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import ij.IJ;
import ij.ImagePlus;
import ij.gui.GenericDialog;
import ij.plugin.filter.PlugInFilter;
import ij.process.ByteProcessor;
import ij.process.ColorProcessor;
import ij.process.ImageProcessor;
import java.awt.Color;
/**
* @author Xavier Philippeau
*
* LaplaceBeltrami Plugin.
*
* Anisotropic Feature-Preserving Denoising using the Laplace-Beltrami operator
*/
public class LaplaceBeltrami_ implements PlugInFilter {
private ImagePlus imgOrig = null;
private int itermax = 0;
private boolean autostop=false;
private double step=0;
/**
* This method gets a reference to the image to be locally ranked
* and returns the filter capabilities.
* @param arg calls for the "about" information.
* @param imp This is the image to be processed
*
* @return Returns DOES_8G + DOES_RGB or DONE.
*/
public int setup(String arg, ImagePlus imp) {
// about...
if (arg.equals("about")) {
showAbout();
return DONE;
}
// else...
if (imp==null) return DONE;
//original image
this.imgOrig = imp ;
// Configuration dialog.
GenericDialog gd = new GenericDialog("Parameters");
gd.addNumericField("Integration step",0.1,1);
gd.addNumericField("Iterations (-1: auto)",-1,0);
while(true) {
gd.showDialog();
if ( gd.wasCanceled() ) return DONE;
this.step = (double) gd.getNextNumber();
this.itermax = (int) gd.getNextNumber();
if (this.step<=0) continue;
if (this.itermax<-1) continue;
break;
}
gd.dispose();
if (this.itermax==-1) {
this.autostop = true;
this.itermax=Integer.MAX_VALUE;
}
return DOES_8G+DOES_RGB;
}
/**
* Filters use this method to process the image. If the
* SUPPORTS_STACKS flag was set, it is called for each slice in
* a stack. ImageJ will lock the image before calling
* this method and unlock it when the filter is finished.
*/
public void run(ImageProcessor ip) {
// project image to HSV color space
ByteProcessor work = null;
if (this.imgOrig.getBitDepth()==24) work=transformRGB(this.imgOrig);
if (this.imgOrig.getBitDepth()==8) work=transformGray(this.imgOrig);
// show new image
ImagePlus newImg = new ImagePlus(this.imgOrig.getTitle()+"_LaplaceBeltrami", this.imgOrig.getProcessor());
newImg.show();
// filter
ByteProcessor previous = work;
int previousdiff = Integer.MAX_VALUE;
for(int i=0;i<this.itermax;i++) {
IJ.showProgress((float)i/this.itermax);
IJ.showStatus("Iteration: "+i);
// compute one step
work = LaplaceBeltramiFilter(work,this.step);
// project image to RGB color space
ImageProcessor newIp = null;
if (this.imgOrig.getBitDepth()==24) newIp=invTransformRGB(this.imgOrig,work);
if (this.imgOrig.getBitDepth()==8) newIp=invTransformGray(this.imgOrig,work);
newImg.setProcessor(null,newIp);
newImg.updateAndDraw();
// auto exit at idempotence
if (this.autostop) {
int diff=compare(work,previous);
if (diff<=0) break;
int rate = (previousdiff-diff);
if (rate<=0) {
this.itermax = this.itermax+1;
} else {
this.itermax = i+2+diff/rate;
}
previousdiff=diff;
previous=work;
}
}
IJ.showStatus("Done");
IJ.showProgress(0);
}
// RGB -> HSV
private ByteProcessor transformRGB(ImagePlus img) {
ByteProcessor bp = new ByteProcessor(img.getWidth(),img.getHeight());
for (int y = 0; y < img.getHeight(); y++) {
for (int x = 0; x < img.getWidth(); x++) {
int[] lrgb = img.getPixel(x,y);
float[] hsb = Color.RGBtoHSB(lrgb[0],lrgb[1],lrgb[2],null);
bp.set(x,y,(int)(hsb[2]*255));
}
}
return bp;
}
// GRAY -> HSV
private ByteProcessor transformGray(ImagePlus img) {
ByteProcessor bp = new ByteProcessor(img.getWidth(),img.getHeight());
for (int y = 0; y < img.getHeight(); y++) {
for (int x = 0; x < img.getWidth(); x++) {
int[] lrgb = img.getPixel(x,y);
bp.set(x,y,lrgb[0]);
}
}
return bp;
}
// HSV -> RGB
private ImageProcessor invTransformRGB(ImagePlus img, ByteProcessor bp) {
ImageProcessor out = new ColorProcessor(img.getWidth(),img.getHeight());
for (int y = 0; y < img.getHeight(); y++) {
for (int x = 0; x < img.getWidth(); x++) {
int[] lrgb = img.getPixel(x,y);
float[] hsb = Color.RGBtoHSB(lrgb[0],lrgb[1],lrgb[2],null);
int rgb = Color.HSBtoRGB(hsb[0],hsb[1],bp.get(x,y)/255f);
out.set(x,y,rgb);
}
}
return out;
}
// HSV -> GRAY
private ImageProcessor invTransformGray(ImagePlus img, ByteProcessor bp) {
ImageProcessor out = new ByteProcessor(img.getWidth(),img.getHeight());
for (int y = 0; y < img.getHeight(); y++) {
for (int x = 0; x < img.getWidth(); x++) {
out.set(x,y,bp.get(x,y));
}
}
return out;
}
// About...
private void showAbout() {
IJ.showMessage("Laplace-Beltrami...","Laplace-Beltrami Filter by Pseudocode");
}
// Compare two images
private int compare(ByteProcessor c,ByteProcessor c1) {
int diff=0;
for (int y=0;y<c.getHeight();y++) {
for (int x=0;x<c.getWidth();x++) {
if (Math.abs(c.get(x,y)-c1.get(x,y))>0) diff++;
}
}
return diff;
}
// compute cotangent of the 2 vectors u and v
private double cotangent(int ux,int uy,int uz, int vx,int vy,int vz) {
double uv = ux*vx + uy*vy + uz*vz;
int vpx = uz*vy - uy*vz;
int vpy = ux*vz - uz*vx;
int vpz = ux*vy - uy*vx;
double vp = Math.sqrt( vpx*vpx + vpy*vpy + vpz*vpz );
if (vp==0) return Double.MAX_VALUE;
return Math.abs(uv)/vp;
}
// compute area of a 3D triangle
private double area(int xa,int ya,int va,int xb,int yb,int vb,int xc,int yc,int vc) {
int ux = xa-xb;
int uy = ya-yb;
int uz = va-vb;
int vx = xc-xb;
int vy = yc-yb;
int vz = vc-vb;
int vpx = uz*vy - uy*vz;
int vpy = ux*vz - uz*vx;
int vpz = ux*vy - uy*vx;
double area = Math.sqrt(vpx*vpx + vpy*vpy + vpz*vpz)/2;
return area;
}
// Laplace-Beltrami operator (divergence of the gradient)
public ByteProcessor LaplaceBeltramiFilter(ByteProcessor c, double dt) {
int width = c.getWidth();
int height = c.getHeight();
int n=8;
int[] dx = new int[] {-1,0,1,1,1,0,-1,-1};
int[] dy = new int[] {-1,-1,-1,0,1,1,1,0};
ByteProcessor c2 = new ByteProcessor(width,height);
// For each pixel of the image
for (int y=0; y<height; y++) {
for (int x=0; x<width; x++) {
int z = c.get(x, y);
c2.set(x, y, z);
// Laplace-Beltrami Operator
// -------------------------
//
// L[i] = 1/2A * Sum[ ( cotan(Alphaij) + cotan(Betaij) ) * ( V(j) - V(i) ) ]
// j in N(i)
//
// V(x): Value (intensity,height) of pixel x
// N(x) : neighboors of pixel x
// A : Global Area (sum) of surrounding triangles
// Alphaij, Betaij : Opposite angles of triangles containing the edge (i,j)
//
double laplace=0; double area=0;
for(int i=0;i<n;i++) {
// previous vertex
int xp = x+dx[(i+n-1) % n];
if (xp<0 || xp>=width) continue;
int yp = y+dy[(i+n-1) % n];
if (yp<0 || yp>=height) continue;
int zp = c.get(xp, yp);
// actual vertex
int xk = x+dx[i];
if (xk<0 || xk>=width) continue;
int yk = y+dy[i];
if (yk<0 || yk>=height) continue;
int zk = c.get(xk, yk);
// next vertex
int xn = x+dx[(i+1) % n];
if (xn<0 || xn>=width) continue;
int yn = y+dy[(i+1) % n];
if (yn<0 || yn>=height) continue;
int zn = c.get(xn, yn);
// cotangent of opposite angles of the 2 triangles
double cotgt_alpha = cotangent(x-xp,y-yp,z-zp, xk-xp,yk-yp,zk-zp);
double cotgt_beta = cotangent(x-xn,y-yn,z-zn, xk-xn,yk-yn,zk-zn);
// area of the 2 triangles
double area_alpha = area(x,y,z, xp,yp,zp, xk,yk,zk);
double area_beta = area(x,y,z, xn,yn,zn, xk,yk,zk);
// addd to iteration variable
laplace += (cotgt_alpha+cotgt_beta)*(zk-z);
area += area_alpha+area_beta;
}
laplace/=2*area;
// Compute new value:
//
// dI/dt ~= ( I(t+dt) - I(t) ) / dt
// ==> I(t+dt) ~= I(t) + dt * (dI/dt) ~= I(t) + dt * L[I(t)]
int v=(int)Math.rint( c.get(x, y) + dt*laplace );
if (v<0) v=0;
if (v>255) v=255;
c2.set(x, y, v);
}
}
return c2;
}
} |
