converter of bitmap image series into ansys en- vironment

CONVERTER OF BITMAP IMAGE SERIES INTO ANSYS EN- 

VIRONMENT 

Petr Koňas 

Ing. Petr KOŇAS, Ph.D., MENDEL UNIVERSITY OF AGRICULTURE AND FORESTRY, 

Zemědělská 3, 613 00 Brno, Czech Republic, konas@mendelu.cz 

Anotace 

Práce shrnuje vytvořený algoritmus tvorby konečně prvkové sítě (KP) odvozené z bitmapové 

předlohy. Je detailně popsán proces registrace, segmentace a síťování. Pro zpracování obrázků 

byly použity C++ knihovny STL projektů Insight Toolkit (ITK) a Visualization Toolkit (VTK). 

Za tímto účelem byla sestavena multiplatformní aplikace WOOD3D uvolněná pod licencí GNU 

GPL. Je obsaženo několik metod pro segmentaci a především různé způsoby konturování. Byly 

naprogramovány čtyřstěnné a šestistěnné typy sítí. Jsou zmíněny některé jednoduché způsoby 

zlepšení kvality sítě. Byla provedena verifikace a testování aplikace na vytvořených anatomických 

preparátech smrku a ořechu. Jsou uvedeny metody přípravy anatomických preparátů. Zformovaná 

síť byla použita v jednoduché mechanické analýze. 

Annotation 

The work summarizes created algorithms for formation of finite element (FE) mesh which is derived 

from bitmap pattern. Process of registration, segmentation and meshing is described in detail. 

C++ library of STL from Insight Toolkit (ITK) Project together with Visualization Toolkit 

(VTK) is used for base processing of images. Several methods for appropriate mesh output are 

discussed. Multiplatform application WOOD3D for the task under GNU GPL license was assembled. 

Several methods of segmentation and mainly different ways of contouring were included. 

Tetrahedral and rectilinear types of mesh were programmed. Improving of mesh quality in some 

simple ways is mentioned. Testing and verification of final program on wood anatomy samples 

of spruce and walnut was realized. Methods of microscopic anatomy samples preparation are 

depicted. Final utilization of formed mesh in the simple structural analysis was performed. 

Introduction 

Main goal of the project, automatic mesh generation from bitmap source is under focus of many 

research teams. Unfortunately, a lot of them develop useful code just for commercial use. Similar 

task to our project is conversion of CT images from medical analysis into the finite element 

meshes which was investigated in many papers. Many patents were released in this area. We 

should mention mainly works Finnigan et al. (1994) focused on converting of tomography images 

into finite element models, Johnson (1999) aimed on anisotropic representation of scanned 

object and Usami et al. (2008) who extrapolates the inner volume of shell based geometry. 

The work presents implementation of several methods of image registration, filtration and segmentation 

together with Delaunay method (Delaunay B. 1934), dividing cubes method (Grosland 

et al. 2002) and modified octree method (Yerry 1984, Schneiders 1996). The article discuss main 

problems in image analysis due to incompatible colour spaces, samples preparation, thresholding 

ANSYS konference 2008 

16. ANSYS FEM Users’ Meeting & 14. ANSYS CFD Users’ Meeting 

Luhačovice 5, - 7, listopadu 2008 

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and final conversion into finite element mesh. Assembling of mentioned tasks together and evaluated 

application are main original results of the work. 

Materials and methods 

Registration 

Input images obtained by hand way are usually bad shaped and not precisely positioned. Common 

way to solve this problem is utilization of registration algorithms. In spite of it, the task of 

registration is very complex problem. Registration process should compensate translation, rotation 

and rescaling of images. When the sequence of images just overlay without registering the 

final composed image proves discontinuity of anatomy elements. For thin closely positioned 

samples the change can be very small (Fig. 1 a), but more distant samples can consist of very 

different structure with minimal linkage with other images in sequence (Fig. 1 b). 

a) b) 

Figure 1: sequence of a) 3 images with 10.3% of continuity defined by amount of white colour, 

b) 5 images with 3.3% of continuity both overlaid without registration. Each slice is coloured by 

different colour. 

Registration process compensates the error in position and small deformation of samples. It also 

admits small discontinuities between two succeeding images. Of course too much discontinuities 

can led into more significant error during registration than small deviation of simple overlaid 

images. When the registration process (by affine transform) is applied the final transformed images 

can prove relatively small increasing of anatomical elements succession (defined e.g. by 

integral opening of image measured by one specified colour). In presented example only 0.6% 

difference in comparison of overlaid images with registration and without registration process 

will occur for sequence of 3 images and 1.2% difference will occur for 5 images in the whole 

tested region (Fig. 1, 2). Therefore, the registration process rapidly increases chance to successful 

realization of the following steps, especially the process of segmentation and forming of the finite 

element mesh. 




- 2 -

a) b) 

Figure 2: sequence of a) 3 images with 10.9% of continuity, b) 5 images overlaid images formed 

by implemented registration with 4.5% of continuity. 

In presented application the affine transform with registration based on moments is implemented 

by itk::AffineTransform class. This class represents an affine transform by rotation, scaling, 

shearing and translation of two sequential input 2D images by comparing of them and transforming 

the second image. Transformation of pixel position is driven by eq. 1 (Yoo 2004). 

⎛x' ⎞ ⎡M11 M12 M13 ⎤ ⎛x− Cx ⎞ ⎛Tx + Cx 

⎞ 

⎜ ⎟ 

y' 

⎢ 

M12 M22 M 

⎥ ⎜ ⎟ ⎜ ⎟ 

= 

⎢ 

23 

⎥ 

⋅ y− Cy + Ty + Cy 

(1) 

⎜z' ⎟ ⎢M31 M32 M ⎥ ⎜ 

33 

z− C ⎟ ⎜ 

z 

Tz + C ⎟ 

⎝ ⎠ ⎣ ⎦ ⎝ ⎠ ⎝ z ⎠ 

x,y,z is original position, C x ,C y ,C z is center of rotation, T x ,T y ,T z is vector of translation, M ij are affine transform coefficients. 

Mapping of pixels intensity values from space of fixed image into the moving image is made by 

class of linear interpolator itk::LinearInterpolateImageFunction, which evaluates intensity values 

on non-grid values of moving image, which is generally deformed according to the fixed image. 

Filtering of image 

Filtering plays very useful role in image processing. In programmed application it is used mainly 

for emphasizing of anatomy structures and suppressing of image noise. Filters in program are 

formed by thresholding code for separation of background and foreground parts of image or they 

are formed by convolution techniques. Thresholdig separates pixels by simple rule of Eq. 2 for 

Otsu Filter and Eq. 3 describes thresholding for binary filter. 

⎧W 1 

for w 

x,y,(z) 

< Th 

w 

x,y,(z) 

= ⎨ 

(2) 

⎩W 2 

for w 

x,y,(z) 

> Th 

W 1 ,W 2 are colour intensity values; w x,y,(z) is output pixel value on position x,y,(z); Th is threshold value 

⎧W 1 

for Th1 < w 

x,y,(z) 

< Th 

2 

w 

x,y,(z) 

= ⎨ (3) 

⎩ W otherwise 

2 

Th 1 and Th 2 are threshold limits within the image intensities of structure can occur. 

Convolution is defined by Eq. 4, 5 (Terry 2004, Žára 2004). 




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m 

x,y x,y x−i,y−j i,j 

i=− m j=−m 

m 

P ⊗ Q = ∑∑ P ⋅Q 

(4) 

P is 2D image, Q is kernel 

m m m 

Px,y,z ⊗ Qx,y,z = ∑∑∑ Px −i,y−j ⋅Qi,j 

(5) 

i=− m j=− m k=−m 

P is 3D image, Q is kernel 

In presented program two thresholding filters were used. By utilization of ITK two following 

filters were included. Otsu filter based on itkOtsuThresholdImageFilter class and binary filter 

based onf itkBinaryThresholdImageFilter were used. Both of them thresholds image according to 

appropriate threshold. Whereas Otsu filter (Otsu 1979) automatically computes value of threshold 

by maximizing of variance in (Eq. 6), binary filter allows defining the user value for sensitive 

separation of structure from image background. 

2 

σ Th = p Th p Th μ Th − μ Th 

(6) 

( ) ( ) ( )( ( ) ( )) 2 

b 1 2 1 2 

p 1 (Th) is probability of first interval below threshold Th, p 2 (Th) is probability of second interval above the threshold 

Th, μ 1 resp. μ 2 is mean of the first resp. second interval 

Thresholds of binary filter can be manually defined by user or good approximation is automatically 

computed from mean value of image (Eq. 7) and image covariance (Eq. 8). Mean value of 

pixels within the selected region is computed by itk::MeanCalculator and 

itk::CovarianceCalculator classes. 

X max ,Y max ,(Z max ) 

1 

μ = 

∑ wi,j,(k) 

(7) 

Xmax ⋅Y max 

⋅(Z max 

) i,j,(k) = 1 

X max , Y max , Z max are pixel sizes in x, y, z direction 

Xmax, Y max ,(Z max ) 

( wi,j,(k) 

μ ) 

∑ 

2 

(8) 

i,j,(k) = 1 

2 

σ = − 

Thresholding 

Thresholding can be defined in two phases of image processing. First phase is just before assembling 

of 3D image from image series, where user can choose thresholding filters for elimination 

of different light measurement conditions which lead to incompatibility of colour spaces between 

images within the series and thus problematic or impossible phases of registration, segmentation 

and mesh forming. Next phase separates the structure from all colour spaces of image series. 

Contouring is made by another class (itkSimpleContourExtractorImageFilter). Objects of this 

class mask pixels of image on interface of structure and image background. Precisely, it selects 

pixels which are within the set of the structure (the last boundary). Although the class offers definition 

of radius of interest (and this way the size of kernel for convolution), only one pixel 

neighbourhood is taken into account, because of shortening of computing time. 

Meshing of segmented image by tetrahedral elements forms anisotropic mesh. For FE environments 

good approximation of structure on its boundary is important. Narrow bend around edges 

of structure is obtained by application of mean filter (itk::MeanImageFilter). It is simple convolution 

with the kernel: 




- 4 -

⎡1 1 1⎤ 

1 

Q = 

⎢ 1 1 1 

⎥ 

9 ⎢ ⎥ 

(9) 

⎢⎣ 

1 1 1 ⎥⎦ 

Meshing/tetrahedralization/cubes dividing 

Meshing is realized by vtkDelaunay3D class (Gelas 2008, Shewchuk J.R. 1998), which triangulates 

the significant points of the image and forms unstructured grid of tetrahedral elements. 

Similar approach, but not purely in ITK has been realized in project of tetrahedral mesh generation 

for medical imaging (Fedorov 2005). This work is probable one of the most important works 

in OpenSource field for quality tetrahedral mesh generation from image series. Unfortunately 

project consists of large amount of source code from various authors which leads to incompatibility 

with modern form of ITK and VTK. Code is also focused on MR images and not for series of 

separate 2D images. Big portion of code use the project PETSc which is not CMake based and lot 

of difficulties with platform dependent code makes almost impossible to generalize the code into 

the pure ITK platform independent program. 

Mesh with good quality provides implemented code of huge project MIMx. This code forms 

regular unstructured hexahedral rectilinear mesh with prescribed size of elements (Fig. 17, 18). 

Also modulus of elasticity can be computed on base of image intensity and input estimation of 

Young modulus of the structure. This part of code was developed in MIMx project and described 

in Carter 1977. 

Results and discussion 

In the project spruce wood (Picea abies (L.) Karst.) and walnut wood (Juglans Regia L.) as input 

anatomy samples were used. Spruce wood is more appropriate for initial image analysis due to 

simple structure. Walnut wood was used for validation of code robustness because of complex 

structure of wood. Application is in this phase without GUI and user has to specify parameters in 

command line for specific control. Numerous parameters allow detail control of program in all 

phases and almost in all available variables of individual object methods. 

-first N 

Number of the first image of series (it is assumed in format 

img00x.png). Usually it is 1 

-last N 

Number of the last image of series. 

-file filename 

Filename of output VTK file 

-size Sx Sy Sz 

Size of region subtracted from image. Size is defined as vector by 

three numbers in pixels. Default is full size of image. 

-origin Ox Oy Oz 

Origin for subtracted region. Origin is defined as vector by three 

numbers in pixels. Default is 0 0 0 

-filter_lower LowerIntensity Lower intensity value for binary thresholding filter. Default is 0. 

-filter_upper UpperIntensity Upper intensity value for binary thresholding filter. If no value is 

defined, then optimal value is automatically computed. 

-filter_file filename Filename for output VTK file of thresholded image. 

-filter N 

0=Otsu thresholding filter, 1=Binary thresholding filter 

-mesh_size Size 

Size of output elements (in pixels) 




- 5 -

-scale Cx Cy Cz 

Scaling coefficients. Scaling is defined as vector by three numbers. 

Default is 1 1 1 

-tetra 0|1 

0=no tetrahedrons will be created 

1=tetrahedrons are created 

-tetra_type 0|1 

0=no tetras will be created from hexahedral mesh 

1=tetras will be created from hexahedral mesh 

-reduced 0|1 

0=reduction of pixels for tetrahedralization is performed 

1=reduction is performed 

-prefiltered 0|1 

0=no prefiltering of individual input images is performed 

1=prefiltering will be realized 

-smoothed 0|1 

0=smoothing with mean filter is performed 

1=smoothing is performed 

-registered 0|1 

0=individual images are not registestered 

1=images are registered at the beginning 

-alpha N 

Size of element which is filtered out of mesh (in pixels) 

I: Command line parameters of application WOOD3D 

Program code is relatively huge (more than 1500 code lines). Partial description in the text is 

done by simplification and idealization of program code. Most of mentioned methods keeps C++ 

notation and style and should be also readable for users non skilled in programming. The following 

diagram represents the schematic flow of application for image analysis and final output of 

ANSYS APDL script (Fig. 3). Created program starts by reading of individual images (Fig. 4), 

which form automatically 3D VTK image with full colour space of each image (Fig. 5). 




- 6 -

itkImageReader 

reads individual image 

Thresholding of 2D image according to the computed threshold 

itkOtsuThresholdImageFilter × itkBinaryThresholdImageFilter 

itkAffineTransform 

registration of images 

itkImageSeriesReader 

reads serie of 2D images 

itkImageWriter 

writes prefiltered imaged 

itkRegionOfInterestImageFilter 

reads defined region of interest 

itkChangeInformationImageFilter 

spacing of image 

itkImageSeriesWriter 

writing of 3D image into the file 

Computing of the simple statistics 

itkStatistics::ScalarImageToListAdaptor 

itkStatistics::MeanCalculator mean of image intensity 

itkStatistics::CovarianceCalculator covariance of image intensity 

Computing of the threshold for binary thresholding filters Th1 = 0,Th 

2 

= μ+ 

σ 

Thresholding of 3D image according to the computed threshold 

itkOtsuThresholdImageFilter × itkBinaryThresholdImageFilter 

itkImageFileWriter 

writes thresholded 

image into the file 

Forming of contoured image object from thresholded image 

itkSimpleContourExtractorImageFilter(Radius) contourfilter 

Forming of object contourplane(Radius) from contourimage object by contourfilter 

from each plane of contourimage 

Smoothing the contoured 3D image by 

itkMeanImageFilter(Radius) 

Reducing the number of positive pixels for 

mesh tetrahedralization 

Meshing 

- rectilinear mesh 

itkMimxImageToVTKUnstructuredGridFilter 

- tetrahedralized rectilinear mesh 

vtkDelaunay3D 

- tetrahedralized mesh derived directly 

from previous step 

- unstructured grid 

Forming a mesh nodes from reduced image 

and adding mesh nodes for user defined 

mesh level (and lower) from rectilinear mesh 

Removing of bad shaped tetrahedrons 

Removing of ghost cells 

Writing the mesh into the APDL script 

(ANSYS FEM sw) 

Fig. 3 Diagram of application flow 




- 7 -

. 

Fig. 4 Input image series is formed from individual pictures. The difference in colour spaces is 

apparent. Contrast and intensity is not constant. Spruce wood on the left and walnut wood on the 

right. 

Fig. 5 3D VTK image formed from image series with detail. Spruce wood on the left and walnut 

wood on the right. 

User can process native images by thresholding without any modification. For such purpose the 

3D VTK image is used. Thresholding is realized by Otsu filter (Fig. 6) or binary filter (Fig. 7). 

Pictures demonstrates significant differences between utilization of each filter. In both cases automatic 

derivation of threshold was used. Thresholds for binary filter are defined by mean value 

and covariance of the selected region of image (Eq. 10) or can be defined manually by user. 

Th 

1 

= 0 or user defined 

N N N 

1 ⎛ 1 ⎞ 

Th 

2 

= ∑w i 

+ ∑ wi wi 

or user defined 

N 

⎜ − ∑ 

i= 1 i= 1 N 

⎟ 

⎝ 

i= 

1 ⎠ 

2 

(10) 




- 8 -

Fig. 6 3D VTK image thresholded by 

Otsu filter with detail 

Fig. 7 3D VTK image thresholded by binary 

filter with detail 

In many cases the thresholding of 3D VTK image formed from native images can produce discontinuous 

image. This effect is caused by colour spaces of individual images which are too far 

each another. As was mentioned, application offers prefiltering of input images for such case on 

user request. Prefiltering means thresholding of each image before the 3D VTK image is assembled 

together. Thresholding is done by Otsu filter (Fig. 8) or binary filter again (Fig. 9). User defines 

the filter just once for all thresholding operations made in application. Prefiltering unifies 

colour spaces in input images which results into emphasized contours of structure and improving 

of the structure continuity in third dimension (compare Fig. 6-9). 

Fig. 8 3D VTK image prefiltered 

and thresholded by Otsu filter 

with detail 

Fig. 9 3D VTK image prefiltered and 

thresholded by binary filter with detail 

Prefiltered images can be registered by sequence of successive filters and transformed for compensation 

of small errors in position and deformation. First, registration computes parameters for 

translation and rotation of successive image for optimal positioning. In second phase the optimal 




- 9 -

scale is computed. Optimization runs in 300 steps (number assure robustness for many tested 

cases). Registered images are written into transformed files with prefix tmp (Fig. 10). Output 

parameters of registration are printed in standard console. In figure with spruce anatomy samples 

the change is relatively small (up to 100 px of translation, up to 3 degrees of rotation). 

Fig. 10 3D VTK image prefiltered and thresholded 

by Otsu filter with registration 

Fig. 11 3D VTK image prefiltered with 

affine registration; green colour represents 

change (rotation, translation) after 

registration 

Prefiltered and registered image are thresholded again. In the case, prefiltering is more formal, 

just for events of residues after prefiltering and registration. Resulted 3D image shows bigger 

structure continuity (Fig. 11). Registration mainly compensates errors in image acquisition due to 

deformation of anatomy samples (swelling/shrinkage, relaxation), non-uniform cuts, small failures, 

… etc.). 

Next itk::ImageSeriesReader is initiated for reading of 

the whole native/prefiltered and/or registered image 

series. User defines the requested region of interest in 

command line. This region is extracted from filtered 

images and appropriate spacing is set. Spacing defines 

the real distance of voxels in the space. Thus, final 

mesh will be in metric space with real scale. 

After spacing the contouring process starts. Contouring 

plays key role for the following process of structure 

segmentation. Contouring selects boundaries of cell’s 

lumen (Fig. 12). In application the contour is saved 

with all points on the boundary (lumen). All other 

points are approximated and reduced for reasonable 

count of finite elements derived just on pixels from 

contour filter. Full covering of cells lumen boundary is 

realized for accurate meshing on curved edges. Thus, a 

lot of elements is created in these regions allowing FE 

Fig. 12 3D VTK contour image 

prefiltered and thresholded by 

Otsu filter with detail 

approximation of regions appropriate for multi(physical) tasks. Contouring processes the whole 

image. Nevertheless, individual plane regions are taken into account in this process and pixels 




- 10 -

forming the lumens boundary are marked for each plane separately. Contours are detected in vicinity 

of each pixels in radius of one pixel (Code 2). Processed image is written into the file. 

Registration is based on itk::ImageRegistrationMethod. It allows compute translation, rotation 

and scaling parameters for optimal images alignment (Code 1). 

registration->SetMetric( metric ); 

registration->SetOptimizer( optimizer ); 

registration->SetInterpolator( interpolator ); 

TransformType::Pointer transform = TransformType::New(); 

registration->SetTransform( transform ); 

fixedImageReader->SetFileName( fixedfilename ); 

movingImageReader->SetFileName( movingfilename ); 

registration->SetFixedImage( fixedImageReader->GetOutput() ); 

registration->SetMovingImage( movingImageReader->GetOutput() ); 

fixedImageReader->Update(); 

typedef itk::CenteredTransformInitializer< TransformType, FixedImageType, 

MovingImageType > TransformInitializerType; 

TransformInitializerType::Pointer initializer = 

TransformInitializerType::New(); 

initializer->SetTransform( transform ); 

initializer->SetFixedImage( fixedImageReader->GetOutput() ); 

initializer->SetMovingImage( movingImageReader->GetOutput() ); 

initializer->MomentsOn(); 

initializer->InitializeTransform(); 

registration->SetInitialTransformParameters( transform->GetParameters() ); 

typedef OptimizerType::ScalesType OptimizerScalesType; 

OptimizerScalesType optimizerScales( transform->GetNumberOfParameters() ); 

optimizerScales = translationScale; 

optimizer->SetScales( optimizerScales ); 

optimizer->SetMaximumStepLength( steplength ); 

optimizer->SetNumberOfIterations( maxNumberOfIterations ); 

optimizer->MinimizeOn(); 

registration->StartRegistration(); 

Code 1: Registration of image series. Moving image is consequent image which is registered 

according to previous (fixed) image. 




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for (int i=0; iSetInput( contourimage); 

plane->SetRegionOfInterest( Region ); 

contour->SetInput(plane->GetOutput()); 

contour->SetRadius(1); 

contour->Update(); 

itk::ImageRegionIterator it(contour->GetOutput(), Region); 

for ( ; !it.IsAtEnd(); ++it) 

{ 

pindex = it.GetIndex(); 

pvalue=contour->GetOutput()->GetPixel(pindex); 

contour->GetOutput()->TransformIndexToPhysicalPoint(pindex,cpoint); 

cpoint[2]=i; 

isvalid=contourimage->TransformPhysicalPointToIndex(cpoint,ppindex); 

ppindex[2]=i; 

if (!isvalid) std::cout InsertNextPoint(vtk_point); 

mesh_grid_size = max_grid_size/2^i; 

} 

Code 3: Adding grid points into points of mesh 




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for ( i = 1; i < mesh_levels = (log(max_grid_size)/log(2)); i++ ) 

if ( pixel_value == is_positive_in_tresholded_image && 

pixel_value == is_nonzero_in_meanfilter && 

pixel_position % mesh_grid_size == 0) 

{ 

mesh_image -> SetPixel(pixel,1); 

vtk_point = pixel_position; 

points -> InsertNextPoint(vtk_point); 

mesh_grid_size = max_grid_size/2^i; 

} 

Code 4: Adding grid points near the edge of structure into points of mesh 

Fig. 14 3D VTK contour image prefiltered 

and thresholded by Otsu filter with 

detail. Mesh points added. 

Fig. 14 Tetrahedralized mesh (48k elements) 

without tesssellation with prefiltering 

and registering 

Points formed by the way mentioned above are triangulated by Delaunay algorithm with object of 

class vtkDelaunay3D (Fig. 14). The appropriate parameter alpha has to be defined for removing 

of elements with size bigger than alpha. 

vtkDelaunay3D* tets=vtkDelaunay3D::New(); 

tets->AddInput(points); 

if ( user_defined_alpha == 0) 

alpha=max_grid_size; 

tets->SetAlpha( alpha); 

tets->SetTolerance(1.0); 

tets->Update(); 

Code 5: Tetrahedralization of selected points 




- 13 -

Above objects generates a lot of bad shaped elements which are not appropriate for FE analysis. 

Therefore the mesh is tessellated by objects of vtkTessellatorFilter class. This class works directly 

on vtkUnstructuredGrid class and generates the same class on the output. It allowed simple 

implementation of filter for grid tessellation. Disadvantage of this old and temporary class (according 

to VTK Documentation project statement) is slow triangulation based on Delaunay 

method. As a possibility appears in vtkGenericCellTessellator and vtkOrderedTriangulator 

(Shroeder 2004) classes which offer very quick and parallelized/threaded algorithm for triangulation 

of reduced voxels together with definition of error metrics for finite elements which have to 

be tessellated. 

Fig. 16 Deformation field on tetrahedralized 

mesh. Source image was registered 

and prefiltered. 

Fig. 15 Deformation field on hexahedral 

mesh. Source image was registered and 

prefiltered. 

As an alternative to Delaunay tetrahedralization the MIMx code for hexahedral mesh generation 

was also included. Formed mesh has good quality in comparison with Delaunay triangulation 

mainly due to regular cells which approximate the image. Cells are very small and are able to 

describe very thin geometries (thin cell walls, small sized lumens). It is apparent mainly for 

rough grids of tetrahedralized mesh and big spaced image slices where lumens can collapse together 

(compare Fig. 14 and Fig. 18. On the contrary hexahedral mesh forms discontinuous 

boundaries on cell walls. Sharp rectangular boundaries of hexahedral mesh can make difficult the 

following FE analysis. Edges and points on these boundaries acts as singular points and negatively 

influence accuracy of solution (compare Fig. 15 where several singular areas occur with 

tetrahedralized Fig. 16). Advantage of MIMx code is also support of threads which accelerates 

run of application on multicored CPUs (Code 6). 




- 14 -

imageToHexMeshFilter->SetInput( meanfilter->GetOutput() ); 

imageToHexMeshFilter->SetMaskImage(filtered_image); 

imageToHexMeshFilter->SetMeshIndexOffset( 1 ); 

imageToHexMeshFilter->SetComputeMeshPropertiesOn( ); 

imageToHexMeshFilter->SetComputeMeshNodeNumberingOn( ); 

imageToHexMeshFilter->SetMeshResampleSize( mesh_size); 

imageToHexMeshFilter->SetNumberOfThreads(n_core*n_cpu); 

imageToHexMeshFilter->SetImageThreshold( threshold ); 

Code 6: MIMx code for hexahedral mesh from image 

Third implemented code for meshing of image voxels forms unstructured grid with anisotropic 

irregular mesh similar to tetra mesh, but it is formed by divided cubes as in previous code. The 

mesh is created by declared and modified octree algorithm. Unfortunately the grid can not be 

used simply in the FE environments such as ANSYS which demand the structured and well connected 

mesh. This output can be used for geometry entities just in the moment. Several other 

tools (e.g. ICEM CFD) are able to form the FE mesh from geometry created by this way. This 

requires extensive amount of time and computing resources nowadays and is not yet in appropriate 

form for common utilization. 

Fig. 17 Unstructured hexahedral mesh generated 

by implemented MIMx code (detail). 

Source image was not registered and prefiltered. 

Fig. 18 Unstructured hexahedral mesh (25k 

elements). Source image was registered and 

prefiltered. 




- 15 -

for (long i=0; (i

Fig. 19 Stress field on FE model formed by MIMx hexahedral mesh and loaded by compression 

in transverse direction. Source image was not registered and prefiltered. 

Code environment, compiling and testing 

Code was written in KDevelop and Microsoft Visual C++ IDE GUI environment. Both Linux 

and MS Windows platform were used for compiling and testing of code. Multiplatform code is 

based on project CMake (Martin 2005). Classes of Insight toolkit (ITK) (Yoo et al. 2002) and 

Visual toolkit (VTK) projects were used for assembling the code. Very useful source for our 

work was book Ibáñez 2005 which provided a lot of basic and advantage code for image processing 

and Prata 2004 which was useful for implementation into C++ code. Final binary file is small 

and standalone without any linked libraries. Processing of images for tetrahedral meshes with 

prefiltration and registration takes app. 1.5 hour. Whereas the most time consuming part is registration 

of full images (1 hour) and tetrahedralization (30 minutes). 

CONCLUSION 

The paper presents new original complex tool for image processing which process individual 

images from anatomy samples and forms 3D structure appropriate for quantitative and qualitative 

analysis. Important supplement of application are several implemented codes for derivation of 

finite element mesh from image voxels. Code is robust for anatomy samples prepared in high 

quality. As was proved the application generates mesh with sufficient quality for FE solver, 

namely ANSYS environment. Due to opened GPL license the code offers to other programmers 

possibility to create own code for its specific FE environment (ABAQUS, COMSOL, 

NASTRAN, etc.). Application is still under intensive development. Introduced features are first 

and most important results of this huge and complicated project. 

Created application offers a lot of opportunities for further research in many different scopes. 

Enumeration of geometry of wood structure allows e.g. revealing of microstructure fractal characteristics 

such as Hausdorff dimension for crack analysis on such low scale. It is significant 

challenge to extend analysis in Koňas P. et al. 2008 which tested correlation between fractal dimension 

of wood anatomy structure and impact energy on 2D space and continue in analysis into 

3D space. Analysis of fractal characteristics in full 3D space can finally found causes of failure 

initiation in wood and it also can reveal the estimators of physical and mechanical properties 

from these specific geometrical properties. 

Acknowledgements 

The Research project GP106/06/P363 Homogenization of material properties of wood for tasks 

from mechanics and thermodynamics (Czech Science Foundation) and Institutional research plan 

MSM6215648902 – Forest and Wood: the support of functionally integrated forest management 

and use of wood as a renewable raw material (2005-2010, Ministry of Education, Youth and 

Sport, Czech Republic) supported this work. This work benefited from the use of the Insight Segmentation 

and Registration Toolkit (ITK), open source software developed as an initiative of the 

U.S. National Library of Medicine. 




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REFERENCES 

[1] L. Ibáñez, W. Schroeder, L. Ng, J. Cates, The ITK Software Guide – Second Edition Updated 

for ITK version 2.4, Kitware, Inc. ISBN 1-930934-15-7, pages 804, 2005 

[2] D. R. Carter, W. C. Hayes, The compressive behavior of bone as a two-phase porous structure, 

J of Bone Joint Surgery, 59A: 954-62, 1977 

[3] H. E. Cline, W. E. Lorensen, S. Ludke, C. R. Crawford, and B. C. Teeter, Two Algorithms for 

the Three-Dimensional Reconstruction of Tomograms. Medical Physics, 15(3):320-327, 1986 

[4] CMake: Cross Platform Make, www.cmake.org 

[5] B. Delaunay, Sur la sphère vide. A la memoire de Georges Voronoi. Izv. Akad. Nauk SSSR, 

Otdelenie Matematicheskih i Estestvennyh Nauk, 7 :793-800, 1934 

[6] A. Fedorov, N. Chrisochoides, R. Kikinis, S. Warfield, Tetrahedral mesh generation for 

medical imaging, http://hdl.handle.net/1926/35, 2005 

[7] P. M. Finnigan et al., United States Patent 5345490, Method and apparatus for converting 

computed tomography (CT) data into finite element models, 10/1994 

[8] A. Gelas, A. Gouaillard, S. Megason, Triangular Meshes Dalunay Conforming Filter, 

http://hdl.handle.net/1926/1489, 2008 

[9] N. M. Grosland, T. D. Brown, A voxel-based formulation for contact finite element analysis. 

Comput Methods Biomech Biomed Engin. Feb;5(1):21-32, 2002 

[10] E. Ives, A Guide to Wood Microtomy: Making quality microslides of wood sections. Suffolk, 

UK: Publishing Office Ernie Ives, pages 114, 2001. 

[11] J. B. Johnson, United States Patent 5883629, Recursive and anisotropic method and article 

of manufacture for generating a balanced computer representation of an object, 3/1999 

[12] P. Koňas et al., Study of correlation between the fractal dimension of wood anatomy structure 

and impact energy, European Journal of Mechanics A/Solids (2008), 

doi:10.1016/j.euromechsol.2008.07.005 

[13] K. Martin, B. Hoffman, Mastering CMake – A Cross-Platform Build System, Kitware, Inc., 

USA, pages 250, 2005 

[14] Musculoskeletal Imaging, Modelling and Experimentation (MIMX), Center for Computer 

Aided Design, www.ccad.uiowa.edu/mimx/, 2007 

[15] N. Molino, R. Bridson, J. Teran, R. Fedkiw, A crystalline, red green strategy for meshing 

highly deformable objects with tetrahedra. In: Proceedings of the 12 th International Meshing 

Roundtable. 103-114, 2003 

[16] PETSc (2005): Portable, extensible toolkit for scientific computation. http://wwwunix.mcs.anl.gov/petsc/petsc-2/ 

[17] N. Otsu, A threshold selection method from grey-level histograms, IEEE Trans. Sys., Man., 

Cyber. 9, pp. 62-66, 1979 

[18] S. Prata, Mistroství v C++, Computer Press, Brno, pages 1006, 2004 

[19] R. Schneiders, R. Schindler and F. Weiler, Octree-based Generation of Hexahedral Element 

Meshes, Sandia National Laboratories, pp.2005-216, 1996 

[20] J. R. Shewchuk, Tetrahedral mesh generation by delaunay refinement. In Proceedings of the 

4 th Annual Symposium on Computational Geometry, Association for Computational Machinery, 

pages 86-95, 1998 

[21] W. J. Schroeder, B. Geveci, M. Malaterre. Compatible Triangulations of Spatial Decompositions. 

In Proceedings of Visualization 2004, IEEE Press October 2004 

[22] The Insight Segmentation and Registration Toolkit (ITK), www.itk.org 




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[23] S. S. Usami et al., United States Patent 7372460 B2, Method and program for generating 

volume data from boundary representation data, 5/2008 

[24] Vavrčík, H. – Gryc, V. Metodika výroby mikroskopických preparátů ze vzorků dřeva. Acta 

Universitatis Agriculturae et Silviculturae Mendelianae Brunensis. 2004. č. 4, pp. 169-175. 

[25] VTK Documentation Project (VTK 5.1.0 Documentation), www.vtk.org 

[26] M. A. Yerry, M. S. Shephard, Automatic Three-Dimensional Mesh Generation By The 

Modified Octree Technique, International Journal For Numerical Methods in Engineering, John 

Wiley, Num 20, pp. 1965-1990, 1984 

[27] T. S. Yoo, M. J. Ackerman, W. E. Lorensen, W. Schroeder, V. Chalana, S. Aylward, 

D. Metaxes, R. Whitaker, Engineering and Algorithm Design for an Image Processing API: A 

Technical Report on ITK – The Insight Toolkit. In Proc. Of Medicine Meets Virtual Reality, J. 

Westwood, ed., IOS Press Amsterdam, pp. 586-592, 2002 

[28] T. S. Yoo, Insight into Images – Principles and Practice for Segmentation, Registration, and 

Image Analysis, A K Peters, Ltd. Wellesey, pages 393, 2004 

[29] J. Žára, B. Beneš, J. Sochor a P. Felkel, Moderní počítačová grafika, Computer Press, Brno, 

pages 609, 2004 




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