// Catalano Imaging Library
// The Catalano Framework
//
// Copyright © Diego Catalano, 2012-2016
// diego.catalano at live.com
//
// Copyright © Arlington, 2013
// Copyright © Saulo, 2013
// scsm at ecmp.poli.br
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
//
package Catalano.Imaging.Tools;
import Catalano.Core.DoublePoint;
import Catalano.Imaging.FastBitmap;
/**
* Image Moments.
* Moment invariants are properties of connected regions in binary images that are invariant to translation, rotation and scale.
* They are useful because they define a simply calculated set of region properties that can be used for shape classification and part recognition.
*
* @see HuMoments
* @see ZernikeMoments
* @author Diego Catalano
*/
public final class ImageMoments {
/**
* Don't let anyone instantiate this class.
*/
private ImageMoments() {}
/**
* Compute Raw moment.
* @param fastBitmap Image.
* @param p Order p.
* @param q Order q.
* @return Raw moment.
*/
public static double getRawMoment(FastBitmap fastBitmap, int p, int q) {
int width = fastBitmap.getWidth();
int height = fastBitmap.getHeight();
double m = 0;
for (int i = 0; i < height; i++) {
for (int j = 0; j < width; j++) {
m += Math.pow(i, p) * Math.pow(j, q) * fastBitmap.getGray(i, j);
}
}
return m;
}
/**
* Compute central moment.
* @param fastBitmap Image.
* @param p Order p.
* @param q Order q.
* @return Central moment.
*/
public static double getCentralMoment(FastBitmap fastBitmap, int p, int q) {
DoublePoint centroid = getCentroid(fastBitmap);
return getCentralMoment(fastBitmap, p, q, centroid);
}
/**
* Compute central moment.
* @param fastBitmap Image.
* @param p Order p.
* @param q Order q.
* @param centroid Centroid.
* @return Central moment.
*/
public static double getCentralMoment(FastBitmap fastBitmap, int p, int q, DoublePoint centroid) {
int width = fastBitmap.getWidth();
int height = fastBitmap.getHeight();
double mc = 0;
for (int i = 0; i < height; i++) {
for (int j = 0; j < width; j++) {
mc += Math.pow((i - centroid.x), p) * Math.pow((j - centroid.y), q) * fastBitmap.getGray(i, j);
}
}
return mc;
}
/**
* Compute centroid components.
* @param fastBitmap Image.
* @return Centroid.
*/
public static DoublePoint getCentroid(FastBitmap fastBitmap){
double m00 = ImageMoments.getRawMoment(fastBitmap, 0, 0);
return getCentroid(fastBitmap, m00);
}
/**
* Compute centroid components.
* @param fastBitmap Image.
* @param m00 M00.
* @return Centroid.
*/
public static DoublePoint getCentroid(FastBitmap fastBitmap, double m00){
double m10 = ImageMoments.getRawMoment(fastBitmap, 1, 0);
double m01 = ImageMoments.getRawMoment(fastBitmap, 0, 1);
double x0 = m10 / m00;
double y0 = m01 / m00;
return new DoublePoint(x0, y0);
}
/**
* Compute Covariance XY.
* @param fastBitmap Image.
* @param p Order p.
* @param q Order q.
* @return Covariance.
*/
public static double getCovarianceXY(FastBitmap fastBitmap, int p, int q) {
double mc00 = ImageMoments.getCentralMoment(fastBitmap, 0, 0);
double mc11 = ImageMoments.getCentralMoment(fastBitmap, 1, 1);
return mc11 / mc00;
}
/**
* Compute variance X.
* @param fastBitmap Image.
* @param p Order p.
* @param q Order q.
* @return Variance X.
*/
public static double getVarianceX(FastBitmap fastBitmap, int p, int q) {
double mc00 = ImageMoments.getCentralMoment(fastBitmap, 0, 0);
double mc20 = ImageMoments.getCentralMoment(fastBitmap, 2, 0);
return mc20 / mc00;
}
/**
* Compute variance Y.
* @param fastBitmap Image.
* @param p Order p.
* @param q Order q.
* @return Variace Y.
*/
public static double getVarianceY(FastBitmap fastBitmap, int p, int q) {
double mc00 = ImageMoments.getCentralMoment(fastBitmap, 0, 0);
double mc02 = ImageMoments.getCentralMoment(fastBitmap, 0, 2);
return mc02 / mc00;
}
/**
* Compute orientation in radians.
* @param fastBitmap Image.
* @return Orientation from the image.
*/
public static double getOrientation(FastBitmap fastBitmap){
DoublePoint centroid = getCentroid(fastBitmap);
double cm11 = ImageMoments.getCentralMoment(fastBitmap, 1, 1, centroid);
double cm20 = ImageMoments.getCentralMoment(fastBitmap, 2, 0, centroid);
double cm02 = ImageMoments.getCentralMoment(fastBitmap, 0, 2, centroid);
return 0.5 * Math.atan2(cm20 - cm02, 2 * cm11);
}
/**
* Compute projection skewness.
* @param fastBitmap Image.
* @return Projection skewness.
*/
public static DoublePoint getProjectionSkewness(FastBitmap fastBitmap){
DoublePoint centroid = getCentroid(fastBitmap);
return getProjectionSkewness(fastBitmap, centroid);
}
/**
* Compute projection skewness.
* @param fastBitmap Image.
* @param centroid Centroid.
* @return Projection skewness.
*/
public static DoublePoint getProjectionSkewness(FastBitmap fastBitmap, DoublePoint centroid){
double u30 = ImageMoments.getCentralMoment(fastBitmap, 3, 0, centroid);
double u03 = ImageMoments.getCentralMoment(fastBitmap, 0, 3, centroid);
double u20 = ImageMoments.getCentralMoment(fastBitmap, 2, 0, centroid);
double u02 = ImageMoments.getCentralMoment(fastBitmap, 0, 2, centroid);
double skx = u30 / Math.pow(u20, 1.5);
double sky = u03 / Math.pow(u02, 1.5);
return new DoublePoint(skx, sky);
}
/**
* Compute projection kurtosis.
* @param fastBitmap Image.
* @return Projection kurtorsis.
*/
public static DoublePoint getProjectionKurtosis(FastBitmap fastBitmap){
DoublePoint centroid = getCentroid(fastBitmap);
return getProjectionKurtosis(fastBitmap, centroid);
}
/**
* Compute projection kurtosis.
* @param fastBitmap Image.
* @param centroid Centroid.
* @return Projection kurtorsis.
*/
public static DoublePoint getProjectionKurtosis(FastBitmap fastBitmap, DoublePoint centroid){
double u40 = ImageMoments.getCentralMoment(fastBitmap, 4, 0, centroid);
double u20 = ImageMoments.getCentralMoment(fastBitmap, 2, 0, centroid);
double u04 = ImageMoments.getCentralMoment(fastBitmap, 0, 4, centroid);
double u02 = ImageMoments.getCentralMoment(fastBitmap, 0, 2, centroid);
double skx = (u40 / Math.pow(u20, 2)) - 3;
double sky = (u04 / Math.pow(u02, 2)) - 3;
return new DoublePoint(skx, sky);
}
/**
* Normalized Central Moment.
* @param fastBitmap Image.
* @param p Order p.
* @param q Order q.
* @return Normalized central moment.
*/
public static double getNormalizedCentralMoment(FastBitmap fastBitmap, int p, int q) {
double m00 = ImageMoments.getCentralMoment(fastBitmap, 0, 0);
DoublePoint centroid = getCentroid(fastBitmap, m00);
return getNormalizedCentralMoment(fastBitmap, p, q, centroid, m00);
}
/**
* Normalized Central Moment.
* @param fastBitmap Image.
* @param p Order p.
* @param q Order q.
* @param centroid Centroid.
* @param m00 M00 moment value.
* @return Normalized central moment.
*/
public static double getNormalizedCentralMoment(FastBitmap fastBitmap, int p, int q, DoublePoint centroid, double m00) {
double gama = ((p + q) / 2) + 1;
double mpq = ImageMoments.getCentralMoment(fastBitmap, p, q, centroid);
double m00gama = Math.pow(m00, gama);
if(m00gama == 0) return 0;
return mpq / m00gama;
}
/**
* Abo-Zaid Normalized Central Moment.
* @param fastBitmap Image.
* @param p Order p.
* @param q Order q.
* @return Abo-Zaid normalized central moment.
*/
public static double getZaidNormalizedCentralMoment(FastBitmap fastBitmap, int p, int q){
double mpq = ImageMoments.getCentralMoment(fastBitmap, p, q);
double m00 = ImageMoments.getCentralMoment(fastBitmap, 0, 0);
double m20 = ImageMoments.getCentralMoment(fastBitmap, 2, 0);
double m02 = ImageMoments.getCentralMoment(fastBitmap, 0, 2);
return mpq * (1 / m00)
* Math.pow(m00 / (m20 + m02), (p+q) / 2);
}
}
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