ECSE6963 Biological Image Analysis

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ECSE-6963Biological Image Analysis

• Lecture 4
• Common Medical Imaging Instrument CT Scanner
• Badri Roysam
• Rensselaer Polytechnic Institute, Troy, New York
  12180.

Center for Sub-Surface Imaging Sensing
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Recap

• Basics of biological microscopy
• Transmission light microscopy
• Fluorescence light microscopy
• Confocal microscopy
• Phase objects
• Phase contrast microscopy
• Differential Interference Contrast Microscopy
• Combined methods
• Multiple fluorophores, in combination with other
  modalities to provide structural and functional
  imaging
• Broader Picture
• Probes, media, surfaces, contrast generation
• Reference http//micro.magnet.fsu.edu/primer/inde
  x.html

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Recap Broader Picture
Contrast-Enhancing Agent
Most imaging systems can be thought of in this
general manner
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Medium
Object
Probe
Optical/IR
Electro- magnetic
Fluorescence
X-ray
Acoustic
Absorption
Absorption
Nonlinear Absorption
Dispersion
CW
Pulsed
Modulated
Nonlinear Scattering
Scattering
Scattering
Multi- Spectral
Partially Coherent
Coherent
Diffusion
Diffusive
Phase Object
Clutter
Quantum
Classical
Depolarizing
Inhomogeneous/ Layered
Outside
Inside
Auxiliary
Stationary
Moving
Rough Surface
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X-Ray Imaging
Cervical Spine X-Ray Image
Medium
Object
Probe
X-ray
Absorption
Absorption
Dispersion
Scattering
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X-Ray Tomography
Projection

• Basic Idea
• Take X-Ray projections (shadows) from numerous
  angles ?,
• Reconstruct image of patient f(x,y) from the
  projections!

Nobel Prizes Röentgen (1901) for discovering
X-Rays, Hounsfield Cormack (1979) for Computed
Tomography
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X-Ray Tomography
y

• Basic Idea
• Take X-Ray projections (shadows) from numerous
  angles ?,
• Reconstruct image of patient f(x,y) from the
  projections!

x
X-Rays
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X-Ray Tomography
y

• Basic Idea
• Take X-Ray projections (shadows) from numerous
  angles ?,
• Reconstruct image of patient f(x,y) from the
  projections!

x
X-Rays
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Calculating the Projection
y
Ray sum
Projection
x
This is also known as the Radon transform, or a
ray sum.
Line
t perpendicular distance from origin to line
L(?, t)
? angle made by the normal to line L(?, t)
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Calculating the Projection
u
y
Rotate the x-y axis by angle ?
x
Line
With this,
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The Radon Transform
u
y
Projection
Maps the spatial domain to the domain
(?,t) Note (?,t) are NOT the polar
coordinates of (x, y)
x
Line
A fixed point p (x,y) on the line maps to a
sinusoid in (?,t) space
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The Sinogram
?
t

• Well re-visit sinograms when we study the Hough
  Transform

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The Back-Projection Operator

• Represents the accumulation of the ray-sums of
  all the rays that pass through a point (x, y)
• It is NOT the inverse of the radon transform
  (its an adjoint)

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Practicalities

• This method has an artifact for a finite set of
  angles the background looks like a bunch of
  crossed lines
• Filtered back projection

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More Practicalities

• Weve described the simplest CT scanner
• Newer machines have more complex geometry
• Large fan-shaped X-Ray beam instead of parallel
  beam
• Multiple detectors along a ring instead of just
  one
• Rotate the source and detector ring
• Spiral scanning patterns
• Much better algorithms for reconstruction exist

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Other Imaging Instruments

• Structure imaging
• CT Magnetic Resonance Imaging
• Ultrasound Imaging
• Functional Imaging
• Nuclear Imaging
• Positron Emission Tomography
• Single-Photon Emission Computed Tomography
• Combined Modalities
• Functional structural imaging
• 1999 image of the year, U. of Pittsburgh

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Summary

• The Radon Transform the X-Ray CT Scanner
• The mathematics for other scanners are easier to
  understand once you know filtered back projection
• Next Class
• Image Reconstruction Pre-processing Fundamentals

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Instructor Contact Information

• Badri Roysam
• Professor of Electrical, Computer, Systems
  Engineering
• Office JEC 6046
• Rensselaer Polytechnic Institute
• 110, 8th Street, Troy, New York 12180
• Phone [phone]
• Fax [phone]
• Email roysam_at_ecse.rpi.edu
• Website http//www.rpi.edu/roysab
• NetMeeting ID (for off-campus students)
  128.113.61.80
• Secretary Jeanne Denue, JEC 6049, (518) 276
  6313, denuej_at_ecse.rpi.edu