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

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ECE 468: Digital Image Processing Lecture 16 Prof. Sinisa Todorovic [email protected]
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Outline Image reconstruction from projections (Textbook 5.11) Radon Transform (Textbook 5.11.3)
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Computed Tomography
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Image Projections X-ray computed tomography: X-raying an object from different directions 3D object representation
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Computed Tomography
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Two Equivalent Definitions of the Line y = ax + b x cos θ + y sin θ = ρ
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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 )
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continuous space coordinates Radon Transform g ( ρ , θ ) = −∞ −∞ f ( x, y ) δ ( x cos θ + y sin θ ρ ) dxdy
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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 )
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Example: Radon Transform f ( x, y ) = A , x 2 + y 2 r 2 0 , o.w
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Sinogram = Image of Radon Transform
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Properties of Objects from Sinogram Sinogram symmetric = Object symmetric
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  • Fall '08
  • Lucchese
  • Image processing, Tomographic reconstruction, Radon transform

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