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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 . . 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