/**
 * Copyright (c) 2011, The University of Southampton and the individual contributors.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without modification,
 * are permitted provided that the following conditions are met:
 *
 *   *  Redistributions of source code must retain the above copyright notice,
 *      this list of conditions and the following disclaimer.
 *
 *   *  Redistributions in binary form must reproduce the above copyright notice,
 *      this list of conditions and the following disclaimer in the documentation
 *      and/or other materials provided with the distribution.
 *
 *   *  Neither the name of the University of Southampton nor the names of its
 *      contributors may be used to endorse or promote products derived from this
 *      software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
 * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
package org.openimaj.math.geometry.shape;

import java.util.ArrayList;
import java.util.List;

import org.openimaj.citation.annotation.Reference;
import org.openimaj.citation.annotation.ReferenceType;
import org.openimaj.citation.annotation.References;
import org.openimaj.math.geometry.point.Point2d;
import org.openimaj.math.geometry.point.Point2dImpl;
import org.openimaj.math.geometry.point.PointList;
import org.openimaj.math.geometry.shape.algorithm.GeneralisedProcrustesAnalysis;
import org.openimaj.math.geometry.shape.algorithm.ProcrustesAnalysis;
import org.openimaj.math.matrix.algorithm.pca.PrincipalComponentAnalysis;
import org.openimaj.math.matrix.algorithm.pca.PrincipalComponentAnalysis.ComponentSelector;
import org.openimaj.math.matrix.algorithm.pca.SvdPrincipalComponentAnalysis;
import org.openimaj.util.pair.IndependentPair;

import Jama.Matrix;

/**
 * A 2d point distribution model learnt from a set of {@link PointList}s with
 * corresponding points (the ith point in each {@link PointList} is the same
 * landmark).
 *
 * The pdm models the mean shape and the variance from the mean of the top N
 * principal components. The model is generative and can generate new shapes
 * from a scaling vector. To ensure that newly generated shapes are plausible,
 * scaling vectors have {@link Constraint}s applied to them.
 *
 * @author Jonathon Hare (jsh2@ecs.soton.ac.uk)
 *
 */
@References(references = {
                @Reference(
                                author = { "Cootes, T. F.", "Taylor, C. J." },
                                title = "Statistical Models of Appearance for Computer Vision",
                                type = ReferenceType.Unpublished,
                                month = "October",
                                year = "2001",
                                url = "http://isbe.man.ac.uk/~bim/Models/app_model.ps.gz"
                ),
                @Reference(
                                type = ReferenceType.Inproceedings,
                                author = { "C. J. Taylor", "D. H. Cooper", "J. Graham" },
                                title = "Training models of shape from sets of examples",
                                year = "1992",
                                booktitle = "Proc. BMVC92, Springer-Verlag",
                                pages = { "9", "", "18" }
                )
})
public class PointDistributionModel {
        /**
         * Interface for modelling constraints applied to the scaling vector of
         * {@link PointDistributionModel}s so that generated models are plausible.
         *
         * @author Jonathon Hare (jsh2@ecs.soton.ac.uk)
         */
        public interface Constraint {
                /**
                 * Apply constraints to a scaling vector so that it will generated a
                 * plausible model and return the new constrained vector.
                 *
                 * @param scaling
                 *            the scaling vector to constrain
                 * @param lamda
                 *            the eigenvalues of the {@link PointDistributionModel}
                 * @return the constrained scaling vector
                 */
                public double[] apply(double[] scaling, double[] lamda);
        }

        /**
         * A constraint that does nothing.
         *
         * @author Jonathon Hare (jsh2@ecs.soton.ac.uk)
         *
         */
        public static class NullConstraint implements Constraint {
                @Override
                public double[] apply(double[] in, double[] lamda) {
                        return in;
                }
        }

        /**
         * A constraint that ensures that each individual element of the scaling
         * vector is within +/- x standard deviations of the model.
         *
         * @author Jonathon Hare (jsh2@ecs.soton.ac.uk)
         *
         */
        public static class BoxConstraint implements Constraint {
                double multiplier;

                /**
                 * Construct with the given multiplier of the standard deviation.
                 *
                 * @param multiplier
                 */
                public BoxConstraint(double multiplier) {
                        this.multiplier = multiplier;
                }

                @Override
                public double[] apply(double[] in, double[] lamda) {
                        final double[] out = new double[in.length];

                        for (int i = 0; i < in.length; i++) {
                                final double w = multiplier * Math.sqrt(lamda[i]);
                                out[i] = in[i] > w ? w : in[i] < -w ? -w : in[i];
                        }

                        return out;
                }
        }

        /**
         * Constrain the scaling vector to a hyper-ellipsoid.
         *
         * @author Jonathon Hare (jsh2@ecs.soton.ac.uk)
         *
         */
        public static class EllipsoidConstraint implements Constraint {
                double dmax;

                /**
                 * Construct with the given maximum normalised ellipsoid radius.
                 *
                 * @param dmax
                 */
                public EllipsoidConstraint(double dmax) {
                        this.dmax = dmax;
                }

                @Override
                public double[] apply(double[] in, double[] lamda) {
                        double dmsq = 0;
                        for (int i = 0; i < in.length; i++) {
                                dmsq += in[i] * in[i] / lamda[i];
                        }

                        if (dmsq < dmax * dmax) {
                                return in;
                        }

                        final double sc = dmax / Math.sqrt(dmsq);
                        final double[] out = new double[in.length];
                        for (int i = 0; i < in.length; i++) {
                                out[i] = in[i] * sc;
                        }

                        return out;
                }
        }

        protected Constraint constraint;
        protected PrincipalComponentAnalysis pc;
        protected PointList mean;
        protected int numComponents;
        protected int maxIter = 100;

        /**
         * Construct a {@link PointDistributionModel} from the given data with a
         * {@link NullConstraint}.
         *
         * @param data
         */
        public PointDistributionModel(List<PointList> data) {
                this(new NullConstraint(), data);
        }

        /**
         * Construct a {@link PointDistributionModel} from the given data and
         * {@link Constraint}.
         *
         * @param constraint
         * @param data
         */
        public PointDistributionModel(Constraint constraint, List<PointList> data) {
                this.constraint = constraint;

                // align
                mean = GeneralisedProcrustesAnalysis.alignPoints(data, 5, 10);

                // build data matrix
                final Matrix m = buildDataMatrix(data);

                // perform pca
                this.pc = new SvdPrincipalComponentAnalysis();
                pc.learnBasis(m);

                numComponents = this.pc.getEigenValues().length;
        }

        private Matrix buildDataMatrix(PointList data) {
                final List<PointList> pls = new ArrayList<PointList>(1);
                pls.add(data);
                return buildDataMatrix(pls);
        }

        private Matrix buildDataMatrix(List<PointList> data) {
                final int nData = data.size();
                final int nPoints = data.get(0).size();

                final Matrix m = new Matrix(nData, nPoints * 2);
                final double[][] mData = m.getArray();

                for (int i = 0; i < nData; i++) {
                        final PointList pts = data.get(i);
                        for (int j = 0, k = 0; k < nPoints; j += 2, k++) {
                                final Point2d pt = pts.points.get(k);

                                mData[i][j] = pt.getX();
                                mData[i][j + 1] = pt.getY();
                        }
                }

                return m;
        }

        /**
         * @return the mean shape
         */
        public PointList getMean() {
                return mean;
        }

        /**
         * Set the number of components of the PDM
         *
         * @param n
         *            number of components
         */
        public void setNumComponents(int n) {
                pc.selectSubset(n);
                numComponents = this.pc.getEigenValues().length;
        }

        /**
         * Set the number of components of the PDM using a {@link ComponentSelector}
         * .
         *
         * @param selector
         *            the {@link ComponentSelector} to apply.
         */
        public void setNumComponents(ComponentSelector selector) {
                pc.selectSubset(selector);
                numComponents = this.pc.getEigenValues().length;
        }

        /**
         * Generate a plausible new shape from the scaling vector. The scaling
         * vector is constrained by the underlying {@link Constraint} before being
         * used to generate the model.
         *
         * @param scaling
         *            scaling vector.
         * @return a new shape
         */
        public PointList generateNewShape(double[] scaling) {
                final PointList newShape = new PointList();

                final double[] pts = pc.generate(constraint.apply(scaling, pc.getEigenValues()));

                for (int i = 0; i < pts.length; i += 2) {
                        final float x = (float) pts[i];
                        final float y = (float) pts[i + 1];

                        newShape.points.add(new Point2dImpl(x, y));
                }

                return newShape;
        }

        /**
         * Compute the standard deviations of the shape components, multiplied by
         * the given value.
         *
         * @param multiplier
         *            the multiplier
         * @return the multiplied standard deviations
         */
        public double[] getStandardDeviations(double multiplier) {
                final double[] rngs = pc.getStandardDeviations();

                for (int i = 0; i < rngs.length; i++) {
                        rngs[i] = rngs[i] * multiplier;
                }

                return rngs;
        }

        /**
         * Determine the best parameters of the PDM for the given model.
         *
         * @param observed
         *            the observed model.
         * @return the parameters that best fit the model.
         */
        public IndependentPair<Matrix, double[]> fitModel(PointList observed) {
                double[] model = new double[numComponents];
                double delta = 1.0;
                Matrix pose = null;

                final ProcrustesAnalysis pa = new ProcrustesAnalysis(observed);
                int count = 0;
                while (delta > 1e-6 && count++ < maxIter) {
                        final PointList instance = this.generateNewShape(model);

                        pose = pa.align(instance);

                        final PointList projected = observed.transform(pose.inverse());

                        // TODO: tangent space projection???

                        final Matrix y = buildDataMatrix(projected);
                        final Matrix xbar = new Matrix(new double[][] { pc.getMean() });
                        double[] newModel = (y.minus(xbar)).times(pc.getBasis()).getArray()[0];

                        newModel = constraint.apply(newModel, pc.getEigenValues());

                        delta = 0;
                        for (int i = 0; i < newModel.length; i++)
                                delta += (newModel[i] - model[i]) * (newModel[i] - model[i]);
                        delta = Math.sqrt(delta);

                        model = newModel;
                }

                return new IndependentPair<Matrix, double[]>(pose, model);
        }
}