MAPLE_AREA
Estimate the Area of a Maple Leaf from an Image

MAPLE_AREA, a MATLAB library which uses several approaches to estimate the area of a maple leaf using an image.

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.

The MAPLE_BOUNDARY functions used various MATLAB procedures to turn the maple leaf image into a polygonal curve definining the boundary. The functions in MAPLE_AREA use various sampling techniques to estimate the area of the maple leaf.

Licensing:

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

Languages:

MAPLE_AREA is available in a MATLAB version.

Related Data and Programs:

CONVEX_HULL, a MATLAB program which demonstrates the computation of the convex hull of a set of 2D points.

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

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

HAND_AREA, a MATLAB program which estimates the area of a curve which outlines a person's hand.

HAND_DATA, MATLAB programs which carry out some numerical exercises based on data that came from tracing several points on a person's hand.

maple_area_test

MAPLE_BOUNDARY, a MATLAB library which reads an image of a maple leaf and extracts the list of pixels that form the boundary.

MESH2D_HAND, a MATLAB program which reads in a set of 59 points which outline a human hand, and calls MESH2D, which is able to create a fine triangular mesh of the region outlined by the points.

POLYGON, a dataset directory which contains examples of polygons.

TRIANGULATE, a MATLAB program which triangulates a polygonal region.

Reference:

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

Source Code:

• maple_area_estimate_grid.m, estimates the relative area of a maple leaf using a regular grid.
• maple_area_estimate_grid_test.m
• maple_area_estimate_mc.m, estimates the relative area of a maple leaf using Monte Carlo points.
• maple_area_estimate_mc_test.m
• maple_area_estimate_qmc.m, estimates the relative area of a maple leaf using Quasi Monte Carlo points.
• maple_area_estimate_qmc_test.m
• maple_boundary.m, returns the coordinates of 1776 (x,y) points along the boundary of the maple leaf.
• timestamp.m, prints the current YMDHMS date as a timestamp;