Package gov.nih.mipav.model.algorithms

Class AlgorithmSphereGeneration

java.lang.Object

java.lang.Thread

gov.nih.mipav.model.algorithms.AlgorithmBase

gov.nih.mipav.model.algorithms.AlgorithmSphereGeneration

All Implemented Interfaces:

ActionListener, WindowListener, Runnable, EventListener

public class AlgorithmSphereGeneration
extends AlgorithmBase

This module draws uniformly randomly positioned spheres with a specified radius. Best reference for nearest neighbor distribution for equally sized circles is: "Nearest Neighbor Assessments of Spatial Configurations of Circles rather Than Points" by Daniel Simberloff, Ecology, Vol. 60, No. 4, Aug. 1979, pp. 679-685. d = diameter lambda = mean number per unit area Dr. Daniel Simberloff writes: "In any event, you are probably correct that it would be more logical to caclulate rho for the points only in the interior, not the border region, remembering to leave out the border region when calculating area." mean nearest neighbor value = d + (exp(lambda * PI * d**2)/sqrt(lambda)*integral from t = d*sqrt(2*lambda*PI) to t = infinity of (1/sqrt(2*PI))*exp(-t**2/2)dt. The integral is simply the 1 - Gaussian probability integral. E(nearest neighbor distance squared) = d**2 + 1/(lambda * PI) variance = E(r**2) - [E(r)]**2 = d**2 + 1/(lambda * PI) - [E(r)]**2 standard error = sqrt(variance)/sqrt(N) Get percentile from Gaussian probability integral. If the measured mean is significantly greater than the analytical mean, the distribution is uniform or regular. If the measured mean is signficantly less than than the analytical mean, the distribution is clumped or aggregated. I have derived similar mathematics for Poisson distributed spheres. Consider a Poisson distribution of points in spheres of radius r. The probability that a sphere of radius r about a point contains no points, given a density of points = lambda is exp(-(4/3)*lambda*PI*(r**3)) Thus, 1 - exp(-(4/3)*lambda*PI*(r**3)) is the proportion of nearest neighbor distances invalid input: '<'= r. Differentiate this expression with respect to r to obtain as the probability density function of r, 4*lambda*PI*(r**2)*exp(-(4/3)*lambda*PI*(r**3)). Now find the probability density function for spheres of diameter dm. For 0 invalid input: '<' r invalid input: '<'= dm, 0 For r > dm: 4*lambda*PI*(r**2)*exp(-(4/3)*lambda*PI*(r**3)) * (1 / ( 1 - 4*lambda*PI*integral from r = 0 to r = dm of (r**2)*exp(-(4/3)*lambda*PI*(r**3))dr)) = 4*lambda*PI*(r**2)*exp(-(4/3)*lambda*PI*(r**3)) * (1/ ( 1 + integral from r = 0 to r = dm of exp(-(4/3)*lambda*PI*(r**3))d(-(4/3)*lambda*PI*(r**3)))) = 4*lambda*PI*(r**2)*exp(-(4/3)*lambda*PI*(r**3)) * (1 /(1 + exp(-(4/3)*lambda*PI*(dm**3)) - 1)) = 4*lambda*PI*exp((4/3)*lambda*PI*(dm**3))*(r**2)*exp(-(4/3)*lambda*PI*(r**3)) E(r) = 4*lambda*PI*exp((4/3)*lambda*PI*(dm**3)) * integral from r = dm to r = infinity of (r**3)*exp(-(4/3)*lambda*PI*(r**3))dr = -exp((4/3)*lambda*PI*(dm**3)) * integral from r = dm to r = infinity of rd(exp(-(4/3)*lambda*PI*(r**3))) -exp((4/3)*lambda*PI*(dm**3)) * (-dm*exp(-(4/3)*lambda*PI*(dm**3)) - intergal from r = dm to r = infinity of exp(-(4/3)*lambda*PI*(r**3))dr) = dm + exp((4/3)*lambda*PI*(dm**3))*integral from r = dm to r = infinity of exp(-(4/3)*lambda*PI*(r**3))dr E(r**2) = 4*lambda*PI*exp((4/3)*lambda*PI*(dm**3)) * integral from r = dm to r = infinity of (r**4)*exp(-(4/3)*lambda*PI*(r**3))dr = -exp((4/3)*lambda*PI*(dm**3)) * integral from r = dm to r = infinity of (r**2)*d(exp(-(4/3)*lambda*PI*(r**3))) = -exp((4/3)*lambda*PI*(dm**3) * (-(dm**2)*exp(-(4/3)*lambda*PI*(dm**3)) - integral from r = dm to r = infinity of exp(-(4/3)*lambda*PI*(r**3))d(r**2)) = dm**2 + exp((4/3)*lambda*PI*(dm**3)) * integral from r = dm to r = infinity of 2*r*exp(-(4/3)*lambda*PI*(r**3))dr Integration.MIDINF can be too slow for radius = 0. The Poisson distribution becomes inaccurate at higher densities because the assumption of the Poission distribution of rare events is violated: the mean number of points per sampling unit is not small relative to the maximum possible number of points per sampling unit. I have used the formula from "Nearest-neighbor distribution functions in many-body systems" by S. Torquato, B. Lu. and J. Rubinstein, The American Physical Society Physical Review A, Volume 41, Number 4, February 15, 1990, pp. 2059-2075. vf = volume fraction of spheres e = (1 + vf)/((1 - vf)**3) f = -0.5*vf*(3 + vf)/((1 - vf)**3) g = 0.5*vf*vf/((1 - vf)**3) mean nearest neighbor distance = diameter * (1 + integeral) integral = integral from x = 1 to x = infinity of exp{-vf[8*e*(x*x*x-1) + 12*f*(x*x - 1) + 24*g*(x - 1)]} Torquato developed more accurate equations in 1995 superseding the 1990 equations. In "Nearest-neighbor statistics for packings of hard spheres and disks" by S. Torquato, Physical Review E, Volume 51, Number 4, April, 1995, pp. 3170 - 3182: vf = volume fraction of spheres mean nearest neighbor distance = diameter * (1 + integral) integral = integral from x = 1 to x = infinity of exp{-vf[8*a0*(x*x*x - 1) + 12*a1*(x*x - 1) + 24*a2*(x-1)]} For vf invalid input: '<'= 0.49, the freezing packing fraction: a0 = (1 + vf + vf*vf - vf*vf*vf)/((1 - vf)**3) a1 = 0.5*vf*(3*vf* vf - 4*vf - 3)/((1 - vf)**3) a2 = 0.5*vf*vf*(2 - vf)/((1 - vf)**3) For 0.49 invalid input: '<' vf invalid input: '<' 0.64, random close packing gf(1) = (1 - 0.49/2)/((1 - 0.49)**3) a0 = 1 + 4*vf*gf(1)*(0.64 - 0.49)/(0.64 - vf) a1 = 0.5*(3*vf - 4)/(1 - vf) + 2*(1 - 3*vf)*gf(1)*(0.64 - 0.49)/(0.64 - vf) a2 = 0.5*(2 - vf)/(1 - vf) + (2*vf - 1)*gf(1)*(0.64 - 0.49)/(0.64 - vf) The formula derived by Asim Tewari and A. M. Gokhale is accurate at both low and high densities. The reference is "Nearest-neighbor distances between particles of finite size in three-dimensional uniform random microstructures" by Tewari and Gokhale, Materials Science and Engineering A, Volume 385, Issues 1-2, November, 2004, pp. 332-341. / = 1 + ((2**(-1/6) * (n-1)!)/(([(4/3)*PI]**-1/3) * Gamma[(3*n + 1)/3])) * ((f/f0)**((2*n)/(2*n+1))) where is the mean nth nearest-neighbor distance, f is volume fraction, is the corresponding mean nearest-neighbor distance for a point process, and fo is the volume fraction for the close-packed structure (1.e. PI/sqrt(18) or about 0.74). = ([(4/3)*PI*Nv]**-1/3) * gamma[(3*n + 1)/3] / (n - 1)! = Kn*(Nv)**-1/3 where Nv is the number of points per unit volume.

/ = 1 + B1 * ((f/f0)**2/3) where B1 = ((2**-1/6)/K1) - 1 For spheres of varying radii the formula is modified to

*(Nv**(1/3)) = K1*[ 1 + B1 * (f/f0)**2/3] - (1 - exp(-cv * f)) where cv is the coefficient of variation of the sphere size distribution The reference is "Nearest neighbor distances in uniform-random poly-dispersed microstructures" by A. Tewari and A. M. Gokhale, Materials Science and Engineering A 396 (2005), pp. 22-27. The equation for varying radii is good for sphere volume fractions ranging from 0.0 to 0.25.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
(package private) class	AlgorithmSphereGeneration.IntModelMean
(package private) class	AlgorithmSphereGeneration.IntModelMean2
(package private) class	AlgorithmSphereGeneration.IntModelMeanSquared
(package private) class	AlgorithmSphereGeneration.IntModelMeanSquared2
(package private) class	AlgorithmSphereGeneration.IntTorquato95ModelMean
(package private) class	AlgorithmSphereGeneration.IntTorquato95ModelMean2
(package private) class	AlgorithmSphereGeneration.IntTorquatoModelMean
(package private) class	AlgorithmSphereGeneration.IntTorquatoModelMean2

Nested classes/interfaces inherited from class java.lang.Thread

Thread.Builder, Thread.State, Thread.UncaughtExceptionHandler

Field Summary

Fields

Modifier and Type	Field	Description
static final int	AGGREGATED
static final int	CONSTANT_RADIUS
static final int	CONSTRAINED
private double	highestForbiddenNNDistance
private double	highestRegenerationNNDistance
private int	initialRandomSpheres
private double	lowestForbiddenNNDistance
private double	maximumNearestNeighborDistance
private int	maxRadius
private double	minimumNearestNeighborDistance
private int	minRadius
private int	numSpheres
private int	pattern
private int	radiusDistribution
static final int	RANDOM
static final int	REGULAR
static final int	UNIFORM_RADIUS

Fields inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase

destFlag, destImage, image25D, mask, maxProgressValue, minProgressValue, multiThreadingEnabled, nthreads, progress, progressModulus, progressStep, runningInSeparateThread, separable, srcImage, threadStopped

Fields inherited from class java.lang.Thread

MAX_PRIORITY, MIN_PRIORITY, NORM_PRIORITY

Constructor Summary

Constructors

Constructor	Description
AlgorithmSphereGeneration()	AlgorithmSphereGeneration - default constructor.
AlgorithmSphereGeneration(ModelImage srcImage, int minRadius, int maxRadius, int numSpheres, int pattern, int radiusDistribution, int initialRandomSpheres, double minimumNearestNeighborDistance, double maximumNearestNeighborDistance, double lowestForbiddenNNDistance, double highestForbiddenNNDistance, double highestRegenerationNNDistance)	AlgorithmRandomSphereGeneration.

Method Summary

Modifier and Type	Method	Description
void	finalize()	finalize -
void	runAlgorithm()	Starts the program.

Methods inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase

actionPerformed, addListener, addProgressChangeListener, calculateImageSize, calculatePrincipleAxis, computeElapsedTime, computeElapsedTime, convertIntoFloat, delinkProgressToAlgorithm, delinkProgressToAlgorithmMulti, displayError, errorCleanUp, fireProgressStateChanged, fireProgressStateChanged, fireProgressStateChanged, fireProgressStateChanged, fireProgressStateChanged, generateProgressValues, getDestImage, getElapsedTime, getMask, getMaxProgressValue, getMinProgressValue, getNumberOfThreads, getProgress, getProgressChangeListener, getProgressChangeListeners, getProgressModulus, getProgressStep, getProgressValues, getSrcImage, isCompleted, isImage25D, isMultiThreadingEnabled, isRunningInSeparateThread, isThreadStopped, linkProgressToAlgorithm, linkProgressToAlgorithm, makeProgress, notifyListeners, removeListener, removeProgressChangeListener, run, setCompleted, setImage25D, setMask, setMaxProgressValue, setMinProgressValue, setMultiThreadingEnabled, setNumberOfThreads, setProgress, setProgressModulus, setProgressStep, setProgressValues, setProgressValues, setRunningInSeparateThread, setSrcImage, setStartTime, setThreadStopped, startMethod, windowActivated, windowClosed, windowClosing, windowDeactivated, windowDeiconified, windowIconified, windowOpened

Methods inherited from class java.lang.Thread

activeCount, checkAccess, clone, countStackFrames, currentThread, dumpStack, enumerate, getAllStackTraces, getContextClassLoader, getDefaultUncaughtExceptionHandler, getId, getName, getPriority, getStackTrace, getState, getThreadGroup, getUncaughtExceptionHandler, holdsLock, interrupt, interrupted, isAlive, isDaemon, isInterrupted, isVirtual, join, join, join, join, ofPlatform, ofVirtual, onSpinWait, resume, setContextClassLoader, setDaemon, setDefaultUncaughtExceptionHandler, setName, setPriority, setUncaughtExceptionHandler, sleep, sleep, sleep, start, startVirtualThread, stop, suspend, threadId, toString, yield

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Details

RANDOM

public static final int RANDOM

See Also:

• Constant Field Values

AGGREGATED

public static final int AGGREGATED

See Also:

• Constant Field Values

REGULAR

public static final int REGULAR

See Also:

• Constant Field Values

CONSTRAINED

public static final int CONSTRAINED

See Also:

• Constant Field Values

CONSTANT_RADIUS

public static final int CONSTANT_RADIUS

See Also:

• Constant Field Values

UNIFORM_RADIUS

public static final int UNIFORM_RADIUS

See Also:

• Constant Field Values

numSpheres

private int numSpheres

pattern

private int pattern

minRadius

private int minRadius

maxRadius

private int maxRadius

radiusDistribution

private int radiusDistribution

initialRandomSpheres

private int initialRandomSpheres

minimumNearestNeighborDistance

private double minimumNearestNeighborDistance

maximumNearestNeighborDistance

private double maximumNearestNeighborDistance

lowestForbiddenNNDistance

private double lowestForbiddenNNDistance

highestForbiddenNNDistance

private double highestForbiddenNNDistance

highestRegenerationNNDistance

private double highestRegenerationNNDistance

Constructor Details

AlgorithmSphereGeneration

public AlgorithmSphereGeneration()

AlgorithmSphereGeneration - default constructor.

AlgorithmSphereGeneration

public AlgorithmSphereGeneration(ModelImage srcImage,
 int minRadius,
 int maxRadius,
 int numSpheres,
 int pattern,
 int radiusDistribution,
 int initialRandomSpheres,
 double minimumNearestNeighborDistance,
 double maximumNearestNeighborDistance,
 double lowestForbiddenNNDistance,
 double highestForbiddenNNDistance,
 double highestRegenerationNNDistance)

AlgorithmRandomSphereGeneration.

Parameters:

numSpheres - Number of spheres to be drawn

pattern - RANDOM, AGGREGATED, or REGULAR

initialRandomSpheres - Used in AGGREGATED. initialRandomSpheres are drawn randomly. The rest are drawn with nearestNeighborDistance less than or equal ot maximumNearestNeighborDistance.

minimumNearestNeighborDistance - Used in REGULAR

maximumNearestNeighborDistance - Used in AGGREGATED and REGULAR

lowestForbiddenNNDistance - Used in CONSTRAINED

highestForbiddenNNDistance - Used in CONSTRAINED

srcImg - Blank source image in which spheres will be drawn

radius - Sphere radius

highestRegeneerationNNDistance - Used in CONSTRAINED

Method Details

finalize

public void finalize()

finalize -

Overrides:

finalize in class AlgorithmBase

runAlgorithm

public void runAlgorithm()

Starts the program.

Specified by:

runAlgorithm in class AlgorithmBase