edge

edge, an Octave code which defines some test functions in 1D, 2D and 3D for the detection of edges.

In particular, we look at some simple functional examples in 1D, 2D, and 3D, that is, situations in which a formula is supplied so that the value of a scalar quantity f() can be determined at any point in the region. We are interested in examples in which the quantity f() exhibits jumps. that is, sudden, sharp changes in value.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

edge is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

edge_test

hypersphere_surface, an Octave code which illustrates a procedure for estimating the location of a hypersurface defined by a characteristic function or a signed function.

image_edge, an Octave code which demonstrates a simple procedure for edge detection in images.

shoreline, an Octave code which tries to identify and triangulate the 2D domain over which some function f(x,y) is nonnegative.

Reference:

• Rick Archibald, Anne Gelb, Jungho Yoon,
  Polynomial fitting for edge detection in irregularly sampled signals and images,
  SIAM Journal on Numerical Analysis,
  Volume 43, Number 1, 2006, pages 259-279.
• Rick Archibald, Anne Gelb, Jungho Yoon,
  Determining the location of discontinuities in the derivatives of functions,
  Applied Numerical Mathematics,
  Volume 58, 2008, pages 577-592.
• Larry Shepp, Ben Logan,
  The Fourier reconstruction of a head section,
  IEEE Transactions on Nuclear Science,
  Volume NS-21, June 1974, pages 21-43.
• Larry Shepp,
  Computerized tomography and nuclear magnetic resonance,
  Journal of Computer Assisted Tomography,
  Volume 4, Number 1, February 1980, pages 94-107.

Source Code:

• fx1.m, 1D test function #1, a function with a jump discontinuity at 0.
• fx2.m, 1D test function #2.
• fx3.m, 1D test function #3.
• fx4.m, 1D test function #4.
• fx5.m, 1D test function #5.
• fx6.m, 1D test function #6.
• fx7.m, 1D test function #7.
• fxy1.m, 2D test function #1, discontinuity along a circle.
• fxy2.m, 2D test function #2, the Shepp-Logan 2D phantom.
• fxy3.m, 2D test function #3, the 2d modified Harten function.
• fxy4.m, 2D test function #4, the discontinuous medium wave, P component.
• fxy5.m, 2D test function #5, the discontinuous medium wave, U component.
• fxyz1.m, 3D test function #1, the Shepp-Logan 3D phantom.