maple_boundary

maple_boundary, a MATLAB code which takes an image of a maple leaf and determines the pixels that form the boundary.

For a discussion of quasirandom sampling, Brian Hayes published a picture of a maple leaf and considered how its area could be estimated using a regular grid of points, random sampling, or quasirandom sampling.

For various reasons, it will be interesting to have a copy of this maple leaf image accessible. The MAPLE_BOUNDARY functions use various MATLAB procedures to turn the maple leaf image into a polygonal curve definining the boundary, following which various calculations may be made.

Licensing:

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

Languages:

maple_boundary is available in a MATLAB version.

Related Data and Programs:

convex_hull, a MATLAB code which demonstrates the computation of the convex hull of a set of 2D points.

florida_cvt_geo, MATLAB codes which explore the creation of a centroidal Voronoi Tessellation (CVT) of the state of Florida, based solely on geometric considerations.

florida_cvt_pop, MATLAB codes which explore the creation of a centroidal Voronoi Tessellation (CVT) of the state of Florida, based on population density.

hand_area, a MATLAB code which estimates the area of a curve which outlines a person's hand.

hand_data, a MATLAB code which carries out some numerical exercises based on data that came from tracing several points on a person's hand.

hand_mesh2d, a MATLAB code which reads in points which outline a human hand, and calls mesh2d(), which creates a fine triangular mesh of the region outlined by the points.

human_data, a MATLAB code which starts with an image of simple outline of a human body, tabulates a sequence of points on the outline, creating numerical data defining the boundary. It is then able to fill the region with mesh points and triangulate the region. This allows the region to be analyzed by the finite element method (FEM).

maple_area, a MATLAB code which takes the list of pixels that form the boundary of the image of a maple leaf within a picture, and uses grid, Monte Carlo, and Quasi Monte Carlo sampling to estimate the area of the leaf.

maple_boundary_test

triangulate, a MATLAB code which triangulates a polygonal region.

Reference:

• Brian Hayes,
  Quasirandom Ramblings,
  American Scientist,
  Volume 99, Number 4, July-August 2011, pages 282-287.

Source Code:

• i4mat_transpose_write.m, writes the transpose of an I4MAT to a file.
• maple_boundary.m, extracts a boundary between black exterior and white interior.
• maple_boundary_plot.m makes a plot of the boundary lines of the maple leaf.
• maple_boundary_vertex_plot.m makes a plot of the boundary vertices of the maple leaf.