demo10 of Im2mesh package

demo10 - Different polyline smoothing technique

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 Shape Extract boundaries & find control points Smooth boundary using Taubin method Smooth boundary using CCMA method Plot together Zoom in

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')

Shape

Let's start demo. Import image Shape.tif.

im = imread('Shape.tif');

if size(im,3) == 3; im = rgb2gray( im ); end

imshow( im,'InitialMagnification','fit' );

Extract boundaries & find control points

We use function getCtrlPnts to find and label control points.

% image to polygon boundary

boundsRaw = im2Bounds( im );

% label control points

tf_avoid_sharp_corner = false;

boundsCtrlP = getCtrlPnts( boundsRaw, tf_avoid_sharp_corner, size(im) );

plotBounds(boundsCtrlP, true); % show starting and control points

Smooth boundary using Taubin method

We use function smoothBounds to smooth boundary. Inside function smoothBounds, it's the Taubin smoothing method (https://doi.org/10.1109/ICCV.1995.466848).

lambda = 0.5;

mu = -0.5;

iters = 100;

threshold_num_turning = 4;

threshold_num_vert_Smo = 4;

boundsTaubin = smoothBounds( boundsCtrlP, lambda, mu, iters, ...

threshold_num_turning, threshold_num_vert_Smo );

plotBounds(boundsTaubin);

Smooth boundary using CCMA method

Let's try another smoothing method - Curvature Corrected Moving Average (CCMA) method (https://github.com/UniBwTAS/ccma). Because Im2mesh package has a good and clear workflow, we can easily implement CCMA method via "smoothBoundsCCMA.m". Function smoothBoundsCCMA is just slightly different from function smoothBounds.

Here is some info about the input of function smoothBoundsCCMA.

new_bounds = smoothBoundsCCMA( bounds, w_ma, w_cc, threshold_num_turning, threshold_num_vert )

% w_ma (float): Width parameter for the moving average.

% w_cc (float): Width parameter for the curvature correction.

% w_ma has major impact. Larger w_ma, smoother curve.

% w_cc has little impact.

Let's try it.

w_ma = 30;

w_cc = 3;

threshold_num_turning = 4;

threshold_num_vert_Smo = 4;

boundsCCMA = smoothBoundsCCMA( boundsCtrlP, w_ma, w_cc, ...

threshold_num_turning, threshold_num_vert_Smo );

plotBounds(boundsCCMA);

Plot together

plotBounds2( boundsTaubin, boundsCCMA );

Zoom in

plotBounds2( boundsTaubin, boundsCCMA );

xlim([32.6 58.5])

ylim([45.7 68.2])

Very good! It seems the result of CCMA method is quite similar to that of Taubin method for our data.

% reset image size
set(groot, 'DefaultFigurePosition', 'factory')
% end of demo