| GaussianBlur.java |
package ij.plugin.filter;
import ij.*;
import ij.gui.*;
import ij.process.*;
import ij.util.ThreadUtil;
import java.awt.AWTEvent;
import java.awt.Rectangle;
import java.util.concurrent.Callable;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.concurrent.atomic.AtomicLong;
/** This plug-in filter uses convolution with a Gaussian function for smoothing.
* 'Radius' means the radius of decay to exp(-0.5) ~ 61%, i.e. the standard
* deviation sigma of the Gaussian (this is the same as in Photoshop, but
* different from the 'Gaussian Blur' in ImageJ versions before 1.38u, where
* a value 2.5 times as much had to be entered.
* - Like all convolution operations in ImageJ, it assumes that out-of-image
* pixels have a value equal to the nearest edge pixel. This gives higher
* weight to edge pixels than pixels inside the image, and higher weight
* to corner pixels than non-corner pixels at the edge. Thus, when smoothing
* with very high blur radius, the output will be dominated by the edge
* pixels and especially the corner pixels (in the extreme case, with
* a blur radius of e.g. 1e20, the image will be raplaced by the average
* of the four corner pixels).
* - For increased speed, except for small blur radii, the lines (rows or
* columns of the image) are downscaled before convolution and upscaled
* to their original length thereafter.
*
* Version 03-Jun-2007 M. Schmid with preview, progressBar stack-aware,
* snapshot via snapshot flag; restricted range for resetOutOfRoi
*
* 20-Feb-2010 S. Saalfeld inner multi-threading, modified 29-Aug-2019 M. Schmid
*
*/
public class GaussianBlur implements ExtendedPlugInFilter, DialogListener {
/** for remembering till the next invocation */
private static double sigmaS = 2.0;
private static boolean sigmaScaledS = false;
/** the standard deviation of the Gaussian*/
private double sigma = sigmaS;
/** whether sigma is given in units corresponding to the pixel scale (not pixels)*/
private boolean sigmaScaled = sigmaScaledS;
/** The flags specifying the capabilities and needs */
private int flags = DOES_ALL|SUPPORTS_MASKING|KEEP_PREVIEW;
private ImagePlus imp; // The ImagePlus of the setup call, needed to get the spatial calibration
private boolean hasScale = false; // whether the image has an x&y scale
private int nPasses = 2; // The number of passes (filter directions * color channels * stack slices)
private int nChannels = 1; // The number of color channels
private int pass; // Current pass
private boolean noProgress; // Do not show progress bar
private boolean calledAsPlugin;
/** Method to return types supported
* @param arg unused
* @param imp The ImagePlus, used to get the spatial calibration
* @return Code describing supported formats etc.
* (see ij.plugin.filter.PlugInFilter & ExtendedPlugInFilter)
*/
public int setup(String arg, ImagePlus imp) {
this.imp = imp;
if (imp!=null && imp.getRoi()!=null) {
Rectangle roiRect = imp.getRoi().getBoundingRect();
if (roiRect.y > 0 || roiRect.y+roiRect.height < imp.getDimensions()[1])
flags |= SNAPSHOT; // snapshot for pixels above and/or below roi rectangle
}
return flags;
}
/** Ask the user for the parameters
*/
public int showDialog(ImagePlus imp, String command, PlugInFilterRunner pfr) {
calledAsPlugin = true;;
String options = Macro.getOptions();
boolean oldMacro = false;
nChannels = imp.getProcessor().getNChannels();
setNPasses(1);
if (options!=null) {
if (options.indexOf("radius=") >= 0) { // ensure compatibility with old macros
oldMacro = true; // specifying "radius=", not "sigma=
Macro.setOptions(options.replaceAll("radius=", "sigma="));
}
}
GenericDialog gd = GUI.newNonBlockingDialog(command, imp);
sigma = Math.abs(sigma);
gd.addNumericField("Sigma (Radius):", sigma, 2);
if (imp.getCalibration()!=null && !imp.getCalibration().getUnits().equals("pixels")) {
hasScale = true;
gd.addCheckbox("Scaled Units ("+imp.getCalibration().getUnits()+")", sigmaScaled);
} else
sigmaScaled = false;
gd.addPreviewCheckbox(pfr);
gd.addDialogListener(this);
gd.showDialog(); // input by the user (or macro) happens here
if (gd.wasCanceled()) return DONE;
if (options==null) { // interactive use: remember values as default for the next invocation
sigmaS = sigma;
sigmaScaledS = sigmaScaled;
}
if (oldMacro) sigma /= 2.5; // for old macros, "radius" was 2.5 sigma
IJ.register(this.getClass()); // protect static class variables (parameters) from garbage collection
return IJ.setupDialog(imp, flags); // ask whether to process all slices of stack (if a stack)
}
/** Listener to modifications of the input fields of the dialog */
public boolean dialogItemChanged(GenericDialog gd, AWTEvent e) {
sigma = gd.getNextNumber();
if (sigma < 0 || gd.invalidNumber())
return false;
if (hasScale)
sigmaScaled = gd.getNextBoolean();
return true;
}
/** Set the number of passes of the blur1Direction method. If called by the
* PlugInFilterRunner of ImageJ, an ImagePlus is known and conversion of RGB images
* to float as well as the two filter directions are taken into account.
* Otherwise, the caller should set nPasses to the number of 1-dimensional
* filter operations required.
*/
public void setNPasses(int nPasses) {
this.nPasses = 2 * nChannels * nPasses;
pass = 0;
}
/** This method is invoked for each slice during execution
* @param ip The image subject to filtering. It must have a valid snapshot if
* the height of the roi is less than the full image height.
*/
public void run(ImageProcessor ip) {
double sigmaX = sigmaScaled ? sigma/imp.getCalibration().pixelWidth : sigma;
double sigmaY = sigmaScaled ? sigma/imp.getCalibration().pixelHeight : sigma;
double accuracy = (ip instanceof ByteProcessor || ip instanceof ColorProcessor) ?
0.002 : 0.0002;
Rectangle roi = ip.getRoi();
blurGaussian(ip, sigmaX, sigmaY, accuracy);
}
/** Gaussian Filtering of an ImageProcessor. This method is for compatibility with the
* previous code (before 1.38r) and uses a low-accuracy kernel, only slightly better
* than the previous ImageJ code.
* The 'radius' in this call is different from the one used in ImageJ 1.38r and later.
* Therefore, use blurGaussian(ip, sigma, sigma, accuracy), where 'sigma' is equivalent
* to the 'sigma (radius)' of the Menu, and accuracy should be 0.02 unless better
* accuracy is desired.
*/
@Deprecated
public boolean blur(ImageProcessor ip, double radius) {
Rectangle roi = ip.getRoi();
if (roi.height!=ip.getHeight() && ip.getMask()==null)
ip.snapshot(); // a snapshot is needed for out-of-Rectangle pixels
blurGaussian(ip, 0.4*radius, 0.4*radius, 0.01);
return true;
}
/** Gaussian Filtering of an ImageProcessor
* @param ip The ImageProcessor to be filtered.
* @param sigma Standard deviation of the Gaussian (pixels)
*
* @see ij.process.ImageProcessor#blurGaussian(double)
*/
public void blurGaussian(ImageProcessor ip, double sigma) {
double accuracy = (ip instanceof ByteProcessor||ip instanceof ColorProcessor)?0.002:0.0002;
blurGaussian(ip, sigma, sigma, accuracy);
}
/** Gaussian Filtering of an ImageProcessor
* @param ip The ImageProcessor to be filtered.
* @param sigmaX Standard deviation of the Gaussian in x direction (pixels)
* @param sigmaY Standard deviation of the Gaussian in y direction (pixels)
* @param accuracy Accuracy of kernel, should not be above 0.02. Better (lower)
* accuracy needs slightly more computing time.
*/
public void blurGaussian(ImageProcessor ip, double sigmaX, double sigmaY, double accuracy) {
boolean hasRoi = ip.getRoi().height!=ip.getHeight() && sigmaX>0 && sigmaY>0;
if (hasRoi && !calledAsPlugin)
ip.snapshot();
if (nPasses<=1)
nPasses = ip.getNChannels() * (sigmaX>0 && sigmaY>0 ? 2 : 1);
FloatProcessor fp = null;
for (int i=0; i<ip.getNChannels(); i++) {
fp = ip.toFloat(i, fp);
if (Thread.currentThread().isInterrupted()) return; // interruption for new parameters during preview?
blurFloat(fp, sigmaX, sigmaY, accuracy);
if (Thread.currentThread().isInterrupted()) return;
ip.setPixels(i, fp);
}
if (hasRoi)
resetOutOfRoi(ip, (int)Math.ceil(5*sigmaY)); // reset out-of-Rectangle pixels above and below roi
return;
}
/** Gaussian Filtering of a FloatProcessor. This method does NOT include
* resetOutOfRoi(ip), i.e., pixels above and below the roi rectangle will
* be also subject to filtering in x direction and must be restored
* afterwards (unless the full image height is processed).
* @param ip The FloatProcessor to be filtered.
* @param sigmaX Standard deviation of the Gaussian in x direction (pixels)
* @param sigmaY Standard deviation of the Gaussian in y direction (pixels)
* @param accuracy Accuracy of kernel, should not be above 0.02. Better (lower)
* accuracy needs slightly more computing time.
*/
public void blurFloat(FloatProcessor ip, double sigmaX, double sigmaY, double accuracy) {
if (sigmaX > 0)
blur1Direction(ip, sigmaX, accuracy, true, (int)Math.ceil(5*sigmaY));
if (Thread.currentThread().isInterrupted()) return; // interruption for new parameters during preview?
if (sigmaY > 0)
blur1Direction(ip, sigmaY, accuracy, false, 0);
return;
}
/** Blur an image in one direction (x or y) by a Gaussian, using multiple threads on multiprocessor machines
* @param ip The Image with the original data where also the result will be stored
* @param sigma Standard deviation of the Gaussian
* @param accuracy Accuracy of kernel, should not be > 0.02
* @param xDirection True for bluring in x direction, false for y direction
* @param extraLines Number of lines (parallel to the blurring direction)
* below and above the roi bounds that should be processed.
*/
public void blur1Direction( final FloatProcessor ip, final double sigma, final double accuracy,
final boolean xDirection, final int extraLines) {
final int UPSCALE_K_RADIUS = 2; //number of pixels to add for upscaling
final double MIN_DOWNSCALED_SIGMA = 4.; //minimum standard deviation in the downscaled image
final float[] pixels = (float[])ip.getPixels();
final int width = ip.getWidth();
final int height = ip.getHeight();
final Rectangle roi = ip.getRoi();
final int length = xDirection ? width : height; //number of points per line (line can be a row or column)
final int pointInc = xDirection ? 1 : width; //increment of the pixels array index to the next point in a line
final int lineInc = xDirection ? width : 1; //increment of the pixels array index to the next line
final int lineFromA = (xDirection ? roi.y : roi.x) - extraLines; //the first line to process
final int lineFrom;
if (lineFromA < 0) lineFrom = 0;
else lineFrom = lineFromA;
final int lineToA = (xDirection ? roi.y+roi.height : roi.x+roi.width) + extraLines; //the last line+1 to process
final int lineTo;
if (lineToA > (xDirection ? height:width)) lineTo = (xDirection ? height:width);
else lineTo = lineToA;
final int writeFrom = xDirection? roi.x : roi.y; //first point of a line that needs to be written
final int writeTo = xDirection ? roi.x+roi.width : roi.y+roi.height;
/* large radius (sigma): scale down, then convolve, then scale up */
final boolean doDownscaling = sigma > 2*MIN_DOWNSCALED_SIGMA + 0.5;
final int reduceBy = doDownscaling ? //downscale by this factor
Math.min((int)Math.floor(sigma/MIN_DOWNSCALED_SIGMA), length)
: 1;
/* Downscaling and upscaling blur the image a bit - we have to correct the standard
* deviation for this:
* Downscaling gives std devation sigma = 1/sqrt(3); upscale gives sigma = 1/2 (in downscaled pixels).
* All sigma^2 values add to full sigma^2, which should be the desired value */
final double sigmaGauss = doDownscaling ?
Math.sqrt(sigma*sigma/(reduceBy*reduceBy) - 1./3. - 1./4.)
: sigma;
final int maxLength = doDownscaling ?
(length+reduceBy-1)/reduceBy + 2*(UPSCALE_K_RADIUS + 1) //downscaled line can't be longer
: length;
final float[][] gaussKernel = makeGaussianKernel(sigmaGauss, accuracy, maxLength);
final int kRadius = gaussKernel[0].length*reduceBy; //Gaussian kernel radius after upscaling
final int readFrom = (writeFrom-kRadius < 0) ? 0 : writeFrom-kRadius; //not including broadening by downscale&upscale
final int readTo = (writeTo+kRadius > length) ? length : writeTo+kRadius;
final int newLength = doDownscaling ? //line length for convolution
(readTo-readFrom+reduceBy-1)/reduceBy + 2*(UPSCALE_K_RADIUS + 1)
: length;
final int unscaled0 = readFrom - (UPSCALE_K_RADIUS + 1)*reduceBy; //input point corresponding to cache index 0
//the following is relevant for upscaling only
//IJ.log("reduce="+reduceBy+", newLength="+newLength+", unscaled0="+unscaled0+", sigmaG="+(float)sigmaGauss+", kRadius="+gaussKernel[0].length);
final float[] downscaleKernel = doDownscaling ? makeDownscaleKernel(reduceBy) : null;
final float[] upscaleKernel = doDownscaling ? makeUpscaleKernel(reduceBy) : null;
int numThreads1 = Math.min(Prefs.getThreads(), lineTo-lineFrom);
int numThreads2 = (int)((lineTo - lineFrom)*(long)(writeTo - writeFrom)*gaussKernel[0].length/
(doDownscaling ? 8000 : 16000)) + 1; //use fewer threads if a small task
final int numThreads = Math.min(numThreads1, numThreads2);
final Callable[] callables = new Callable[numThreads];
final AtomicInteger nextLine = new AtomicInteger(lineFrom);
final AtomicLong lastShowProgressTime = new AtomicLong(System.currentTimeMillis());
for ( int t = 0; t < numThreads; t++ ) {
final float[] cache1 = new float[newLength]; //holds data before convolution (after downscaling, if any)
final float[] cache2 = doDownscaling ? new float[newLength] : null; //holds data after convolution
callables[t] = new Callable() {
final public Void call() { /*try{*/
while (!Thread.currentThread().isInterrupted()) {
int line = nextLine.getAndIncrement();
if (line >= lineTo) break;
int pixel0 = line*lineInc;
if ((line&0x1f)==0) { //every 32 lines, check whether progress bar should be updated
long time = System.currentTimeMillis();
if (time - lastShowProgressTime.get() >110) {
lastShowProgressTime.set(time);
showProgress((double)(line-lineFrom)/(lineTo-lineFrom));
}
}
if (doDownscaling) {
downscaleLine(pixels, cache1, downscaleKernel, reduceBy, pixel0, unscaled0, length, pointInc, newLength);
convolveLine(cache1, cache2, gaussKernel, 0, newLength, 1, newLength-1, 0, 1);
upscaleLine(cache2, pixels, upscaleKernel, reduceBy, pixel0, unscaled0, writeFrom, writeTo, pointInc);
} else {
int p = pixel0 + readFrom*pointInc;
for (int i=readFrom; i<readTo; i++ ,p+=pointInc)
cache1[i] = pixels[p];
convolveLine(cache1, pixels, gaussKernel, readFrom, readTo, writeFrom, writeTo, pixel0, pointInc);
}
}
return null;
} /*catch(Exception ex) {IJ.handleException(ex);} }*/
};
}
ThreadUtil.startAndJoin(callables);
showProgress(1.0);
pass++;
if (pass > nPasses) pass = 1;
}
/** Scale a line (row or column of a FloatProcessor or part thereof)
* down by a factor <code>reduceBy</code> and write the result into
* <code>cache</code>.
* Input line pixel # <code>unscaled0</code> will correspond to output
* line pixel # 0. <code>unscaled0</code> may be negative. Out-of-line
* pixels of the input are replaced by the edge pixels.
* @param pixels input array
* @param cache output array
* @param kernel downscale kernel, runs form -1.5 to +1.5 in downscaled coordinates
* @param reduceBy downscaling factor
* @param pixel0 index in pixels array corresponding to start of line or column
* @param unscaled0 index in input line corresponding to output line index 0, May be negative.
* @param length length of full input line or column
* @param pointInc spacing of values in input array (1 for lines, image width for columns)
* @param newLength length of downscaled data
*/
final static private void downscaleLine(final float[] pixels, final float[] cache, final float[] kernel,
final int reduceBy, final int pixel0, final int unscaled0, final int length, final int pointInc, final int newLength) {
int p = pixel0 + pointInc*(unscaled0-reduceBy*3/2); //pointer in pixels array
final int pLast = pixel0 + pointInc*(length-1);
for (int xout=-1; xout<=newLength; xout++) {
float sum0 = 0, sum1 = 0, sum2 = 0;
for (int x=0; x<reduceBy; x++, p+=pointInc) {
float v = pixels[p<pixel0 ? pixel0 : (p>pLast ? pLast : p)];
sum0 += v * kernel[x+2*reduceBy];
sum1 += v * kernel[x+reduceBy];
sum2 += v * kernel[x];
}
if (xout>0) cache[xout-1] += sum0;
if (xout>=0 && xout<newLength) cache[xout] += sum1;
if (xout+1<newLength) cache[xout+1] = sum2;
}
}
/** the above code is equivalent to the following one; but the above code is faster
* - above: accesses each pixel in the pixels array only once
* - below: accesses each pixel in the pixels array 3 times, more cache misses */
/*final static private void downscaleLine(final float[] pixels, final float[] cache, final float[] kernel,
final int reduceBy, final int pixel0, final int unscaled0, final int length, final int pointInc, final int newLength) {
final int xin = unscaled0 - reduceBy/2;
int p = pixel0 + pointInc*xin;
final int pLast = pixel0 + pointInc*(length-1);
for (int xout=0; xout<newLength; xout++) {
float v = 0;
for (int x=0; x<reduceBy; x++, p+=pointInc) {
int pp = p-pointInc*reduceBy;
v += kernel[x] * pixels[pp<pixel0 ? pixel0 : (pp>pLast ? pLast : pp)];
v += kernel[x+reduceBy] * pixels[p<pixel0 ? pixel0 : (p>pLast ? pLast : p)];
pp = p+pointInc*reduceBy;
v += kernel[x+2*reduceBy] * pixels[pp<pixel0 ? pixel0 : (pp>pLast ? pLast : pp)];
}
cache[xout] = v;
}
}*/
/* Create a kernel for downscaling. The kernel function preserves
* norm and 1st moment (i.e., position) and has fixed 2nd moment,
* (in contrast to linear interpolation).
* In scaled space, the length of the kernel runs from -1.5 to +1.5,
* and the standard deviation is 1/2.
* Array index corresponding to the kernel center is
* unitLength*3/2
*/
final static private float[] makeDownscaleKernel (final int unitLength) {
final int mid = unitLength*3/2;
final float[] kernel = new float[3*unitLength];
for (int i=0; i<=unitLength/2; i++) {
final double x = i/(double)unitLength;
final float v = (float)((0.75-x*x)/unitLength);
kernel[mid-i] = v;
kernel[mid+i] = v;
}
for (int i=unitLength/2+1; i<(unitLength*3+1)/2; i++) {
final double x = i/(double)unitLength;
final float v = (float)((0.125 + 0.5*(x-1)*(x-2))/unitLength);
kernel[mid-i] = v;
kernel[mid+i] = v;
}
return kernel;
}
/** Scale a line up by factor <code>reduceBy</code> and write as a row
* or column (or part thereof) to the pixels array of a FloatProcessor.
*/
final static private void upscaleLine (final float[] cache, final float[] pixels, final float[] kernel,
final int reduceBy, final int pixel0, final int unscaled0, final int writeFrom, final int writeTo, final int pointInc) {
int p = pixel0 + pointInc*writeFrom;
for (int xout = writeFrom; xout < writeTo; xout++, p+=pointInc) {
final int xin = (xout-unscaled0+reduceBy-1)/reduceBy; //the corresponding point in the cache (if exact) or the one above
final int x = reduceBy - 1 - (xout-unscaled0+reduceBy-1)%reduceBy;
pixels[p] = cache[xin-2]*kernel[x]
+ cache[xin-1]*kernel[x+reduceBy]
+ cache[xin]*kernel[x+2*reduceBy]
+ cache[xin+1]*kernel[x+3*reduceBy];
}
}
/** Create a kernel for upscaling. The kernel function is a convolution
* of four unit squares, i.e., four uniform kernels with value +1
* from -0.5 to +0.5 (in downscaled coordinates). The second derivative
* of this kernel is smooth, the third is not. Its standard deviation
* is 1/sqrt(3) in downscaled cordinates.
* The kernel runs from [-2 to +2[, corresponding to array index
* 0 ... 4*unitLength (whereby the last point is not in the array any more).
*/
final static private float[] makeUpscaleKernel (final int unitLength) {
final float[] kernel = new float[4*unitLength];
final int mid = 2*unitLength;
kernel[0] = 0;
for (int i=0; i<unitLength; i++) {
final double x = i/(double)unitLength;
final float v = (float)((2./3. -x*x*(1-0.5*x)));
kernel[mid+i] = v;
kernel[mid-i] = v;
}
for (int i=unitLength; i<2*unitLength; i++) {
final double x = i/(double)unitLength;
final float v = (float)((2.-x)*(2.-x)*(2.-x)/6.);
kernel[mid+i] = v;
kernel[mid-i] = v;
}
return kernel;
}
/** Convolve a line with a symmetric kernel and write to a separate array,
* possibly the pixels array of a FloatProcessor (as a row or column or part thereof)
*
* @param input Input array containing the line
* @param pixels Float array for output, can be the pixels of a FloatProcessor
* @param kernel "One-sided" kernel array, kernel[0][n] must contain the kernel
* itself, kernel[1][n] must contain the running sum over all
* kernel elements from kernel[0][n+1] to the periphery.
* The kernel must be normalized, i.e. sum(kernel[0][n]) = 1
* where n runs from the kernel periphery (last element) to 0 and
* back. Normalization should include all kernel points, also these
* not calculated because they are not needed.
* @param readFrom First array element of the line that must be read.
* <code>writeFrom-kernel.length</code> or 0.
* @param readTo Last array element+1 of the line that must be read.
* <code>writeTo+kernel.length</code> or <code>input.length</code>
* @param writeFrom Index of the first point in the line that should be written
* @param writeTo Index+1 of the last point in the line that should be written
* @param point0 Array index of first element of the 'line' in pixels (i.e., lineNumber * lineInc)
* @param pointInc Increment of the pixels array index to the next point (for an ImageProcessor,
* it should be <code>1</code> for a row, <code>width</code> for a column)
*/
final static private void convolveLine( final float[] input, final float[] pixels, final float[][] kernel, final int readFrom,
final int readTo, final int writeFrom, final int writeTo, final int point0, final int pointInc) {
final int length = input.length;
final float first = input[0]; //out-of-edge pixels are replaced by nearest edge pixels
final float last = input[length-1];
final float[] kern = kernel[0]; //the kernel itself
final float kern0 = kern[0];
final float[] kernSum = kernel[1]; //the running sum over the kernel
final int kRadius = kern.length;
final int firstPart = kRadius < length ? kRadius : length;
int p = point0 + writeFrom*pointInc;
int i = writeFrom;
for (; i<firstPart; i++,p+=pointInc) { //while the sum would include pixels < 0
float result = input[i]*kern0;
result += kernSum[i]*first;
if (i+kRadius>length) result += kernSum[length-i-1]*last;
for (int k=1; k<kRadius; k++) {
float v = 0;
if (i-k >= 0) v += input[i-k];
if (i+k<length) v+= input[i+k];
result += kern[k] * v;
}
pixels[p] = result;
}
final int iEndInside = length-kRadius<writeTo ? length-kRadius : writeTo;
for (;i<iEndInside;i++,p+=pointInc) { //while only pixels within the line are be addressed (the easy case)
float result = input[i]*kern0;
for (int k=1; k<kRadius; k++)
result += kern[k] * (input[i-k] + input[i+k]);
pixels[p] = result;
}
for (; i<writeTo; i++,p+=pointInc) { //while the sum would include pixels >= length
float result = input[i]*kern0;
if (i<kRadius) result += kernSum[i]*first;
if (i+kRadius>=length) result += kernSum[length-i-1]*last;
for (int k=1; k<kRadius; k++) {
float v = 0;
if (i-k >= 0) v += input[i-k];
if (i+k<length) v+= input[i+k];
result += kern[k] * v;
}
pixels[p] = result;
}
}
/** Create a 1-dimensional normalized Gaussian kernel with standard deviation sigma
* and the running sum over the kernel
* Note: this is one side of the kernel only, not the full kernel as used by the
* Convolver class of ImageJ.
* To avoid a step due to the cutoff at a finite value, the near-edge values are
* replaced by a 2nd-order polynomial with its minimum=0 at the first out-of-kernel
* pixel. Thus, the kernel function has a smooth 1st derivative in spite of finite
* length.
*
* @param sigma Standard deviation, i.e. radius of decay to 1/sqrt(e), in pixels.
* @param accuracy Relative accuracy; for best results below 0.01 when processing
* 8-bit images. For short or float images, values of 1e-3 to 1e-4
* are better (but increase the kernel size and thereby the
* processing time). Edge smoothing will fail with very poor
* accuracy (above approx. 0.02)
* @param maxRadius Maximum radius of the kernel: Limits kernel size in case of
* large sigma, should be set to image width or height. For small
* values of maxRadius, the kernel returned may have a larger
* radius, however.
* @return A 2*n array. Array[0][n] is the kernel, decaying towards zero,
* which would be reached at kernel.length (unless kernel size is
* limited by maxRadius). Array[1][n] holds the sum over all kernel
* values > n, including non-calculated values in case the kernel
* size is limited by <code>maxRadius</code>.
*/
public float[][] makeGaussianKernel(final double sigma, final double accuracy, int maxRadius) {
int kRadius = (int)Math.ceil(sigma*Math.sqrt(-2*Math.log(accuracy)))+1;
if (maxRadius < 50) maxRadius = 50; // too small maxRadius would result in inaccurate sum.
if (kRadius > maxRadius) kRadius = maxRadius;
float[][] kernel = new float[2][kRadius];
for (int i=0; i<kRadius; i++) // Gaussian function
kernel[0][i] = (float)(Math.exp(-0.5*i*i/sigma/sigma));
if (kRadius < maxRadius && kRadius > 3) { // edge correction
double sqrtSlope = Double.MAX_VALUE;
int r = kRadius;
while (r > kRadius/2) {
r--;
double a = Math.sqrt(kernel[0][r])/(kRadius-r);
if (a < sqrtSlope)
sqrtSlope = a;
else
break;
}
for (int r1 = r+2; r1 < kRadius; r1++)
kernel[0][r1] = (float)((kRadius-r1)*(kRadius-r1)*sqrtSlope*sqrtSlope);
}
double sum; // sum over all kernel elements for normalization
if (kRadius < maxRadius) {
sum = kernel[0][0];
for (int i=1; i<kRadius; i++)
sum += 2*kernel[0][i];
} else
sum = sigma * Math.sqrt(2*Math.PI);
double rsum = 0.5 + 0.5*kernel[0][0]/sum;
for (int i=0; i<kRadius; i++) {
double v = (kernel[0][i]/sum);
kernel[0][i] = (float)v;
rsum -= v;
kernel[1][i] = (float)rsum;
//IJ.log("k["+i+"]="+(float)v+" sum="+(float)rsum);
}
return kernel;
}
/** Set the processed pixels above and below the roi rectangle back to their
* previous value (i.e., snapshot buffer). This is necessary since ImageJ
* only restores out-of-roi pixels inside the enclosing rectangle of the roi
* (If the roi is non-rectangular and the SUPPORTS_MASKING flag is set).
* @param ip The image to be processed
* @param radius The range above and below the roi that should be processed
*/
public static void resetOutOfRoi(ImageProcessor ip, int radius) {
Rectangle roi = ip.getRoi();
int width = ip.getWidth();
int height = ip.getHeight();
Object pixels = ip.getPixels();
Object snapshot = ip.getSnapshotPixels();
int y0 = roi.y-radius; // the first line that should be reset
if (y0<0) y0 = 0;
for (int y=y0,p=width*y+roi.x; y<roi.y; y++,p+=width)
System.arraycopy(snapshot, p, pixels, p, roi.width);
int yEnd = roi.y+roi.height+radius; // the last line + 1 that should be reset
if (yEnd>height) yEnd = height;
for (int y=roi.y+roi.height,p=width*y+roi.x; y<yEnd; y++,p+=width)
System.arraycopy(snapshot, p, pixels, p, roi.width);
}
private void showProgress(double percent) {
if (noProgress) return;
percent = (pass + percent)/nPasses;
IJ.showProgress(percent);
}
public void showProgress(boolean showProgressBar) {
noProgress = !showProgressBar;
}
}