demo06 of Im2mesh package

demo06 - 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.
Table of Contents
Note Setup Circle 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.
Im2mesh_GUI: https://www.mathworks.com/matlabcentral/fileexchange/179684-im2mesh_gui-2d-image-to-finite-element-mesh
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.
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')

Circle

Let's start demo. Import image Circle.tif.
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.threshold_num_turning = 0;
opt.threshold_num_vert_Smo = 0;
opt.tolerance = 0.01; % do not simplify polyline
[vert,tria,tnum] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 6 683 1094 10 715 1737 20 723 2772 20 723 2772 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 10 945 1094 10 945 1094 20 1011 9263 25 1016 9544 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 153 9422
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.threshold_num_turning = 10;
opt.threshold_num_vert_Smo = 20;
opt.tolerance = 0.01; % do not simplify polyline
[vert,tria,tnum] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 6 678 1186 10 708 1596 20 713 2369 20 713 2369 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 10 891 1186 10 891 1186 20 919 7026 25 922 7161 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 101 7089
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