/**
 * 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
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package org.openimaj.math.model.fit;

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

import org.openimaj.math.model.EstimatableModel;
import org.openimaj.math.model.fit.residuals.ResidualCalculator;
import org.openimaj.math.util.distance.DistanceCheck;
import org.openimaj.math.util.distance.ThresholdDistanceCheck;
import org.openimaj.util.CollectionSampler;
import org.openimaj.util.UniformSampler;
import org.openimaj.util.pair.IndependentPair;

/**
 * The RANSAC Algorithm (RANdom SAmple Consensus)
 * <p>
 * For fitting noisy data consisting of inliers and outliers to a model.
 * </p>
 * <p>
 * Assume: M data items required to estimate parameter x N data items in total
 * </p>
 * <p>
 * 1.) select M data items at random <br>
 * </br> 2.) estimate parameter x <br>
 * </br> 3.) find how many of the N data items fit (i.e. have an error less than
 * a threshold or pass some check) x within tolerence tol, call this K <br>
 * </br> 4.) if K is large enough (bigger than numItems) accept x and exit with
 * success <br>
 * </br> 5.) repeat 1..4 nIter times <br>
 * </br> 6.) fail - no good x fit of data
 * </p>
 * <p>
 * In this implementation, the conditions that control the iterations are
 * configurable. In addition, the best matching model is always stored, even if
 * the fitData() method returns false.
 *
 * @author Jonathon Hare (jsh2@ecs.soton.ac.uk)
 *
 * @param <I>
 *            type of independent data
 * @param <D>
 *            type of dependent data
 * @param <M>
 *            concrete type of model learned
 */
public class RANSAC<I, D, M extends EstimatableModel<I, D>> implements RobustModelFitting<I, D, M> {
        /**
         * Interface for classes that can control RANSAC iterations
         */
        public static interface StoppingCondition {
                /**
                 * Initialise the stopping condition if necessary. Return false if the
                 * initialisation cannot be performed and RANSAC should fail
                 *
                 * @param data
                 *            The data being fitted
                 * @param model
                 *            The model to fit
                 * @return true if initialisation is successful, false otherwise.
                 */
                public abstract boolean init(final List<?> data, EstimatableModel<?, ?> model);

                /**
                 * Should we stop iterating and return the model?
                 *
                 * @param numInliers
                 *            number of inliers in this iteration
                 * @return true if the model is good and iterations should stop
                 */
                public abstract boolean shouldStopIterations(int numInliers);

                /**
                 * Should the model be considered to fit after the final iteration has
                 * passed?
                 *
                 * @param numInliers
                 *            number of inliers in the final model
                 * @return true if the model fits, false otherwise
                 */
                public abstract boolean finalFitCondition(int numInliers);
        }

        /**
         * Stopping condition that tests the number of matches against a threshold.
         * If the number exceeds the threshold, then the model is considered to fit.
         */
        public static class NumberInliersStoppingCondition implements StoppingCondition {
                int limit;

                /**
                 * Construct the stopping condition with the given threshold on the
                 * number of data points which must match for a model to be considered a
                 * fit.
                 *
                 * @param limit
                 *            the threshold
                 */
                public NumberInliersStoppingCondition(int limit) {
                        this.limit = limit;
                }

                @Override
                public boolean init(List<?> data, EstimatableModel<?, ?> model) {
                        if (limit < model.numItemsToEstimate()) {
                                limit = model.numItemsToEstimate();
                        }

                        if (data.size() < limit)
                                return false;
                        return true;
                }

                @Override
                public boolean shouldStopIterations(int numInliers) {
                        return numInliers >= limit; // stop if there are more inliers than
                        // our limit
                }

                @Override
                public boolean finalFitCondition(int numInliers) {
                        return numInliers >= limit;
                }
        }

        /**
         * Stopping condition that tests the number of matches against a percentage
         * threshold of the whole data. If the number exceeds the threshold, then
         * the model is considered to fit.
         */
        public static class PercentageInliersStoppingCondition extends NumberInliersStoppingCondition {
                double percentageLimit;

                /**
                 * Construct the stopping condition with the given percentage threshold
                 * on the number of data points which must match for a model to be
                 * considered a fit.
                 *
                 * @param percentageLimit
                 *            the percentage threshold
                 */
                public PercentageInliersStoppingCondition(double percentageLimit) {
                        super(0);
                        this.percentageLimit = percentageLimit;
                }

                @Override
                public boolean init(List<?> data, EstimatableModel<?, ?> model) {
                        this.limit = (int) Math.rint(percentageLimit * data.size());
                        return super.init(data, model);
                }
        }

        /**
         * Stopping condition that tests the number of matches against a percentage
         * threshold of the whole data. If the number exceeds the threshold, then
         * the model is considered to fit.
         */
        public static class ProbabilisticMinInliersStoppingCondition implements StoppingCondition {
                private static final double DEFAULT_INLIER_IS_BAD_PROBABILITY = 0.1;
                private static final double DEFAULT_PERCENTAGE_INLIERS = 0.25;
                private double inlierIsBadProbability;
                private double desiredErrorProbability;
                private double percentageInliers;

                private int numItemsToEstimate;
                private int iteration = 0;
                private int limit;
                private int maxInliers = 0;
                private double currentProb;
                private int numDataItems;

                /**
                 * Default constructor.
                 *
                 * @param desiredErrorProbability
                 *            The desired error rate
                 * @param inlierIsBadProbability
                 *            The probability an inlier is bad
                 * @param percentageInliers
                 *            The percentage of inliers in the data
                 */
                public ProbabilisticMinInliersStoppingCondition(double desiredErrorProbability, double inlierIsBadProbability,
                                double percentageInliers)
                {
                        this.desiredErrorProbability = desiredErrorProbability;
                        this.inlierIsBadProbability = inlierIsBadProbability;
                        this.percentageInliers = percentageInliers;
                }

                /**
                 * Constructor with defaults for bad inlier probability and percentage
                 * inliers.
                 *
                 * @param desiredErrorProbability
                 *            The desired error rate
                 */
                public ProbabilisticMinInliersStoppingCondition(double desiredErrorProbability) {
                        this(desiredErrorProbability, DEFAULT_INLIER_IS_BAD_PROBABILITY, DEFAULT_PERCENTAGE_INLIERS);
                }

                @Override
                public boolean init(List<?> data, EstimatableModel<?, ?> model) {
                        numItemsToEstimate = model.numItemsToEstimate();
                        numDataItems = data.size();
                        this.limit = calculateMinInliers();
                        this.iteration = 0;
                        this.currentProb = 1.0;
                        this.maxInliers = 0;

                        return true;
                }

                @Override
                public boolean finalFitCondition(int numInliers) {
                        return numInliers >= limit;
                }

                private int calculateMinInliers() {
                        double pi, sum;
                        int i, j;

                        for (j = numItemsToEstimate + 1; j <= numDataItems; j++)
                        {
                                sum = 0;
                                for (i = j; i <= numDataItems; i++)
                                {
                                        pi = (i - numItemsToEstimate) * Math.log(inlierIsBadProbability)
                                                        + (numDataItems - i + numItemsToEstimate) * Math.log(1.0 - inlierIsBadProbability) +
                                                        log_factorial(numDataItems - numItemsToEstimate) - log_factorial(i - numItemsToEstimate)
                                                        - log_factorial(numDataItems - i);
                                        /*
                                         * Last three terms above are equivalent to log( n-m choose
                                         * i-m )
                                         */
                                        sum += Math.exp(pi);
                                }
                                if (sum < desiredErrorProbability)
                                        break;
                        }
                        return j;
                }

                private double log_factorial(int n) {
                        double f = 0;
                        int i;

                        for (i = 1; i <= n; i++)
                                f += Math.log(i);

                        return f;
                }

                @Override
                public boolean shouldStopIterations(int numInliers) {

                        if (numInliers > maxInliers) {
                                maxInliers = numInliers;
                                percentageInliers = (double) maxInliers / numDataItems;

                                // System.err.format("Updated maxInliers: %d\n", maxInliers);
                        }
                        currentProb = Math.pow(1.0 - Math.pow(percentageInliers, numItemsToEstimate), ++iteration);
                        return currentProb <= this.desiredErrorProbability;
                }
        }

        /**
         * Stopping condition that allows the RANSAC algorithm to run until all the
         * iterations have been exhausted. The fitData method will return true if
         * there are at least as many inliers as datapoints required to estimate the
         * model, and the model will be the one from the iteration that had the most
         * inliers.
         */
        public static class BestFitStoppingCondition implements StoppingCondition {
                int required;

                @Override
                public boolean init(List<?> data, EstimatableModel<?, ?> model) {
                        required = model.numItemsToEstimate();
                        return true;
                }

                @Override
                public boolean shouldStopIterations(int numInliers) {
                        return false; // just iterate until the end
                }

                @Override
                public boolean finalFitCondition(int numInliers) {
                        return numInliers > required; // accept the best result as a good
                        // fit if there are enough inliers
                }
        }

        protected M model;
        protected ResidualCalculator<I, D, M> errorModel;
        protected DistanceCheck dc;

        protected int nIter;
        protected boolean improveEstimate;
        protected List<IndependentPair<I, D>> inliers;
        protected List<IndependentPair<I, D>> outliers;
        protected List<IndependentPair<I, D>> bestModelInliers;
        protected List<IndependentPair<I, D>> bestModelOutliers;
        protected StoppingCondition stoppingCondition;
        protected List<? extends IndependentPair<I, D>> modelConstructionData;
        protected CollectionSampler<IndependentPair<I, D>> sampler;

        /**
         * Create a RANSAC object with uniform random sampling for creating the
         * subsets
         *
         * @param model
         *            Model object with which to fit data
         * @param errorModel
         *            object to compute the error of the model
         * @param errorThreshold
         *            the threshold below which error is deemed acceptable for a fit
         * @param nIterations
         *            Maximum number of allowed iterations (L)
         * @param stoppingCondition
         *            the stopping condition
         * @param impEst
         *            True if we want to perform a final fitting of the model with
         *            all inliers, false otherwise
         */
        public RANSAC(M model, ResidualCalculator<I, D, M> errorModel,
                        double errorThreshold, int nIterations,
                        StoppingCondition stoppingCondition, boolean impEst)
        {
                this(model, errorModel, new ThresholdDistanceCheck(errorThreshold), nIterations, stoppingCondition, impEst);
        }

        /**
         * Create a RANSAC object with uniform random sampling for creating the
         * subsets
         *
         * @param model
         *            Model object with which to fit data
         * @param errorModel
         *            object to compute the error of the model
         * @param dc
         *            the distance check that tests whether a point with given error
         *            from the error model should be considered an inlier
         * @param nIterations
         *            Maximum number of allowed iterations (L)
         * @param stoppingCondition
         *            the stopping condition
         * @param impEst
         *            True if we want to perform a final fitting of the model with
         *            all inliers, false otherwise
         */
        public RANSAC(M model, ResidualCalculator<I, D, M> errorModel,
                        DistanceCheck dc, int nIterations,
                        StoppingCondition stoppingCondition, boolean impEst)
        {
                this(model, errorModel, dc, nIterations, stoppingCondition, impEst, new UniformSampler<IndependentPair<I, D>>());
        }

        /**
         * Create a RANSAC object
         *
         * @param model
         *            Model object with which to fit data
         * @param errorModel
         *            object to compute the error of the model
         * @param errorThreshold
         *            the threshold below which error is deemed acceptable for a fit
         * @param nIterations
         *            Maximum number of allowed iterations (L)
         * @param stoppingCondition
         *            the stopping condition
         * @param impEst
         *            True if we want to perform a final fitting of the model with
         *            all inliers, false otherwise
         * @param sampler
         *            the sampling algorithm for selecting random subsets
         */
        public RANSAC(M model, ResidualCalculator<I, D, M> errorModel,
                        double errorThreshold, int nIterations,
                        StoppingCondition stoppingCondition, boolean impEst, CollectionSampler<IndependentPair<I, D>> sampler)
        {
                this(model, errorModel, new ThresholdDistanceCheck(errorThreshold), nIterations, stoppingCondition, impEst,
                                sampler);
        }

        /**
         * Create a RANSAC object
         *
         * @param model
         *            Model object with which to fit data
         * @param errorModel
         *            object to compute the error of the model
         * @param dc
         *            the distance check that tests whether a point with given error
         *            from the error model should be considered an inlier
         * @param nIterations
         *            Maximum number of allowed iterations (L)
         * @param stoppingCondition
         *            the stopping condition
         * @param impEst
         *            True if we want to perform a final fitting of the model with
         *            all inliers, false otherwise
         * @param sampler
         *            the sampling algorithm for selecting random subsets
         */
        public RANSAC(M model, ResidualCalculator<I, D, M> errorModel,
                        DistanceCheck dc, int nIterations,
                        StoppingCondition stoppingCondition, boolean impEst, CollectionSampler<IndependentPair<I, D>> sampler)
        {
                this.stoppingCondition = stoppingCondition;
                this.model = model;
                this.errorModel = errorModel;
                this.dc = dc;
                nIter = nIterations;
                improveEstimate = impEst;

                inliers = new ArrayList<IndependentPair<I, D>>();
                outliers = new ArrayList<IndependentPair<I, D>>();
                this.sampler = sampler;
        }

        @Override
        public boolean fitData(final List<? extends IndependentPair<I, D>> data)
        {
                int l;
                final int M = model.numItemsToEstimate();

                bestModelInliers = null;
                bestModelOutliers = null;

                if (data.size() < M || !stoppingCondition.init(data, model)) {
                        return false; // there are not enough points to create a model, or
                        // init failed
                }

                sampler.setCollection(data);

                for (l = 0; l < nIter; l++) {
                        // 1
                        final List<? extends IndependentPair<I, D>> rnd = sampler.sample(M);
                        this.setModelConstructionData(rnd);

                        // 2
                        if (!model.estimate(rnd))
                                continue; // bad estimate

                        errorModel.setModel(model);

                        // 3
                        int K = 0;
                        inliers.clear();
                        outliers.clear();
                        for (final IndependentPair<I, D> dp : data) {
                                if (dc.check(errorModel.computeResidual(dp)))
                                {
                                        K++;
                                        inliers.add(dp);
                                } else {
                                        outliers.add(dp);
                                }
                        }

                        if (bestModelInliers == null || inliers.size() >= bestModelInliers.size()) {
                                // copy
                                bestModelInliers = new ArrayList<IndependentPair<I, D>>(inliers);
                                bestModelOutliers = new ArrayList<IndependentPair<I, D>>(outliers);
                        }

                        // 4
                        if (stoppingCondition.shouldStopIterations(K)) {
                                // generate "best" fit from all the iterations
                                inliers = bestModelInliers;
                                outliers = bestModelOutliers;

                                if (improveEstimate) {
                                        if (inliers.size() >= model.numItemsToEstimate())
                                                if (!model.estimate(inliers))
                                                        return false;
                                }
                                final boolean stopping = stoppingCondition.finalFitCondition(inliers.size());
                                // System.err.format("done: %b\n",stopping);
                                return stopping;
                        }
                        // 5
                        // ...repeat...
                }

                // generate "best" fit from all the iterations
                if (bestModelInliers == null) {
                        bestModelInliers = new ArrayList<IndependentPair<I, D>>();
                        bestModelOutliers = new ArrayList<IndependentPair<I, D>>();
                }

                inliers = bestModelInliers;
                outliers = bestModelOutliers;

                if (bestModelInliers.size() >= M)
                        if (!model.estimate(bestModelInliers))
                                return false;

                // 6 - fail
                return stoppingCondition.finalFitCondition(inliers.size());
        }

        @Override
        public List<? extends IndependentPair<I, D>> getInliers()
                        {
                return inliers;
                        }

        @Override
        public List<? extends IndependentPair<I, D>> getOutliers()
                        {
                return outliers;
                        }

        /**
         * @return maximum number of allowed iterations
         */
        public int getMaxIterations() {
                return nIter;
        }

        /**
         * Set the maximum number of allowed iterations
         *
         * @param nIter
         *            maximum number of allowed iterations
         */
        public void setMaxIterations(int nIter) {
                this.nIter = nIter;
        }

        @Override
        public M getModel() {
                return model;
        }

        /**
         * Set the underlying model being fitted
         *
         * @param model
         *            the model
         */
        public void setModel(M model) {
                this.model = model;
        }

        /**
         * @return whether RANSAC should attempt to improve the model using all
         *         inliers as data
         */
        public boolean isImproveEstimate() {
                return improveEstimate;
        }

        /**
         * Set whether RANSAC should attempt to improve the model using all inliers
         * as data
         *
         * @param improveEstimate
         *            should RANSAC attempt to improve the model using all inliers
         *            as data
         */
        public void setImproveEstimate(boolean improveEstimate) {
                this.improveEstimate = improveEstimate;
        }

        /**
         * Set the data used to construct the model
         *
         * @param modelConstructionData
         */
        public void setModelConstructionData(List<? extends IndependentPair<I, D>> modelConstructionData) {
                this.modelConstructionData = modelConstructionData;
        }

        /**
         * @return The data used to construct the model.
         */
        public List<? extends IndependentPair<I, D>> getModelConstructionData() {
                return modelConstructionData;
        }

        @Override
        public int numItemsToEstimate() {
                return model.numItemsToEstimate();
        }
}