demo05 of Im2mesh package

demo05 - Thresholds in polyline smoothing
Cite as: Ma, J., & Li, Y. (2025). Im2mesh: A MATLAB/Octave package for generating finite element mesh based on 2D multi-phase image (2.1.5). Zenodo. https://doi.org/10.5281/zenodo.14847059
Jiexian Ma, mjx0799@gmail.com Project website List of demo
Table of Contents
Note Initialize Import Image When thresholds are zeros Set thresholds for polyline smoothing

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. No need to install any MATLAB toolboxes when running this demo.

Initialize

Before we start, please set folder "Im2mesh_Matlab" as your current folder of MATLAB.
clearvars
Set default image size.
x = 250; y = 250; width = 250; height = 250;
set(groot, 'DefaultFigurePosition', [x,y,width,height])
% To reset:
% set(groot, 'DefaultFigurePosition', 'factory')
We use the following command to add the folder 'mesh2d-master' to the path of MATLAB.
addpath(genpath('mesh2d-master'))

Import Image

im = imread('Circle.tif');
if size(im,3) == 3; im = rgb2gray( im ); end
imshow( im,'InitialMagnification','fit' );
Zoom in
imshow( im,'InitialMagnification','fit' );
xlim([40.8 66.2])
ylim([29.3 54.2])

When thresholds are zeros

opt = [];
% thresholds for polyline smoothing
opt.thresh_turn = 0;
opt.thresh_vert_smooth = 0;
opt.tolerance = 0.01; % do not simplify polyline
[vert,tria,tnum] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 6 654 1078 10 688 1711 19 695 2637 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 10 924 1078 10 924 1078 20 991 9028 30 997 9363 38 999 9395 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 289 9291 20 7 9291 30 6 9291
plotMeshes(vert,tria,tnum)
Zoom in
plotMeshes(vert,tria,tnum)
xlim([41.6 67.0])
ylim([36.2 61.1])
We saw some polygons were disappeared when compared to the input image. This disappearing issue is caused by polyline over-smoothing.
We can set thresholds for polyline smoothing to avoid this issue.

Set thresholds for polyline smoothing

opt = [];
% thresholds for polyline smoothing
opt.thresh_turn = 10;
opt.thresh_vert_smooth = 20;
opt.tolerance = 0.01; % do not simplify polyline
[vert,tria,tnum] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 6 672 1172 10 702 1604 19 706 2352 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 10 896 1172 10 896 1172 20 926 7192 25 928 7304 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 103 7246
plotMeshes(vert,tria,tnum)
Zoom in
plotMeshes(vert,tria,tnum)
xlim([41.6 67.0])
ylim([36.2 61.1])
The new boundaries are better.
% reset image size
set(groot, 'DefaultFigurePosition', 'factory')
% end of demo