This plug-in computes spatial moments up to the 4th order for the
selected (rectangular) ROI, along with some parameters derived from them.
Results are displayed in the main ImageJ window, in addition
to those set for ImageJ’s Measure command ‘Analyze|Set Measurements
To export to a text file, use ‘File|Save As|Measurements’.
or right-click on the table and select ‘Save As’
Note that spatial moments are a very simple and powerful way to describe the
spatial distribution of values, provided they have a sufficiently strong
central tendency, that is, a tendency to cluster around some particular
value. This implies that “background” pixel values (e.g. zones where the
quantity of interest, such as concentration, is zero), are small.
Conversely, zones of high concentration (density, etc.) should also have a
high pixel values. This can lead to meaningless results, for example, in the
case of uncalibrated images, where (white) background pixels are equal to 255
(for an 8-bit greyscale image).
** Interpretation of spatial moments **
* order 0 = TOTAL MASS [units: concentration, density, etc.]
* order 1 = location of CENTRE OF MASS in x and y from 0,0 [units: L]
* order 2 = VARIANCE around centroid in x and y [units: L^2]
* order 3 = coeff. of SKEWNESS (symmetry) in x and y [units: n/a]
--> =0 : SYMMETRIC distribution
--> <0 : Distribution asymmetric to the LEFT
(tail extends left of centre of mass)
--> >0 : Distribution asymmetric to the RIGHT
(tail extends right of centre of mass)
* order 4 = KURTOSIS (flatness) in x and y [units: n/a]
--> =0 : Gaussian (NORMAL) distribution
--> <0 : Distribution FLATTER than normal
--> >0 : Distribution MORE PEAKED than normal
--> <-1.2: BIMODAL (or multimodal) distribution
** Parameters derived from 2nd moments ** (from Awcock (1995)
"Applied Image Processing")
* ELONGATION (ECCENTRICITY) = Ratio of longest to shortest
distance vectors rom the object's centroid to its boundaries
* ORIENTATION = For elongated objects, describes the
orientation (in degrees) of the "long" direction with
respect to horizontal (x axis)
Analyze/Set Measurements dialog in ImageJ 1.34l or later, which has
“Skewness” and “Kurtosis” check boxes.
Authors: Hemerson Pistori (pistori at ec.ucdb.br) and Eduardo Rocha Costa (eduardo.rocha at poli.usp.br) History: 2002/07/29: First version 2006/01/18: Can find circles with arbitrary radius 2008/10/30:
Author: Paul Baggethun, an engineer in Pittsburgh, PA History: 2002/05/01: First version 2009/05/14: Works with batch mode macros Source: Radial_Profile.java Installation: Download Radial_Profile.class to the