Visual Redundancy

Vicente González Ruiz

July 5, 2022

Contents

 1 Color (\(\text {RGB}\))
 2 Spatial (2D)
 3 Temporal
 4 Resources

Usually, some part of the data in an image is redundant (can be removed without loss of information).

1 Color (\(\text {RGB}\))

In \(\text {RGB}\) images, the color of a pixel depends on the frequency of the light that the pixel represents. Such information can be represented in a number of different encoding systems known as color spaces. Among all those systems, the \(\text {RGB}\) color space is the most used because \(\text {RGB}\) images can be obtained directly from the light signal using color filters.1

The \(\text {RGB}\) color model has evident physical advantages and it is straightforward and easy to manage, but also, in general, is quite redundant. In the case of a \(\text {RGB}\) image, the three components of each pixel are usually highly correlated in the sense that, for example, if the \(\text {R}\) component of a pixel has a high value, the other components will be also high, with a high probability. This means that if we use an encoding system that takes into consideration this redundancy, we can express the same information2 using a smaller number of bits (reducing thus the length of the code-stream).

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Figure 1: Effect (visual) of chroma subsamplig in the \(\text {YCrCb}\) domain. See this notebook.

Visual color redundancy (generated by the way that humans perceive the chrominance) is exploited by most color models used in image and video compression, such as \(\text {YCrCb}\) and \(\text {YCoCg}\). This can be see in the Fig. 1.

2 Spatial (2D)

Spatial redundancy is present basically in images, because pixels tend to be similar to their neighbors or tend to repeat textures. See Fig 2.

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Figure 2: Spatial redundancy in images.

Humans are more sensitive to low-frequency image data than high-frequency data. In addition, luminance information is more important than chrominance information [1].

3 Temporal

Temporal redundancy is shown by sequences of samples when those samples are similar in value and when paterns of samples tend to repeat. Temporal redundancy is found in all those time-dependant signals, such as audio and video, among others.

Temporal redundancy can be removed by most audio and video codecs.

Most video codecs use motion compensation to remove temporal redundancy.

4 Resources

[1]   Ahmet Kondoz. Visual Media Coding and Transmission. John Wiley & Sons, 2009.

1Specifically, a red (R) filter, a green (G) filter and a blue (B) filter.

2Or almost the same amount of information, depending on the accuracy of the computations.