Operators/Features/MorphologyAnalyzer2D
The MorphologyAnalyer2D operator implements a large collection of features to characterize the shape of image regions.
Name of Plugin/Operator
de.unihalle.informatik.MiToBo.features.MorphologyAnalyzer2D
Latest News
The MorphologyAnalyzer2D is currently under active development. Some of the features already documented below will become available in the next version 1.8.6 of MiToBo which is to be released soon.
Main features
 extracts a large collection of features to characterize region shape and morphology
 handles different types of input, i.e., label images and ImageJ ROIs
 optionally provides visualization of extracted features
Usage
To run the MorphologyAnalyzer2D perform the following steps:
 install MiToBo by following the instructions on the Installation page
 run MiToBo and start the operator runner by selecting the menu item MiToBo Runner from Plugins > MiToBo
 in the selection menu navigate to 'de.unihalle.informatik.MiToBo.features' and select the operator MorphologyAnalyzer2D
This will bring up the operator window of the MorphologyAnalyzer2D.
Input data
The operator supports two different types of input data:
 label image: an image where for each region the pixels are expected to be uniquely labeled, i.e. all have the same intensity value; all pixels being labeled with 0 are treated as background
 regions (in ImageJ ROI format): here regions can directly be imported from ImageJ's ROI manager or be read from ROI files in specific formats from disk; also manual input of region data is supported
Calibration information
Many of the features refer to measuring lengths or areas of region entities. The units to be used for these measurements can freely be configured.
If appropriate calibration data is available from the given input data, e.g., as meta information in a label image, this data is automatically used and displayed.
But, the user can overwrite the calibration by manually specifiying the size of a pixel in the desired units.
E.g., with regard to microscopy images a common unit are microns and a proper calibration requires to provide information on the size of a pixel in microns.
Important note:
The operator always assumes square pixels, i.e. the pixel lengths in x and y dimension are assumed to be equal.
If this does not hold for an image or ROI data some of the feature values will be incorrect!
Lengths are first measured in pixels by the operator and areas in square pixels. Subsequently the numbers are then converted to the specified units, e.g., converted to microns or square microns based on the given size of a pixel.
Configuration of features to extract
The configuration window allows to select and configure the set of features to be extracted:
Name of Option  Description 
Calculate area  Activates area feature <math>\scriptstyle A(R)</math> which is measured in terms of the number of pixels in a region. 
Calculate perimeter  Activates perimeter feature <math>\scriptstyle P(R)</math> which is calculated from the 8neighborhood contour of the region; the contour is extracted and then traced pixel by pixel where each horizontal or vertical step yields a distance of 1 and each diagonal step a distance of <math>\scriptstyle \sqrt{2}</math>; the result for the region perimeter is given by the sum of all distances between pairs of neighboring pixels along the contour. 
Calculate length and width  Activates calculation of length <math>\scriptstyle L(R)</math> and width <math>\scriptstyle W(R)</math> of a region. The length and width of a region can be interpreted as twice the lengths of the major and minor axes of an ellipse fit to the region pixels. They are calculated as follows: <math>\scriptstyle L(R) = 2 \cdot \sqrt{\frac{2\cdot \left( \mu_{2,0} + \mu_{0,2} + \sqrt{ (\mu_{2,0}\mu_{0,2})^2+4\mu_{1,1}^2}\right)}{\mu_{0,0}}}</math> and <math>\scriptstyle W(R) = 2 \cdot \sqrt{\frac{2\cdot \left( \mu_{2,0} + \mu_{0,2}  \sqrt{(\mu_{2,0}\mu_{0,2})^2+4\mu_{1,1}^2}\right)}{\mu_{0,0}}}</math> The <math>\scriptstyle \mu_{k,l}</math> are central moments, <math>\scriptstyle \mu_{k,l} = \sum_{(x,y) \in R} (x \bar{x})^k (y\bar{y})^l</math>, with <math>\scriptstyle (\bar{x},\bar{y})</math> being the centroid of the region. For further details refer to R. Prokop/A. Reeves, A Survey of MomentBased Techniques for Unoccluded Object Representation and Recognition, Graphical Models and Image Processing (CVGIP), pp. 438460, 1992. 
Calculate circularity  Activates the circularity feature <math>\scriptstyle C(R)</math> which is calculated from region area and perimeter as follows: <math>\scriptstyle C(R) = \frac{4 \pi A(R)}{P(R)^2}</math>. 
Calculate eccentricity  Activates the eccentricity feature <math>\scriptstyle E(R)</math> which is calculated based on region moments as follows: <math>\scriptstyle E(R) = \frac{(\mu_{2,0}\mu_{0,2})^2+4\mu_{1,1}^2}{\mu_{2,0} + \mu_{0,2}}</math>. 
Calculate solidity  Activates the solidity feature which is defined as <math>\scriptstyle S(R) = \frac{A(R)}{A_{CH}(R)}</math> where <math>\scriptstyle A_{CH}</math> is the area of the convex hull of the region. 
Calculate margin roughness  Activates the margin roughness feature which quantifies the deviation of the average curvature of the region contour compared to a perfect circle.
For further details refer to T. McLellan, J. Endler, The Relative Success of Some Methods for Measuring and Describing the Shape of Complex Objects, Systematic Biology, Vol. 47, No. 2, pp. 264281, June 1998. 
Analyze protrusions and indentations  Activates the analysis of convex sections (indentations) and concave sections (protrusions) along a contour. This analysis results in 12 features:

Calculate skeleton branch features  Activates extraction of various features from the skeleton of a region. This analysis results in 6 features:

Calculate concavity information  Activates the extraction of two features based on a local concavity measure:

Calculate convex hull measures  Activates the extraction of some features based on the convex hull of a region:

Fractional digits  allows to specify the accuracy in calculating features, i.e. the number of decimal places used in the result tables 
Show curvature analysis info image?  if enabled, an additional result image is generated visualizing features based on curvature 
Show skeleton analysis info image?  if enabled, an additional result image is generated visualizing skeleton features 
Verbose  turns on output of additional debug messages; the messages are shown in the console 