[ITK] [ITK-users] Euler Characteristic of "filled" objects
Dr. Roman Grothausmann
grothausmann.roman at mh-hannover.de
Mon Apr 28 07:51:51 EDT 2014
Dear mailing list members,
I'd like to calculate the Euler Characteristic
(http://en.wikipedia.org/wiki/Euler_characteristic) of "filled" objects
(represented in binary 3D images).
Using vtkThreshold I get a vtkUnstructuredGrid containing vtkPoints and vtkCells
of type VTK_Voxel.
To calculate the Euler Characteristic Xi of the "unfilled" objects I'd do:
xiu= numPoints - numEdges + numFaces;
(all values based on the output of vtkGeometryFilter for with numFaces==number
of 2D cells)
(e.g. xiu for a unfilled Cube/Voxel:
8 verts - 12 edges + 6 faces
= 2 == 1 connected_Component - 0 handles + 1 cavity)
To calculate the Euler Characteristic Xi of the "unfilled" objects I'd do:
xif= numPoints - numEdges + numFaces - numVoxel;
(all values based on the output of vtkThreshold directly)
(e.g. xif for a filled Cube/Voxel:
8 verts - 12 edges + 6 faces - 1 volumeElement
= 1 == 1 connected_Component - 0 handles + 0 cavity)
Getting the number of Edges is easily done with vtkExtractEdges but how can I
get the number of Faces if no face-cells exist in the output of vtkThreshold?
Is there kind of vtkExtractFaces, which (unlike vtkGeometryFilter) extracts also
the faces of 3D-cells fully contained in the inside of the vtkUnstructuredGrid?
Do I have to create the 6 faces for each VTK_Voxel manually?
And if so, how can I prevent the creation of duplicate faces or merge these in a
second step?
Or is there a far easier way to calculate the Euler Characteristic of "filled"
objects represented in binary 3D images?
In another try I used ITK with itkQuadEdgeMesh, which does support Orientations
but seemingly no 3D cells, so I guess it won't be easy to get the number of
volume elements there for the calculation of xif.
Any help or hints are very much appreciated
Roman
--
Dr. Roman Grothausmann
Tomographie und Digitale Bildverarbeitung
Tomography and Digital Image Analysis
Institut für Funktionelle und Angewandte Anatomie, OE 4120
Medizinische Hochschule Hannover
Carl-Neuberg-Str. 1
D-30625 Hannover
Tel. +49 511 532-9574
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