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© 2000 Jeff B. Pelz. Fourier Synthesis Sinusoidal Functions as Building Blocks for Spatial Vision.

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Presentation on theme: "© 2000 Jeff B. Pelz. Fourier Synthesis Sinusoidal Functions as Building Blocks for Spatial Vision."— Presentation transcript:

1 © 2000 Jeff B. Pelz

2

3 Fourier Synthesis Sinusoidal Functions as Building Blocks for Spatial Vision

4 © 2000 Jeff B. Pelz Sinusoidal Function F( ) = sin( ) sin( )

5 © 2000 Jeff B. Pelz sin(0) = 0.0

6 © 2000 Jeff B. Pelz sin(45) = 0.7

7 © 2000 Jeff B. Pelz sin(90) = 1.0

8 © 2000 Jeff B. Pelz sin(135) = 0.7

9 © 2000 Jeff B. Pelz sin(180) = 0.0

10 © 2000 Jeff B. Pelz sin(225) = - 0.7

11 © 2000 Jeff B. Pelz sin(270) = - 1.0

12 © 2000 Jeff B. Pelz sin(315) = - 0.7

13 © 2000 Jeff B. Pelz sin(360) = sin(0) = 0.0

14 © 2000 Jeff B. Pelz F(x) = sin(x) sin( )

15 © 2000 Jeff B. Pelz F(x) = sin(x)

16 © 2000 Jeff B. Pelz F(x) = sin(x)

17 © 2000 Jeff B. Pelz F(x) = sin(x)

18 © 2000 Jeff B. Pelz F(x) = sin(x)

19 © 2000 Jeff B. Pelz F(x) = square(x)

20 © 2000 Jeff B. Pelz Two-dimensional F(x,y) Horizontal position (x) Vertical position (y)

21 © 2000 Jeff B. Pelz Two-dimensional F(x,y) Horizontal position (x) Vertical position (y)

22 © 2000 Jeff B. Pelz F(x,y) = one of an infinite functions of (x,y)

23 © 2000 Jeff B. Pelz One-dimensional F(x) = square(x)

24 © 2000 Jeff B. Pelz F(x) = square(x) sin(x)

25 © 2000 Jeff B. Pelz F(x) = square(x) sin(x)

26 © 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x)

27 © 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x)

28 © 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x)

29 © 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x) + 1 / 9 sin(9x)

30 © 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x) + 1 / 9 sin(9x) + 1 / 11 sin(11x)

31 © 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x) + 1 / 9 sin(9x) + 1 / 11 sin(11x) + 1 / 13 sin(13x)

32 © 2000 Jeff B. Pelz F(x) = sin(x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x) + 1 / 9 sin(9x) + … / 25 sin(25x)

33 © 2000 Jeff B. Pelz F(x) = 1sin(1x) + 1 / 3 sin(3x) + 1 / 5 sin(5x) + 1 / 7 sin(7x) + 1 / 9 sin(9x) + … / 25 sin(25x) [freq components]

34 © 2000 Jeff B. Pelz F( ) = (1, 1) +( 1 / 3,3) +( 1 / 5, 5) + ( 1 / 7, 7) + ( 1 / 9, 9) + …...

35 © 2000 Jeff B. Pelz F( ) = 1, 0, 1 / 3, 0, 1 / 5, 0, 1 / 7, 0, 1 / 9, …... Spatial domain Frequency domain

36 © 2000 Jeff B. Pelz Fourier Pairs

37 © 2000 Jeff B. Pelz Fourier Pairs

38 © 2000 Jeff B. Pelz Fourier Pairs

39 © 2000 Jeff B. Pelz Fourier Pairs

40 © 2000 Jeff B. Pelz Fourier Pairs

41 © 2000 Jeff B. Pelz Fourier Pairs

42 © 2000 Jeff B. Pelz Fourier Pairs

43 © 2000 Jeff B. Pelz Fourier Pairs

44 © 2000 Jeff B. Pelz Fourier Pairs

45 © 2000 Jeff B. Pelz Low-pass Filtering

46 © 2000 Jeff B. Pelz High-pass Filtering

47 © 2000 Jeff B. Pelz Frequency Channels

48 © 2000 Jeff B. Pelz

49 2D Gabor Functions

50 © 2000 Jeff B. Pelz


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