CS-F441: SELECTED TOPICS FROM COMPUTER

SCIENCE (DEEP LEARNING FOR NLP & CV)

Lecture-KT-06: Frequency

Dr. Kamlesh Tiwari,Assistant Professor,

Department of Computer Science and Information Systems,BITS Pilani, Rajasthan-333031 INDIA

Oct 18, 2019 (Campus @ BITS-Pilani July-Dec 2019)

Fourier Transform

Any signal (function) can be written as sum of various sin and coswaves (terms)

F [g × h] = F [g]× F [h]g × h = F−1[F [g]× F [h]]

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Fourier Transform

Any signal (function) can be written as sum of various sin and coswaves (terms)

F [g × h] = F [g]× F [h]g × h = F−1[F [g]× F [h]]

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Fourier Transform

Any signal (function) can be written as sum of various sin and coswaves (terms)

F [g × h] = F [g]× F [h]g × h = F−1[F [g]× F [h]]

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Gaussian filtering has smooth image but box

Gaussian Box

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Gaussian filtering has smooth image but box

Gaussian Box

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SamplingThrow away every other row and column (to get half size image)

Aliasing Problem

Sub sampling may be dangerous: Funny stripped shirt.Wagon wheels rolling in the wrong way in movies.

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SamplingThrow away every other row and column (to get half size image)

Aliasing Problem

Sub sampling may be dangerous: Funny stripped shirt.Wagon wheels rolling in the wrong way in movies.

STCS-DL4NLP&CV (CS-F441) Campus @ BITS-Pilani Lecture-KT-06 (Oct 18, 2019) 4 / 9

SamplingThrow away every other row and column (to get half size image)

Aliasing Problem

Sub sampling may be dangerous: Funny stripped shirt.Wagon wheels rolling in the wrong way in movies.

STCS-DL4NLP&CV (CS-F441) Campus @ BITS-Pilani Lecture-KT-06 (Oct 18, 2019) 4 / 9

Nyquist Shannon Sampling TheoremSampling frequency must be ≥ 2 × fmax

Sample more oftenSub Sampling: Get rid of all the frequencies that are greater thanhalf of the new sampling frequency

I Some information would be lost but it is better then aliasingI Apply smoothing filter

Figure: Sub-sampling without & with pre-filtering

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Nyquist Shannon Sampling TheoremSampling frequency must be ≥ 2 × fmax

Sample more oftenSub Sampling: Get rid of all the frequencies that are greater thanhalf of the new sampling frequency

I Some information would be lost but it is better then aliasingI Apply smoothing filter

Figure: Sub-sampling without & with pre-filtering

STCS-DL4NLP&CV (CS-F441) Campus @ BITS-Pilani Lecture-KT-06 (Oct 18, 2019) 5 / 9

Nyquist Shannon Sampling TheoremSampling frequency must be ≥ 2 × fmax

Sample more oftenSub Sampling: Get rid of all the frequencies that are greater thanhalf of the new sampling frequency

I Some information would be lost but it is better then aliasingI Apply smoothing filter

Figure: Sub-sampling without & with pre-filteringSTCS-DL4NLP&CV (CS-F441) Campus @ BITS-Pilani Lecture-KT-06 (Oct 18, 2019) 5 / 9

Hybrid Images

A. Oliva, A. Torralba, P.G. Schyns “Hybrid Images”, SIGGRAPH 2006

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Hybrid Images

A. Oliva, A. Torralba, P.G. Schyns “Hybrid Images”, SIGGRAPH 2006

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Campbell-Robson Contrast Sensitivity CurveWhen we see an image fromfar away, we are effectivelysub-sampling itHuman visual system is moresensitive to contrast thanabsolute luminance

Human contrast sensitivity shows a typical band-pass filter shape. -Campbell and Robson (1968)

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Campbell-Robson Contrast Sensitivity CurveWhen we see an image fromfar away, we are effectivelysub-sampling itHuman visual system is moresensitive to contrast thanabsolute luminance

Human contrast sensitivity shows a typical band-pass filter shape. -Campbell and Robson (1968)

STCS-DL4NLP&CV (CS-F441) Campus @ BITS-Pilani Lecture-KT-06 (Oct 18, 2019) 7 / 9

Campbell-Robson Contrast Sensitivity CurveWhen we see an image fromfar away, we are effectivelysub-sampling itHuman visual system is moresensitive to contrast thanabsolute luminance

Human contrast sensitivity shows a typical band-pass filter shape. -Campbell and Robson (1968)

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Example Hybrid Image

The hybrid font becomes invisible at few meters. The bottom textremains easy to read at relatively long distances.

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Thank You!

Thank you very much for your attention!

Queries ?

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