Two-Dimensional Imaging

Winter 2012-2013

 

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Week of / topics


Jan. 4

  • Overview and class procedures
  • Basic concepts and notation
  • Examples of digital images
  • Coherent and incoherent images
  • Computer representations of images
  • Histograms, contrast, and stretching images

Jan. 11

  • Coherent and incoherent imaging mechanisms
  • Methods of representation
  • Functions of two variables
  • Projections
  • Image simulation

Jan. 18

  • Monday - Martin Luther King Day, no class
  • Two-dimensional impulses
  • Shah function and Line impluses
  • Ring impulse functions
  • Derivatives of impulse functions

Jan. 25

  • The two-d Fourier transform
  • Analysis vs. synthesis
  • Corrugation viewpoint
  • Transform pairs
  • Theorems for the two-d Fourier transform
  • FFTs

Feb. 1

  • Image spectra
  • Digital implementation of the shift theorem
  • Convolution in two dimensions
  • Cross- and autocorrelation
  • Central value and volume of autocorrelation

Feb. 8

  • Midterm Examination through Lecture 2/3
  • The two-dimensional convolution theorem
  • Point response of a system
  • Factorization and separation
  • Assignment and Discussion of Final Project

Feb. 15

  • Monday - President's Day, no class
  • Sampling and interpolation
  • Sampling functions
  • Fourier transform of the sampling function
  • Convolutional models
  • Seismic imaging beneath the Earth's surface

Feb. 22

  • Rotational symmetry
  • Bessel functions and the Hankel transform
  • Jinc and sinc functions

Mar. 1

  • Tomography and medical imaging
  • Antennas and radio astronomy
  • Aperture synthesis

Mar. 8

  • Interferometry
  • Generating high-resolution pictures of the skies
  • Other applications of two-dimensional imaging
  • Last day of class Mar. 10

Mar. 15

  • FINAL PROJECT DUE, NOON, MARCH 15