ECE
ECE468_16

# ECE468_16 - ECE 468 Digital Image Processing Lecture 16...

• Notes
• 3

This preview shows pages 1–13. Sign up to view the full content.

ECE 468: Digital Image Processing Lecture 16 Prof. Sinisa Todorovic [email protected]

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

Outline Image reconstruction from projections (Textbook 5.11) Radon Transform (Textbook 5.11.3)
Computed Tomography

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

Image Projections X-ray computed tomography: X-raying an object from different directions 3D object representation
Computed Tomography

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

Two Equivalent Definitions of the Line y = ax + b x cos θ + y sin θ = ρ
Radon Transform A point in the projection is the ray-sum along x cos θ k + y sin θ k = ρ j g ( ρ j , θ k )

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
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 )

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

Example: Radon Transform f ( x, y ) = A , x 2 + y 2 r 2 0 , o.w
Sinogram = Image of Radon Transform

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

Properties of Objects from Sinogram Sinogram symmetric = Object symmetric
This is the end of the preview. Sign up to access the rest of the document.
• Fall '08
• Lucchese
• Image processing, Tomographic reconstruction, Radon transform

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern