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Camera calibration techniques and associated code
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/**
 * 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
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
package org.openimaj.image.camera;

import org.openimaj.math.geometry.point.Point2d;
import org.openimaj.math.geometry.point.Point2dImpl;
import org.openimaj.math.geometry.point.Point3d;
import org.openimaj.math.matrix.MatrixUtils;

import Jama.Matrix;

/**
 * A model of the extrinsic parameters of a pinhole (projective) camera
 * (translation in 3d space, and 3d rotation matrix), coupled with the camera's
 * intrinsic parameters.
 * 
 * @author Jonathon Hare ([email protected])
 */
public class Camera {
	/**
	 * The intrinsic parameters of this camera
	 */
	public CameraIntrinsics intrinsicParameters;

	/**
	 * The rotation of this camera in world coordinates
	 */
	public Matrix rotation;

	/**
	 * The position of this camera in world coordinates
	 */
	public Point3d translation;

	/**
	 * Compute the homography of this camera to the z=0 plane based on it's
	 * parameters: H = KA, where A = [r1 r2 t] and r1 and r2 are the first and
	 * second columns of the rotation matrix, and K is the calibration matrix.
	 * 
	 * @return the camera's homography
	 */
	public Matrix computeHomography() {
		final Matrix A = rotation.copy();
		A.set(0, 2, translation.getX());
		A.set(1, 2, translation.getY());
		A.set(2, 2, translation.getZ());

		final Matrix H = intrinsicParameters.calibrationMatrix.times(A);
		MatrixUtils.times(H, 1.0 / H.get(2, 2));

		return H;
	}

	/**
	 * Project a 2d point (technically a 3d point on the z=0 world plane)
	 * 
	 * @param pt
	 *            the point to project in world coordinates
	 * @return the image coordinates
	 */
	public Point2d project(Point2d pt) {
		final Matrix H = this.computeHomography();

		final Point2d p = pt.transform(H);

		return intrinsicParameters.applyDistortion(p);
	}

	/**
	 * Project a 3d point onto the image plane
	 * 
	 * @param pt
	 *            the point to project in world coordinates
	 * @return the image coordinates
	 */
	public Point2d project(Point3d pt) {
		final Matrix ptm = new Matrix(new double[][] { { pt.getX() }, { pt.getY() }, { pt.getZ() }, { 1 } });
		final double[][] rv = rotation.getArray();
		final Matrix Rt = new Matrix(new double[][] {
				{ rv[0][0], rv[0][1], rv[0][2], translation.getX() },
				{ rv[1][0], rv[1][1], rv[1][2], translation.getY() },
				{ rv[2][0], rv[2][1], rv[2][2], translation.getZ() },
		});
		final Matrix ARt = intrinsicParameters.calibrationMatrix.times(Rt);

		final Matrix pr = ARt.times(ptm);

		final Point2dImpl p = new Point2dImpl(pr.get(0, 0) / pr.get(2, 0), pr.get(1, 0) / pr.get(2, 0));

		return intrinsicParameters.applyDistortion(p);
	}
}