Software

Disclaimer: The software in these pages is experimental. Use these plugins at your own risk. Although I have made every effort to make sure that they run as intended, there may be bugs and unexpected behaviour in instances that I have not envisaged. Please send any comments, problems or improvements to . Copyright notice: Please check the copyright notices in the source code of each plugin. Some of the plugins are modifications of earlier versions written by other authors and therefore their original copyright notices apply. Please respect the original authors authorship notices. If no specific copyright notice is included, then consider the plugin as free software: you can redistribute it and/or modify it under the terms of the GNU General Public license as published by the Free Software Foundation; either version 2 of the license, or (at your option) any later version. These programs are distributed in the hope that they will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with the programs; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

IsoPhotContour2 (java & class files) Takes a greyscale image and creates a new image [called IsoPhot] with up to 8 contour lines in the grey scale range. The contour lines can be drawn in different selected colours and depth levels. There is an option to draw the contour lines on a white or on a black background (rather than the greyscale data). There is also an option to convert the image to 8 bit colour image when exiting [Cancel] the plugin, otherwise the result is an 8 bit RGB image.

Blend (java & class files) Blends (linearly) two greyscale or RGB images with a chosen mixing ratio.

List_LUTs and LUTs plugins. Files and examples can be found here.

Align_4 (java & class files) This plugin allows manual alignment (movements in the x and y directions) up to 4 images. Supports transparency of the active image and selection of fiducial points (an origin and a target) for easy alignment. The plugin may be useful to build mosaics of smaller images.

Align_RGB_planes (java & class files) This plugin allows to shift (move in the x and y directions) stretch and rotate the red green and blue planes in an RGB image. Includes a macro to resize images so they are not affected by the cropping due to the rotation. Thanks to Leon Espinosa for suggesting the modification to log the net movement of the planes.

Align_Slice (java & class files) This plugin allows to manually shift (move in the x and y directions) stretch and rotate a particular slice in an image stack.

Threshold_Colour ( jar file includes source ) (v1.7, requires ImageJ 1.37e) This plugin (a modification of Bob Dougherty's BandPass2 filter) allows to threshold a colour RGB images in the HSB, RGB, CIE Lab and YUV spaces. It suports extracting the range of HSB, RGB, CIE Lab or YUV values from a sample ROI (any type). Extract the files from the zip archive and put them somewhere in the plugins directory (or subdirectory). The Threshold_Colour entry will appear in the Plugins hierarchy, depending of the subdirectory which the plugin is copied to (I suggest the name "Segmentation" to keep all thresholding plugins).

New! Version 1.7 has a new [Macro] button that generates a macro and sends it to the Recorder window (if active) based on the current plugin settings. The zip file also includes RGB2YUV and RGB2Lab plugins which are necessary for that macro (note that these plugins convert an RGB image to YUV and CIE Lab colour spaces but with values mapped into an 8-bit space).

Anaglyph (java & class files) Creates colour or greyscale, red-cyan or red-green anaglyphs, stereo pairs (crossed view stereo pairs) and depth-map images from the depth data and focused image generated with the extended depth of focus plugin. The Anaglyph plugin expects both the "Topology" and "Output" images to be open (they hold the "topographical map" data and the "on focus" data). For Topology images created using other programmes, they can be 8 or 32 bits, but they should not be re-scaled (i.e. depth plane pixel values should be contiguous in the grey scale and start a 0). Because it cannot be known in advance the acquisition direction of the Z sequence, it may be necessary to invert the view sides when checking the red-cyan anaglyph. The plugin has been tested with only a small number of slices (6~20), so please report any problems.

Colour_Deconvolution (java & class files) This plugin implements stain separation using Ruifrok & Johnston's colour deconvolution method described in [1]. Details and examples can be found here.

ThreePointCircularROI (java & class files) This plugin creates a circular ROI based on 3 user selected points on an image. The log window reports the coordinates of the centre of the circle and its radius. Co-linear points (that define an impossible circle) return a radius of -1.

Colour_Correct (java & class files) This plugin corrects the colours of an image by first subtracting the mean RGB values of a number of selected points considered to be 'black' and then subtracts the background by performing the ratio of the image and the mean RGB values of a number of points considered to be 'white' minus the 'black'. It does not correct for uneven illumination. The procedure is:

image = [(original-black)/(white-black)]*255.

Convex_Hull_Plus (java & class files) This plugin calculates the convex hull and the minimum bounding circle of a binary set (formed by white or black particles).
The Convex Hull is the smallest convex polygon that contains the set. The plugin uses the 'wrapping around' (Graham scan) algorithm.
The Minimum Bounding Circle is the smallest circle that contains the set. An algorithm was modified from Xavier Draye's posting to the ImageJ mailing list. I implemented so it does the calculations based on the convex hull points rather than the whole set (as the points that define the Minimum Bounding Circle must be in the Convex Hull). This should be speed up the computation. Please see the source code for details.
The plugin can display any of the above as a selection or draw them on the image. The plugin also displays in the Log window: the number of points in the Convex Hull, the length of the Convex Hull, the centre coordinates and radius of the Minimal Bounding Circle.
Version 1.1 returns these values in floating point format.
Version 1.2 fixes a bug in the Minimal Bounding Circle routine.

Results_Histogram (java & class files) This plugin creates a histogram from a selected column of the Results Table data. Note that not everything that is shown in the Results window is necessarily in the Results Table. Incorporated into ImageJ 1.35g as the Analyze>Distribution... command.

IJ_Robot (java & class files) This plugin calls the Robot Java class. The purpose of the plugin is to allow the macro language to control other programs via clicking and key presses.
When running the plugin one must specify an 'order' to the robot and some parameters (not all orders require all the parameters).

Move: moves the mouse to a particular position (x, y) on the screen.

[Left|Middle|Right]_Click: Clicks the mouse at a given (x, y) postion with the chose button.

Delay: this is the time in milliseconds that the button is down during a click.

[Left|Middle|Right]_Down: presses the chosen button at the current position (this order does not read the x, y coordinates).

[Left|Middle|Right]_Up: releases the chosen button at the current position (this order does not read the x, y coordinates).

KeyPress: this order will emulate typing the entered string, but will first Click (at the current position), so the cursor is guaranteed to focus in an entry box (maybe this click is not required, please send feedback or suggestions).
KeyPress currently supports the following key presses: 0-9 a-z A-Z space /.,-
To emulate the [enter] key, type the exclamation mark '!'. Other characters are converted to '.'
Note that in Mac OSX with an AZERTY keyboard, the typed string does not get interpreted correctly. Be also aware that some OS do not support some key presses.

GetPixel: reports to the Log window the r,g,b values of the pixel at the specified postion (requires x, y coordinates). It will also return the Width and Height of the screen, as well as the coordinates of the pixel.

CaptureScreen: this is similar to the IJ function Plugins>Utilities>Capture Screen.

A handy way to find the target coordinates is to first grab the screen (which opens as an image in IJ) and check the coordinates with the mouse in IJ (reported in the status bar).

Important!

1. Be very careful with this plugin. It is really easy to end up clicking in unintended places with undesired results. You have been warned!
2. It may be necessary to increase the delay time for clicking orders depending on what is needed to be done and the response time of the target program.
3. It may be also necessary to slow down the macro calls to this plugin between orders by using the macro command: wait(time_in_milliseconds). For instance if you are grabbing an image with an external programme, the grab function may not be available while the snapshot is being taken.

Morphological Operators for ImageJ

BinaryConditionalDilate_.class
This plugin dilates (3x3 neighbourhood, 8-connected) particlesin an image (called seed) inside another image (called mask). The procedure can be applied n of times, or until idempotence if n = -1. In that case the procedure becomes is the same as BinaryReconstruction.

BinaryConditionalErode_.class
This plugin erodes (3x3 neighbourhood, 8-connected) particles in an image (called seed) except what is masked in another image (called mask) (i.e. the mask "protects" what should not be eroded). it can be applied n times, or, until idempotence if n = -1.

BinaryConnectivity_.class
Returns the number of connected pixels (+1) to each foreground pixel (8 neighbours): background = 0, single pixel = 1, end of a line = 2, bifurcations = 3, triple points = 4, etc. Brightness/Contrast must be adjusted to see the result.

BinaryDilate_.class
This plugin performs a 3x3 8-neighbour Binary Dilation of a binary image. The differences with the built in Dilation in ImageJ are:

• It checks that the image is binary [0] & [255]
• Processes all pixels in the image (ImageJ leaves the borders without processing).
• Supports "coefficients" (0-7). This is a logical constrain of the operation to locations where the number of neighbouring pixels in the opposite state is the coefficient: Classical dilation (0), Filling of single pixels holes (7), Filling of small crack lines (6), Filling of (some) irregular holes (5). See reference [2] for further details.
• Can be applied n times without using SetIterations. Use -1 for dilation until the image is idempotent (no more changes).
• BinaryDilateTest.txt is a macro that shows the effect of the different coefficients.

BinaryDilateNoMerge4_.class
BinaryDilateNoMerge8_.class
These plugins perform a conditional binary dilation of a binary image (without merging particles together). The results are similar to a binary watershed transform of the background, partitioning it into areas of influence of the particles. Dilations are done with 4 or 8 pixel structuring elements respectively. The number of iterations can be set. Use -1 for dilation until idempotence.
Very slow, maybe there are better algorithms, but slow seems better than nothing...
If you need to dilate without merging until idempotence, then use the macro Influence_Zones.txt described below.

BinaryErode_.class
This plugin performs a 3x3 8-neighbour Binary Erosion of a binary image.
The differences with the built in Erosion in ImageJ are:

• Processes all pixels in the image (ImageJ leaves the borders without processing)
• Supports "coefficients" (0-7). This is a logical constrain of the operation to locations where the number of opposite state neighbours is the coefficient: Classical erosion (0), Removal of single pixels (7), Pruning of 8-connected lines (6), Removal of (some) irregular particles (5). See reference [2] for further details.
• Can be applied n times without using SetIterations. Use -1 for erosion until the image is idempotent (no more changes).
  
  
• BinaryErodeTest.txt is a macro that shows the effect of the different coefficients.
• BinaryPrune.txt is a macro that prunes all the branches of a binary skeleton, leaving only the closed loops. See also PruneAll.txt for another pruning method.

BinaryFill_.class
This plugin fills holes in 8-connected particles (and also in child-particles) of a binary image. This function was incorporated in ImageJ v.1.31o (Process->Binary->Fill holes).

• Fill_Border_Holes.txt
  Fills holes including those touching the borders of the image This cannot be done with the "Fill Holes" command alone. Holes are assumed to be not only the traditional 4-connected background elements, but also those that touch the image borders, but extending no more than 2 contiguous borders (i.e. touching one border or a corner).
• Hole_Counter.txt
  Counts the number of particles, holes and Euler number of a binary image (with white particles on a black background). The Euler number is the number of particles minus the number of holes and it is a measure of the topology of the image. (Works only for white particles on a black background).
• FillHolesReconstruct.txt
  Fills holes of white particles on a black background, using the traditional method of reconstructing the inverse of the background using the (empty parts of) borders of the image as seeds.

BinaryFilterReconstruct_.class
This plugin filters 8-connected particles in a binary image that otherwise would disappear after n erosions. The difference with morphological Opening is that BinaryFilterReconstruct preserves the original shape or the particles (Opening tends to smooth the boundaries of particles). The algorithm is n erosions, followed by a Binary Reconstruction of the original image based on the eroded image as the seed.
New in 1.3 Changed 'dilations in a mask' for 'floodfill8 in the mask from the seed' to speed up.

BinaryHitOrMiss_.class
This plugin returns the locations of the image that match the kernel pattern.
The pattern is a 3x3 neighbourhood where 0=empty, 1=set, 2=don't care.

• Corners.txt: Returns the corners of a binary particle based on the Hit-or-miss transform.

BinaryLabel8_.class
ImageJ plugin for labelling particles (8 neighbours) in a binary image.
Can label up to 65530 particles in a unique greyscale value (from 1 to 65531), after that, the colours are recycled.
The output is a new 16 bit greyscale image with re-scaled brightness.

The ideal look up table (LUT) to maximise the contrast between labelled particles is glasbey.lut (included in the zip file). Please read about it in Chris Glasbey's website (the link to the paper is http://www.bioss.ac.uk/staff/chris/colorpaper.pdf ).

BinaryReconstruct_.class
This is a very powerful morphological operation that reconstructs (retains) 8-connected particles in an image (called mask) based on markers present in another image (called seed).
Morphological Reconstruction consists of dilating the seeds inside the mask (so particles that do not have seeds are not reconstructed).
New in 1.5 Changed 'dilations in a mask' for 'floodfill8 in the mask from the seed' to speed up.
This procedure is called "Feature-AND" in reference [2].

• Hysteresis.txt: This macro uses Binary Reconstruction to aid thresholding an image.
  Hysteresis thresholding is useful to segment edge gradients. The macro assumes that the object is bright (usually the gradient after applying some edge detector).
  First set the threshold of the "safe zone" (for sure belongs to the "object") then set the threshold for the "unsafe zone" (for sure is outside the "object"). The in-between zone is called the "fuzzy zone". Hysteresis thresholding adds those parts of the fuzzy zone that are connected to the safe zone.
  The macro creates 2 images: "Reconstructed" is the hysteresis-thresholded image, while "Result of Result" shows the safe zone (white), the pixels added to the safe zone (yellow), the pixels of the fuzzy zone not added (purple) and the unsafe zone (black).
  The "Reconstructed" image corresponds to the white+yellow components of the "Result of Result" image.
  
  BinaryKillBorders_.txt: This macro uses the reconstruction of the intersection of the image border with a 1 pixel thick box boundary to eliminate particles touching any of the borders of the image. The current version uses flood filling which is much quicker.

BinaryThick_.class
BinaryThick2_.class
These two plugins dilate the locations of the image that match one (BinaryThick_.class) or two (BinaryThick2_.class) kernel patterns.
First dilates then rotates the kernel, if set to do so. The pattern is a 3x3 neighbourhood where 0=empty, 1=set, 2=don't care.

• ConvexHull1.txt: a morphological convex hull -- square shape (not the true convex hull)
• ConvexHull2.txt: a morphological convex hull -- diamond shape (not the true convex hull)
• ConvexHull3.txt: a morphological strong convex hull. If done with 'rotate 90' it gives a quasi-convex hull (not the true convex hull)

BinaryThin_.class
BinaryThin2_.class
These two plugins erode the locations of the image that match one (BinaryThick_.class) or two (BinaryThick2_.class) kernel patterns.
First erodes then rotates the kernel, if set to do so. The pattern is a 3x3 neighbourhood where 0=empty, 1=set, 2=don't care.

• Boundary4.txt: produces a 4-connected boundary of particles
• Boundary8.txt: produces a 8-connected boundary of particles
• Diagonal8to4.txt: Converts 8 connected white features to 4 connected ones by filling empty diagonal pixel spaces
• H-break.txt: removes the centre of H-connected pixel patterns
• Influence_Zones.txt: creates influence zones by skeletonisation of the background followed by pruning. This is a fast way of "dilation without merging until idempotence"
• MCentroids.txt: creates the morphological centroids by thinning. The centroid of an object with a hole is a ring, otherwise it is a point.
• Prune1.txt: prunes a binary skeleton once.
• PruneAll.txt: prunes a binary skeleton until idempotence.
• Skeleton1.txt: an 8 connected skeleton, different from the one in ImageJ.
• Skeleton2.txt: an 8 connected skeleton, different from the one in ImageJ. It creates many lateral "bones" or branches.
• Skeleton3.txt: similar to skeleton1 but 4-connected.

Domes_.class
This plugin extracts "domes" in a greyscale image.
Domes are bright 8-connected regions of up to given height h (measured from their top downwards) in the greyscale function such that all the pixels around the dome have strictly lower greyscale values.
It can also return "basins" (regionally dark regions) instead of domes.
Domes and basins are good candidates to extract reconstruction markers in images with uneven backgrounds. See reference [3].

• Domes_stack.txt
  This macro extracts the domes (or basins) in a whole stack.
  
  
• RegionalMaxima.txt
• RegionalMinMax.txt
• RegionalMinima.txt
  These 3 macros are used to extract Regional Maxima, Minima or both in a greyscale image. They require the Domes_.class plugin above.
  RegionalMaxima.txt returns the regional maxima as white pixels on a black background.
  RegionalMinima.txt returns the regional minima as black pixels on a white background.
  RegionalMinMax.txt returns the regional maxima as white [255] pixels and the regional minima as black pixels [0] on a grey background [127].
  Regional maxima (and minima) are connected sets of pixels with a given value h (plateau at altitude [or depth] h) such that every pixel in the neighbourhood of the regional maxima (or minima) has a strictly lower (or higher) value.
  All regional maxima (minima) pixels are local maxima (minima), but not all local maxima (minima) pixels are regional maxima (minima). Confusing? See Vincent's reference [3].
  
  
• LocalMaxima.txt
  
• LocalMinMax.txt
  
• LocalMinima.txt
  These 3 macros are used to extract Local Maxima, Minima or both in a greyscale image. Added here for comparison with the 3 Regional macros above.

GreyscaleDilate_.class
GreyscaleErode_.class
These plugins perform a 3x3 Binary Dilation/Erosion of a greyscale image. Same as the Min and Max filters of radius=1 (8 neighbours) in ImageJ, but:

• They deal with black or white foregrounds.
• They can be applied n times.
• GreyscaleTopHat.txt detects light spots of a particular size on a dark background
• GreyscaleWell.txt detects dark spots of a particular on a bright background

Greyscale "Proper" Morphological Filters (macros)

• GreyscaleProperOpen.txt: returns Min(f,COC(f)).
• GreyscaleProperClose.txt:returns Max(f,OCO(f)).
• GreyscaleProperAutomedian.txt: returns Max(OCO(f),Min(f,COC(f))).

GreyscaleReconstruct_.class
This plugin reconstructs a greyscale image (the "mask" image) based on a "seed" image. This is an implementation of the parallel algorithm from [3].
It is very important to read Vincent's paper to understand greyscale reconstruction and its applications.
The reconstruction algorithm is: iterated 8-neighbour geodesic dilations of the seed UNDER the mask image until stability is reached (the idempotent limit).
It supports stacks reconstructed by a single seed image and also a single image reconstructed by a stack of seeds. Based on Calculator_Plus by Wayne Rasband.

Morphological Gradients and 2nd Derivative macros

• MorphologicalGradient1.txt: difference between dilation & erosion.
• MorphologicalGradient2.txt: difference between closing & opening.
• MorphologicalGradient3.txt: difference between MorphologicalGradient1 & MorphologicalGradient2.
• MorphologicalSharpGradient.txt: minimum of ((dilation-original) & (original-erosion)).
• Morphological2Derivative1.txt: original-(average of erosion & dilation).
• Morphological2Derivative2.txt: original-(average of opening & closing).
• Morphological2Derivative3.txt: Morphological2Derivative1-Morphological2Derivative2.
• MorphologicalSmoothing1.txt: average of erosion & dilation.
• MorphologicalSmoothing2.txt: average of opening & closing.

EDM_16bits.txt
This macro produces an Euclidean Distance Map on a binary image [the object over which the EDM is calculated is assumed to be 255 and the background 0]. The macro extends the built in ImageJ command to distances of up to 65535 pixels. The result is a 16 bit image.

Particles4_.class
Particles8_.class
Particles8_Plus.class
These are plugins for estimating various statistics of binary 4- and 8-connected particles.
Warnings!:
1) The plugins assume square pixels only. If your image capture device has an aspect ration different to 1:1, do not use the plugins.
2) These plugins do not return the same values as the built in ImageJ Analyze Particles command because they use an alternative concept to extract area and perimeter. Here, Perimeter and Area are measured from the centres of the boundary pixels of a particle, i.e. the length of the 8-neighbours chain code.
Area disregards "holes" in the particles (i.e. it returns the area inside the boundary), but Pixels returns the number of pixels forming the particle (a particle with holes will therefore have more Area than Pixels).
Also note that here Area is calculated from the polygon formed by the boundary pixels (the chain code). If the particle has no holes, then Area is smaller than Pixels (since the polygon is positioned in the centres of boundary pixels). Note that using this logic, Area for 1 pixel particles is 0, for a 2x2 square it is 1, etc. while the value of Pixels in each particle is what you see.
Likewise, a single pixel particle has a Perimeter of 0, for a 2x2 square it is 4, etc.

Why to write such a plugin?
This was created to return exactly the number of pixels in particles when dealing with synthetic images (such as percolation clusters).
The Analyze Particles command in ImageJ performs a different measurement of the perimeter of particles.

These plugins can label the particles in different colours. Some colours are reserved for the particle detection and various calculations, so there are only 250 labelling colours available (1 to 251). It is therefore possible when using Particles4_ that two 4-connected particles which are corner neighbours could end up labelled with the same colour and therefore look like an 8-connected particle (this could happen when a very large particle is surrounded by many small ones). Although the labelling may be confusing, the statistics generated are correct.(If one only needs to label the particles unequivocally, then it is better to use the BinaryLabel8_.class plugin because it can label up to 65530 particles in unique greyscale values --after that, it also recycles the labelling colour.)

The plugins can draw the centre of mass (rounded to the nearest pixel, labelled or not) of each particle or the start coordinates of each particle (the only pixel with 100% certainty that it belongs to the particle). These may be useful for reconstruction purposes (see the KeepParticlesInRange.txt macro below and BinaryReconstruct_ plugin above).
Filtered particles (smaller than the minimum and larger than the maximum sizes) are deleted from the image.

New in Version 1.6
The labels of the options have been modified so they are consistent with those of the built in Analyzer in ImageJ.
A new option "Overwrite Results" was added to prevent the macro asking to save or delete the current Results when executing from a macro.
The results of the particle analysis are now sent to the ResultsTable, so the data generated can be retrieved from a macro for further processing. The macros below show how to do it.

• KeepLargestParticle.txt is a macro modified from CircularParticles.txt to select the largest particle(s) in a binary image. It uses the built it Analyzer and makes the selection based on the 'Area' of the particles. If the largest particle has holes and child-particles, they will be kept in the image.
• KeepLargestParticlePixels.txt uses Particles8_.class as the analysis engine and selects the largest particle(s) based on the number of 'Pixels' in it. This is different from the 'Area' as it considers holes in the particle. If the largest particle has holes and child-particles, they will not be kept in the image. This example also works with Particles4_.class as analysis engine.
• KeepParticlesInRange.txt is another example that selects particles in the range of 10 to 20 pixels by reconstructing the original image based on the starting coordinates of particles made of 10 to 20 pixels. Do not use Particles4_.class as the analysis engine with this macro because the reconstruction is based on 8-neighbours rather than 4.

New in Version 1.7
The plugin analysis has been extended to include the following new parameters:

• the Maximum Feret's Diameter (Feret) (the longest distance between 2 points in the perimeter),
  
• the coordinates of the points defining the Feret's diameter (FeretX1, FeretY1, FeretX2, FeretY2),
  
• the angle (FAngle) in degrees with the image horizontal (0..180).
  

New in Version 1.8
Fixed bug that did not delete single border pixels when "exclude edge particles" was selected. Added CountCorrect parameter for unbiased counting of particles. This parameter should be used with "exclude edge particles" checked.
Here is the complete list of parameters:

• Slice: Slice number in the stack (if any),
• Number: Blob number in the slice,
• XStart: The x coordinate of the first scanned point in the particle,
• YStart: The y coordinate of the first scanned point in the particle,
• Perim: The Perimeter, calculated from the centres of the boundary pixles,
• Area: The Area inside the polygon defined by the Perimeter,
• Pixels: The number of pixels forming the blob,
• XM: X coordinate of the centre of mass or momentum,
• YM: Y coordinate of the centre of mass or momentum,
• ROIX1: X coordinate of the top-left corner of the ROI that encloses the particle,
• ROIY1: Y coordinate of the top-left corner of the ROI that encloses the particle,
• ROIX2: X coordinate of the bottom-right corner of the ROI that encloses the particle,
• ROIY2: Y coordinate of the bottom-right corner of the ROI that encloses the particle,
• MinR: Radius of the inscribed circle centred at the centre of mass,
• MaxR: Radius of the enclosing circle centred at the centre of mass,
• Feret: Largest axis length,
• FeretX1: X coordinate of the first point of the Feret,
• FeretY1: Y coordinate of the first point of the Feret,
• FeretX2: X coordinate of the second point of the Feret,
• FeretY2: Y coordinate of the second point of the Feret,
• FAngle: Angle (in degrees) of the Feret with the horizontal (0..180),
• Breadth: The largest axis perpendicular to the Feret (not necessarily colinear),
• BrdthX1: X coordinate of the first Breadth point,
• BrdthY1: Y coordinate of the first Breadth point,
• BrdthX2: X coordinate of the second Breadth point,
• BrdthY2: Y coordinate of the second Breadth point,
• CHull: Convex Hull or convex polygon calculated from pixel centres. (This value is the same as the perimeter only for rectangular particles),
• CArea: Area of the Convex Hull polygon,
• MBCX: X coordinate of the Minimal Bounding Circle centre,
• MBCY: Y coordinate of the Minimal Bounding Circle centre,
• MBCRadius: Radius of the Minimal Bounding Circle,
• CountCorrect: This is a correction factor for unbiased counting of particles calculated as CountCorrect=XY/(X-Fx)(Y-Fy), where X and Y are the width and height of the ROI and Fx and Fy are the maximum projected dimensions of the object in the X and Y axes (this is Fx=1+ROIX2-ROIX1 and Fy=1+ROIY2-ROIY1 respectively). This correction factor should be applied with data generated with "exclude edge particles" checked. See [2] p 529.

• AspRatio: Aspect Ratio = Feret/Breadth,
• Circ: Circularity = 4*Pi*Area/Perimeter², sometimes called Form Factor. Note that the value is slightly different from that calculated using the built-in Particle Analyzer because of the way the particle area is estimated,
• Roundness: Roundness = 4*Area/(Pi*Feret²),
• AreaEquivD: Area Equivalent Diameter = sqrt((4/Pi)*Area),
• PerimEquivD: Perimeter Equivalent Diameter = Area/Pi,
• EquivEllipseAr: Equivalent Ellipse Area = (Pi*Feret*Breadth)/4, this is the area of an ellipse with the same long and short axes as the particle,
• Compactness: Compactness = sqrt((4/Pi)*Area)/Feret or alternatively ArEquivD/Feret,
• Solidity: Solidity = Area/Convex_Area,
• Concavity: Concavity = Convex_Area-Area,
• Convexity: Convexity = Convex_Hull/Perimeter,
• Shape: Shape = Perimeter²/Area,
• RFactor: RFactor = Convex_Hull /(Feret*Pi),
• ModRatio: Modification Ratio = (2*MinR)/Feret,
• Sphericity: Sphericity = MinR/MaxR,
• ArBBox: ArBBox = Feret*Breadth. This is the area of the Bounding Box along the Feret diameter, but it is not necessarily the minimal bounding box! (Search the net for "rotating calipers algorithm"),
• Rectang: Rectangularity = Area/ArBBox. This approaches 0 for cross-like objects, 0.5 for squares, pi/4=0.79 for circles and approaches 1 for long rectangles.

• GrIntDen: Greyscale integrated density (the sum of the greyscale values in the particle,
• GrMin: Minimum greyscale values in the particle,
• GrMax: Maximum greyscale values in the particle,
• GrMode: Modal greyscale values in the particle,
• GrMedian: Median greyscale values in the particle,
• GrAverage: Average greyscale values in the particle,
• GrAvDeve: Average deviation of greyscale values in the particle,
• GrStDev: Standard deviation of the greyscale values in the particle,
• GrVar: Variance of the greyscale values in the particle,
• GrSkew: Skewness of the greyscale values in the particle,
• GrKurt: Kurtosis of the greyscale values in the particle,
• GrEntr: Entropy of the greyscale values in the particle.

Classify_Particles.class
This plugin allows to classify the particles based on the data produced by other plugins. Here are all the details.

• [1] Ruifrok AC, Johnston DA. Quantification of histochemical staining by color deconvolution. Anal Quant Cytol Histol 23: 291-299, 2001.
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