Spatio temporal quincunx sub sampling
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Spatio-Temporal Quincunx Sub-Sampling. . . and how we get there David Lyon. Overview. Sampling in Television and Film The problems of aliasing Filtering requirements Conversion between differing formats Problems that can occur

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Spatio-Temporal Quincunx Sub-Sampling

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Spatio-Temporal Quincunx Sub-Sampling

. . and how we get there

David Lyon


Overview

  • Sampling in Television and Film

  • The problems of aliasing

  • Filtering requirements

  • Conversion between differing formats

  • Problems that can occur

  • How we can mitigate some of the problems and maintain or improve quality


Sampling Theory

  • Harry Nyquist – 1889 to 1976

    • “The number of independent pulses that can be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel”


Sampling Theory

  • Harry Nyquist – 1889 to 1976

    • “The number of independent pulses that can be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel”

  • Later Nyquist-Shannon

    • “Exact reconstruction of a continuous-time baseband signal from its samples is possible if the signal is bandlimited and the sampling frequency is greater than twice the signal bandwidth”


Amplitude

Fs

Frequency

Sampling Theory


Amplitude

Fs

Frequency

Sampling Theory

  • Audio:

    • 20kHz bandwidth, Fs = 44.1kHz, 48kHz


Amplitude

Fs

Frequency

Sampling Theory

  • Audio:

    • 20kHz bandwidth, Fs = 44.1kHz, 48kHz

  • Video:

    • 5.75MHz bandwidth, Fs = 13.5MHz

    • 30MHz bandwidth, Fs = 74.25MHz


Amplitude

Fs

Frequency

Aliasing

Nyquist

Frequency


Amplitude

Fs

Frequency

Aliasing

Nyquist

Frequency

  • Frequencies above Fs/2 are “reflected” into the lower portion of the spectrum and become entangled with the low-frequency signals


Amplitude

Fs

Frequency

Aliasing

Nyquist

Frequency

  • Frequencies above Fs/2 are “reflected” into the lower portion of the spectrum and become entangled with the low-frequency signals

  • These signals CANNOT be removed afterwards


Amplitude

Fs

Frequency

Aliasing

Nyquist

Frequency

  • Frequencies above Fs/2 are “reflected” into the lower portion of the spectrum and become entangled with the low-frequency signals

  • These signals CANNOT be removed afterwards

  • Filtering BEFORE sampling is needed


Image Sampling

Temporal – frames

Vertical - lines

Horizontal - pixels


Image Sampling

  • Horizontal resolution

    • Sampling rate of 720, 1280, 1920 or 2048 samples/picture width

      • Resulting resolution of 360, 640, 960 or 1024 cycles/pw


Image Sampling

  • Horizontal resolution

    • Sampling rate of 720, 1280, 1920 or 2048 samples/picture width

      • Resulting resolution of 360, 640, 960 or 1024 cycles/pw

  • Vertical resolution

    • Sampling rate of 480, 576, 720, 1080 samples/picture height

      • Resulting resolution of 240, 288, 360 or 540 cycles/ph


Image Sampling

  • Horizontal resolution

    • Sampling rate of 720, 1280, 1920 or 2048 samples/picture width

      • Resulting resolution of 360, 640, 960 or 1024 cycles/pw

  • Vertical resolution

    • Sampling rate of 480, 576, 720, 1080 samples/picture height

      • Resulting resolution of 240, 288, 360 or 540 cycles/ph

  • Temporal resolution

    • Sampling rate of 24, 25, 30, 50, 60 . . . samples/second

      • Resulting resolution of 12, 15, 25, 30 cycles/sec


Re-sampling

  • Image size changes are common


1080

Amplitude

Vertical Frequency

Potential Alias

480

Amplitude

Vertical Frequency

Re-sampling

  • Image size changes are common

    • Simple example of interpolating a 1080 picture to 480:

      • Input resolution is 540 cycles/ph

      • Output resolution is 240 cycles/ph (division by 2.25)

Filter


Re-sampling

  • Interpolation is only one part of the problem

    • Filtering is needed to control the signal spectrum and avoid the introduction of aliases

    • Simple interpolators are generally poor filters


Re-sampling

  • Interpolation is only one part of the problem

    • Filtering is needed to control the signal spectrum and avoid the introduction of aliases

    • Simple interpolators are generally poor filters

  • Alias terms are “folded” about the Nyquist point

    • Inverted in frequency, inverted “movement”

    • Highly noticeable to the human eye, which references its own internal 3D model


Re-sampling

  • Interpolation is only one part of the problem

    • Filtering is needed to control the signal spectrum and avoid the introduction of aliases

    • Simple interpolators are generally poor filters

  • Alias terms are “folded” about the Nyquist point

    • Inverted in frequency, inverted “movement”

    • Highly noticeable to the human eye, which references its own internal 3D model

  • Alias terms left in the image will be shifted again in any subsequent operations

    • Potentially cumulative problems


Restricted by practical limitations

Linked by aspect ratio and pixel shape

3D Sampling

Temporal – frames

Vertical - lines

Horizontal - pixels


Spatial Frequency

No of Lines

Potential alias

Potential alias

Frame Rate

Temporal Frequency

Spatio-Temporal Sampling

Temporal – frames

Spectrum

Spatial - lines


Spatial Frequency

No of Lines

Potential alias

Potential alias

Frame Rate

Temporal Frequency

Spatio-Temporal Sampling

  • Filtering:

    • Spatial – optical LPF and lens MTF

Temporal – frames

Spectrum

Spatial - lines


Spatial Frequency

No of Lines

Potential alias

Potential alias

Frame Rate

Temporal Frequency

Spatio-Temporal Sampling

  • Filtering:

    • Spatial – optical LPF and lens MTF

    • Temporal – integration time of sensor system

Temporal – frames

Spectrum

Spatial - lines


Potential alias

Potential alias

Spatio-Temporal Sub-Sampling

Spatial Frequency

  • Where is the filter?

No of Lines

Temporal – frames

Spectrum

Frame Rate

Spatial - lines

Temporal Frequency


Horizontal

?

Up-conversion

Spatial Frequency

No of Lines

Temporal

Frame Rate

Vertical

Spectrum

Temporal Frequency


Horizontal

?

Up-conversion

Spatial Frequency

  • Adaptive filtering

No of Lines

Temporal

Frame Rate

Vertical

Spectrum

Temporal Frequency


Horizontal

?

Up-conversion

Spatial Frequency

  • Adaptive filtering

  • Motion compensation

No of Lines

Temporal

Frame Rate

Vertical

Spectrum

Temporal Frequency


Film

1080p

720p

480i

1080i

1080p (24)

Format Interchange

Spatial Frequency

500c/ph

250c/ph

0c/ph

0c/s

15c/s

30c/s

Temporal Frequency


Film

1080p

720p

480i

1080i

1080p (24)

Format Interchange

  • Conversion between formats requires care

Spatial Frequency

500c/ph

250c/ph

0c/ph

0c/s

15c/s

30c/s

Temporal Frequency


Film

1080p

720p

480i

1080i

1080p (24)

Format Interchange

  • Conversion between formats requires care

  • Mixing formats such as film and video is to be avoided

Spatial Frequency

500c/ph

250c/ph

0c/ph

0c/s

15c/s

30c/s

Temporal Frequency


Film

1080p

720p

480i

1080i

1080p (24)

Format Interchange

  • Conversion between formats requires care

  • Mixing formats such as film and video is to be avoided

  • 1080p down-conversion might raise new challenges

Spatial Frequency

500c/ph

250c/ph

0c/ph

0c/s

15c/s

30c/s

Temporal Frequency


96

Amplitude

Frequency

48

Amplitude

Frequency

Over-sampling

  • Commonly applied to audio – eg 96kHz down to 48kHz

    • Allows the use of a high performance digital filter:

Filter


Over-sampling

  • Commonly applied to audio – eg 96kHz down to 48kHz

    • Allows the use of a high performance digital filter:


Over-sampling

  • Commonly applied to audio – eg 96kHz down to 48kHz

    • Allows the use of a high performance digital filter:

  • 1080p allows similar gains for outputs of 720p and 1080i

    • Good temporal filtering must introduce delay


Over-sampling

  • Commonly applied to audio – eg 96kHz down to 48kHz

    • Allows the use of a high performance digital filter:

  • 1080p allows similar gains for outputs of 720p and 1080i

    • Good temporal filtering must introduce delay

  • Film sampling at >1080 lines/ph also allows controlled down-sampling


Conclusion

  • Spatio-temporal quincunx sub-sampling (aka interlace) is likely to be with us for some time


Conclusion

  • Spatio-temporal quincunx sub-sampling (aka interlace) is likely to be with us for some time

  • Modern cameras and processing can stress the format unless care is taken


Conclusion

  • Spatio-temporal quincunx sub-sampling (aka interlace) is likely to be with us for some time

  • Modern cameras and processing can stress the format unless care is taken

    • Imprinted alias is difficult (or impossible) to remove

    • Camera integration is an important filter for interlace


Conclusion

  • Spatio-temporal quincunx sub-sampling (aka interlace) is likely to be with us for some time

  • Modern cameras and processing can stress the format unless care is taken

    • Imprinted alias is difficult (or impossible) to remove

    • Camera integration is an important filter for interlace

  • Poor anti-alias filtering leads to additional compression concatenation artefacts


Conclusion

  • Spatio-temporal quincunx sub-sampling (aka interlace) is likely to be with us for some time

  • Modern cameras and processing can stress the format unless care is taken

    • Imprinted alias is difficult (or impossible) to remove

    • Camera integration is an important filter for interlace

  • Poor anti-alias filtering leads to additional compression concatenation artefacts

  • 1080p down-conversion could make the stress worse


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