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### Highlights from Geometric measures in 2D/3D images

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# Geometric measures in 2D/3D images

09 Nov 2011 (Updated )

Measure of geometric parameters in 2D or 3D images (surface area, perimeter, Euler Number...)

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Description

Contains various functions for measuring or estimating geometric quantities from 2D or 3D images.

Parameters available for 2D images are:
* the area (number of pixels)
* the perimeter (based on Crofton formula)
* the(2D) Euler Number

Parameters available for 3D images are:
* the volume,
* the surface area (measured using the Crofton formula),
* the surface area of the interface between two labels
* the mean breadth (also known as integral of mean curvature),
* the (3D) Euler Number

Most functions work both for binary and label images. It is possible to specify options (connectivity for Euler Number, number of directions for perimeter or surface area), as well as image resolution in each direction. For some parameters, it is also possible to estimate the density with respect to image area or volume.

Example 1: measure perimeter in 2D label image
p = imPerimeter(lbl)
p =
184.8668 154.9495 185.1921 267.1690 187.3183 179.5038 182.7406 180.8445 155.5049 155.5049

Example 2: measure surface area in 3D binary image
bin = imclose(img>0, ones([5 5 3]));
S = imSurface(bin, [1 1 2.5]) % specify resolution
ans =
2.7291e+004

Required Products Image Processing Toolbox
MATLAB release MATLAB 7.9 (R2009b)
Other requirements Can be used without image processing toolbox with slight modifications of sources (it is only used to accelerate processing of label images).
05 Mar 2014

Hi Sara,
For 3D objects you can compute surface area or volume using following code:
surf = imSurface(BIN); vol = imVolume(BIN);
(assuming BIN is a logical array containing the binarisation of the structure).

You can specify resolution as a 1-by-3 row vector containing size of voxel in x, y and z directions. Ex:
surf = imSurface(BIN, [2.5 2.5 5.2]);

04 Mar 2014

hi , may you give the complite code for measuring 3D size of the object located in calibrated space please ? any one

12 Mar 2012

It helps me for feature Extraction from Handwritten Characters. Thank you Devid.

25 Nov 2011

Hi Sven,
I have a code for computing inertia ellipsoid of a set of points. I can adapt it easily to compute inertia ellipsoid of a binary image. I try to package it and submit it soon !

23 Nov 2011

Hi David, the ability to specify image resolution is a big plus. Nice work. One thing that I find is that I wish the regular IP "Orientation" and "Majory/MinorAxis" statistics could be implemented for 3D. For instance, from a 3D mask I generally want to know "is this a long thin blob or a more rounded blob". Basically, the moments of inertia of the blob would be hugely helpful. Any plans to implement this?