distribution; the chance of occurrence is greatest for values in the middle of the range. It is possible to obtain triangular distribution by combining two separate RPDF sources.

      The Gaussian PDF distribution has a normal distribution. This bell-shaped or Gaussian curve is characteristic of dither generated by analog sources such as microphone preamplifiers. If a recording's bit depth is sufficient, the preamplifier noise will be adequate to dither the recording.

      Noise shaping is a filtering procedure that modifies the spectral energy of quantization error, often to deemphasize frequencies to which the ear is most sensitive or to entirely separate signal and noise bands. Whether dither is inserted inside or outside of the feedback loop of the noise shaper affects its final spectrum if it is utilized. If within, the dither is considered as part of the error signal and formed in conjunction with the real

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