demo01 of Im2mesh package
demo01 - Demonstrate function im2mesh, which use MESH2D as mesh generator.
Note
I suggest familiarizing yourself with Im2mesh_GUI before learning Im2mesh package. With graphical user interface, Im2mesh_GUI will help you better understand the workflow and parameters of Im2mesh package.
If you are using Im2mesh package in MATLAB, you need to install MATLAB Image Processing Toolbox and Mapping Toolbox because Im2mesh package use a few functions in these toolboxes.
Setup
Before we start, please set folder "Im2mesh_Matlab" as your current folder of MATLAB.
Set default image size.
x = 250; y = 250; width = 250; height = 250;
set(groot, 'DefaultFigurePosition', [x,y,width,height])
% set(groot, 'DefaultFigurePosition', 'factory')
Function im2mesh use a mesh generator called MESH2D (developed by Darren Engwirda). We can use the following command to add the folder 'mesh2d-master' to the path of MATLAB. addpath(genpath('mesh2d-master'))
Kumamon
Let's start demo01. We'll demostate the usage of function im2mesh.
Import image kumamon.tif.
im = imread('kumamon.tif');
if size(im,3) == 3; im = rgb2gray( im ); end
imshow( im,'InitialMagnification','fit' );
Show the grayscale levels in the image
intensity = unique( im );
Let's use function im2mesh to generate meshes based on the kumamon image. We will use default settings. Note that function im2mesh has incorporated the workflow that you saw in im2mesh_GUI: extract polygonal boundaries from image, search & label control points, smooth boundary, simplify boundary, select phase, and generate mesh.
[ vert, tria, tnum ] = im2mesh( im );
Refine triangulation...
-------------------------------------------------------
|ITER.| |CDT1(X)| |CDT2(X)|
-------------------------------------------------------
6 153 235
10 171 485
14 173 534
Refine triangulation...
-------------------------------------------------------
|ITER.| |CDT1(X)| |CDT2(X)|
-------------------------------------------------------
7 266 235
10 275 1233
19 285 1904
Smooth triangulation...
-------------------------------------------------------
|ITER.| |MOVE(X)| |DTRI(X)|
-------------------------------------------------------
4 492 1886
8 143 1886
12 5 1886
Function im2mesh has 3 ouptut variables: vert, tria, tnum. They defines linear elements of generated triangular mesh.
vert - Node data. N-by-2 array.
tria - Node numbering for each triangle. M-by-3 array.
tnum - Label of material phase. P-by-1 array.
We can plot the mesh using function plotMeshes.
plotMeshes( vert, tria, tnum )
Mesh quality
We can use function tricost to check the mesh quality. Function tricost is written by by Darren Engwirda.
tricost( vert, tria, tnum );
We can get the mean value of Q.
mean(triscr2( vert, tria ))
Wonderful! Let's check the total number of triangles in the mesh.
That's a lot of triangles.
Change parameter
We can change the parameters of function im2mesh to see whether it help to reduce the number of triangles.
opt = []; % initialize. opt is a structure array.
opt.tolerance = 1; % default value for opt.tolerance is 0.3
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation...
-------------------------------------------------------
|ITER.| |CDT1(X)| |CDT2(X)|
-------------------------------------------------------
6 104 133
10 117 231
12 118 236
Refine triangulation...
-------------------------------------------------------
|ITER.| |CDT1(X)| |CDT2(X)|
-------------------------------------------------------
6 175 133
10 190 709
17 201 846
Smooth triangulation...
-------------------------------------------------------
|ITER.| |MOVE(X)| |DTRI(X)|
-------------------------------------------------------
4 188 838
8 7 838
plotMeshes( vert, tria, tnum )
Now, the number of triangles decreases a lot. That's great.
Parameters of function im2mesh
As I showed before, there're two ways to call function im2mesh.
Variable opt means options. It's a structure array used to stored input parameters for function im2mesh. We can take a look at the default value of opt.
You don't need to memorize the names of these parameters. The meaning of these parameters are listed the file "Im2mesh functions and parameters.pdf". Please refer to "Im2mesh_GUI Tutorial.pdf" about how to choose the value of these parameters. You may change the default values by editting function setOption in "im2mesh.m".
Quadratic element
Function im2mesh can also generate quadratic element via the following syntax.
Ouput variables - vert, tria, tnum define linear elements.
Ouput variables - vert2, tria2, tnum define quadratic elements.
Their meanings are as follows.
vert - Node data. N-by-2 array.
tria - Node numbering for each triangle. M-by-3 array.
tnum - Label of material phase. P-by-1 array.
vert2 - Node data (2nd order element). P-by-2 array. Due to new vertices, the length of vert2 is much longer than vert.
tria2 - Node numbering for each triangle (2nd order element). M-by-6 array.
You can also plot mesh using function plotMeshes, or eveluate mesh quality using function tricost.
Example 1
Let's show some examples with different opt.
opt.tolerance = 1e-10; % no polyline simplification
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation...
-------------------------------------------------------
|ITER.| |CDT1(X)| |CDT2(X)|
-------------------------------------------------------
6 720 1339
10 743 1688
20 772 3682
20 772 3682
Refine triangulation...
-------------------------------------------------------
|ITER.| |CDT1(X)| |CDT2(X)|
-------------------------------------------------------
10 887 1339
16 904 1339
20 909 5990
30 917 10916
30 917 10916
Smooth triangulation...
-------------------------------------------------------
|ITER.| |MOVE(X)| |DTRI(X)|
-------------------------------------------------------
4 3455 10814
8 1351 10814
12 144 10814
16 1 10814
20 5 10814
24 0 10814
plotMeshes( vert, tria, tnum );
Example 2
opt.select_phase = [1 2 4]; % select phase for meshing
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation...
-------------------------------------------------------
|ITER.| |CDT1(X)| |CDT2(X)|
-------------------------------------------------------
3 88 121
9 99 196
Refine triangulation...
-------------------------------------------------------
|ITER.| |CDT1(X)| |CDT2(X)|
-------------------------------------------------------
5 154 121
10 168 682
16 173 756
Smooth triangulation...
-------------------------------------------------------
|ITER.| |MOVE(X)| |DTRI(X)|
-------------------------------------------------------
4 174 746
8 8 746
plotMeshes( vert, tria, tnum );
set(groot, 'DefaultFigurePosition', 'factory')