ECE468_17 - ECE 468 Digital Image Processing Lecture 17...

Info icon This preview shows pages 1–10. Sign up to view the full content.

ECE 468: Digital Image Processing Lecture 17 Prof. Sinisa Todorovic [email protected]
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Outline Homework 5 due Fourier-Slice Theorem (Textbook 5.11.4) Homework 6
Image of page 2
continuous space coordinates Radon Transform g ( ρ , θ ) = −∞ −∞ f ( x, y ) δ ( x cos θ + y sin θ ρ ) dxdy
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

continuous space coordinates Radon Transform g ( ρ , θ ) = −∞ −∞ f ( x, y ) δ ( x cos θ + y sin θ ρ ) dxdy discrete space coordinates g ( ρ , θ ) = M 1 x =0 N 1 y =0 f ( x, y ) δ ( x cos θ + y sin θ ρ )
Image of page 4
Properties of the Radon Transform g ( ρ , θ + 180 ) = −∞ −∞ f ( x, y ) δ ( x cos( θ + 180 ) + y sin( θ + 180 ) ρ ) dx dy = −∞ −∞ f ( x, y ) δ ( x cos θ y sin θ ρ ) dx dy = g ( ρ , θ )
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

1D Fourier Transform of the Projection G ( ω , θ ) = −∞ g ( ρ , θ )e j 2 πωρ d ρ
Image of page 6
1D FT of the Projection -- Properties G ( ω , θ + 180 ) =?
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

1D FT of the Projection -- Properties G ( ω , θ + 180 ) =? G ( ω , θ + 180 ) = −∞ g ( ρ , θ + 180 )e j 2 πωρ d ρ = −∞ g ( ρ , θ )e j 2 πωρ d ρ
Image of page 8
1D FT of the Projection -- Properties G ( ω , θ + 180 ) =?
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 10
This is the end of the preview. Sign up to access the rest of the document.
  • Fall '08
  • Lucchese
  • Image processing, Sin, Cos, Radon transform, fourier slice theorem

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern