edge
edge,
a MATLAB 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.
Related Data and Programs:
edge_test
hypersphere_surface,
a MATLAB code which
illustrates a procedure for estimating the location of a hypersurface
defined by a characteristic function or a signed function.
image_edge,
a MATLAB code which
demonstrates a simple procedure for edge detection in images.
shoreline,
a MATLAB 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 259279.

Rick Archibald, Anne Gelb, Jungho Yoon,
Determining the location of discontinuities in the derivatives
of functions,
Applied Numerical Mathematics,
Volume 58, 2008, pages 577592.

Larry Shepp, Ben Logan,
The Fourier reconstruction of a head section,
IEEE Transactions on Nuclear Science,
Volume NS21, June 1974, pages 2143.

Larry Shepp,
Computerized tomography and nuclear magnetic resonance,
Journal of Computer Assisted Tomography,
Volume 4, Number 1, February 1980, pages 94107.
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 SheppLogan 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 SheppLogan 3D phantom.
Last revised on 09 January 2019.