#! /usr/bin/python

import numpy as np
from math import sqrt
from skimage.io import imread
from skimage.color import rgb2gray
from scipy.optimize import minimize
from sklearn.cross_validation import LeaveOneOut

from apriltag import AprilTagDetector
from tag36h11_mosaic import TagMosaic
from projective_math import WeightedLocalHomography, SqExpWeightingFunction
from gp import GaussianProcess, sqexp2D_covariancef



def create_local_homography_object(bandwidth, magnitude, lambda_):
    """
    Helper function for creating WeightedLocalHomography objects
    """
    H = WeightedLocalHomography(SqExpWeightingFunction(bandwidth, magnitude))
    H.regularization_lambda = lambda_
    return H


def local_homography_error(theta, t_src, t_tgt, v_src, v_tgt):
    """
    This is the objective function used for optimizing parameters of
    the `SqExpWeightingFunction` used for local homography fitting

    Parameters:
    -----------
       `theta` = [ `bandwidth`, `magnitude`, `lambda_` ]:
            parameters of the `SqExpWeightingFunction`

    Arguments:
    -----------
        `t_src`: list of training source points
        `t_tgt`: list of training target points
        `v_src`: list of validation source points
        `v_tgt`: list of validation target points
    """
    H = create_local_homography_object(*theta)
    for s, t in zip(t_src, t_tgt):
        H.add_correspondence(s, t)

    v_mapped = np.array([ H.map(s)[:2] for s in v_src ])
    return ((v_mapped - v_tgt)**2).sum(axis=1).mean()


#--------------------------------------
class GPModel(object):
#--------------------------------------
    def __init__(self, points_i, values):
        assert len(points_i) == len(values)

        X = points_i
        S = np.cov(X.T)

        meanV = np.mean(values, axis=0)
        V = values - np.tile(meanV, (len(values), 1))

        self._meanV = meanV
        self._gp_x = GPModel._fit_gp(X, S, V[:,0])
        self._gp_y = GPModel._fit_gp(X, S, V[:,1])


    @staticmethod
    def _fit_gp(X, covX, t):
        xx, xy, yy = covX[0,0], covX[0,1], covX[1,1]

        # Perform hyper-parameter optimization with different
        # initial points and choose the GP with best model evidence
        theta0 = np.array(( t.std(), sqrt(xx), sqrt(yy), xy, 10. ))
        best_gp = GaussianProcess.fit(X, t, sqexp2D_covariancef, theta0)

        for tau in xrange(50, 800, 100):
            theta0 = np.array(( t.std(), tau, tau, 0, 10. ))
            gp = GaussianProcess.fit(X, t, sqexp2D_covariancef, theta0)
            if gp.model_evidence() > best_gp.model_evidence():
                best_gp = gp

        return best_gp


    def predict(self, X):
        V = np.vstack([ self._gp_x.predict(X), self._gp_y.predict(X) ]).T
        return V + np.tile(self._meanV, (len(X), 1))


def process(filename):
    #
    # Conventions:
    # a_i, b_i
    #    are variables in image space, units are pixels
    # a_w, b_w
    #    are variables in world space, units are meters
    #
    print '\n========================================'
    print '  File: ' + filename
    print '========================================\n'

    im = imread(filename)
    im = rgb2gray(im)
    im = (im * 255.).astype(np.uint8)

    tag_mosaic = TagMosaic(0.0254)
    detections = AprilTagDetector().detect(im)
    print '  %d tags detected.' % len(detections)

    #
    # Sort detections by distance to center
    #
    c_i = np.array([im.shape[1], im.shape[0]]) / 2.
    dist = lambda p_i: np.linalg.norm(p_i - c_i)
    closer_to_center = lambda d1, d2: int(dist(d1.c) - dist(d2.c))
    detections.sort(cmp=closer_to_center)

    mosaic_pos = lambda det: tag_mosaic.get_position_meters(det.id)

    det_i = np.array([ d.c for d in detections ])
    det_w = np.array([ mosaic_pos(d) for d in detections ])

    #
    # To learn a weighted local homography, we find the weighting
    # function parameters that minimize reprojection error across
    # leave-one-out validation folds of the data. Since the
    # homography is local at the center, we only use 9 nearest
    # detections to the center
    #
    det_i9 = det_i[:9]
    det_w9 = det_w[:9]

    def local_homography_loocv_error(theta, args):
        src, tgt = args
        errs = [ local_homography_error(theta, src[t_ix], tgt[t_ix], src[v_ix], tgt[v_ix])
                    for t_ix, v_ix in LeaveOneOut(len(src)) ]
        return np.mean(errs)

    def learn_homography_i2w():
        result = minimize( local_homography_loocv_error,
                    x0=[ 50, 1, 1e-3 ],
                    args=[ det_i9, det_w9 ],
                    method='Powell',
                    options={'ftol': 1e-3} )

        print '\nHomography: i->w'
        print '------------------'
        print '  params:', result.x
        print '    rmse: %.6f' % sqrt(result.fun)
        print '\n  Optimization detail:'
        print '  ' + str(result).replace('\n', '\n      ')

        H = create_local_homography_object(*result.x)
        for i, w in zip(det_i9, det_w9):
            H.add_correspondence(i, w)

        return H

    def learn_homography_w2i():
        result = minimize( local_homography_loocv_error,
                    x0=[ 0.0254, 1, 1e-3 ],
                    method='Powell',
                    args=[ det_w9, det_i9 ],
                    options={'ftol': 1e-3} )

        print '\nHomography: w->i'
        print '------------------'
        print '  params:', result.x
        print '    rmse: %.6f' % sqrt(result.fun)
        print '\n  Optimization detail:'
        print '  ' + str(result).replace('\n', '\n      ')

        H = create_local_homography_object(*result.x)
        for w, i in zip(det_w9, det_i9):
            H.add_correspondence(w, i)

        return H

    #
    # We assume that the distortion is zero at the center of
    # the image and we are interesting in the word to image
    # homography at the center of the image. However, we don't
    # know the center of the image in world coordinates.
    # So we follow a procedure as explained below:
    #
    # First, we learn a homography from image to world
    # Next, we find where the image center `c_i` maps to in
    # world coordinates (`c_w`). Finally, we find the local
    # homography `LH0` from world to image at `c_w`
    #
    H_iw = learn_homography_i2w()
    c_i = np.array([im.shape[1], im.shape[0]]) / 2.
    c_w = H_iw.map(c_i)[:2]
    H_wi = learn_homography_w2i()
    LH0 = H_wi.get_homography_at(c_w)

    print '\nHomography at center'
    print '----------------------'
    print '      c_w =', c_w
    print '      c_i =', c_i
    print 'LH0 * c_w =', H_wi.map(c_w)

    #
    # Obtain distortion estimate
    #       detected + undistortion = mapped
    #  (or) undistortion = mapped - detected
    #
    def homogeneous_coords(arr):
        return np.hstack([ arr, np.ones((len(arr), 1)) ])

    mapped_i = LH0.dot(homogeneous_coords(det_w).T).T
    mapped_i = np.array([ p / p[2] for p in mapped_i ])
    mapped_i = mapped_i[:,:2]

    undistortion = mapped_i - det_i # image + undistortion = mapped
    max_distortion = np.max([np.linalg.norm(u) for u in undistortion])
    print '\nMaximum distortion is %.2f pixels' % max_distortion

    #
    # Fit non-parametric model to the observations
    #
    model = GPModel(det_i, undistortion)

    print '\nGP Hyper-parameters'
    print '---------------------'
    print '  x: ', model._gp_x._covf.theta
    print '        log-likelihood: %.4f' % model._gp_x.model_evidence()
    print '  y: ', model._gp_y._covf.theta
    print '        log-likelihood: %.4f' % model._gp_y.model_evidence()
    print ''
    print '  Optimization detail:'
    print '  [ x ]'
    print '  ' + str(model._gp_x.fit_result).replace('\n', '\n      ')
    print '  [ y ]'
    print '  ' + str(model._gp_y.fit_result).replace('\n', '\n      ')

    #
    # Visualization
    #
    from skimage.filters import scharr
    from matplotlib import pyplot as plt

    plt.style.use('ggplot')
    plt.figure(figsize=(16,10))

    #__1__
    plt.subplot(221)
    plt.title(filename.split('/')[-1])
    plt.imshow(im, cmap='gray')
    plt.plot(det_i[:,0], det_i[:,1], 'o')
    for i, d in enumerate(detections):
        plt.text(d.c[0], d.c[1], str(i),
            fontsize=8, color='white', bbox=dict(facecolor='maroon', alpha=0.75))
    plt.grid()
    plt.axis('equal')

    #__2__
    plt.subplot(222)
    plt.title('Non-linear Homography')

    if False:
        plt.imshow(1.-scharr(im), cmap='bone', interpolation='gaussian')

        from collections import defaultdict
        row_groups = defaultdict(list)
        col_groups = defaultdict(list)

        for d in detections:
            row, col = tag_mosaic.get_row(d.id), tag_mosaic.get_col(d.id)
            row_groups[row] += [ d.id ]
            col_groups[col] += [ d.id ]

        for k, v in row_groups.iteritems():
            a = tag_mosaic.get_position_meters(np.min(v))
            b = tag_mosaic.get_position_meters(np.max(v))
            x_coords = np.linspace(a[0], b[0], 100)
            points = np.array([ H_wi.map([x, a[1]]) for x in x_coords ])
            plt.plot(points[:,0], points[:,1], '-',color='#CF4457', linewidth=2)

        for k, v in col_groups.iteritems():
            a = tag_mosaic.get_position_meters(np.min(v))
            b = tag_mosaic.get_position_meters(np.max(v))
            y_coords = np.linspace(a[1], b[1], 100)
            points = np.array([ H_wi.map([a[0], y]) for y in y_coords ])
            plt.plot(points[:,0], points[:,1], '-',color='#CF4457', linewidth=2)

        plt.plot(det_i[:,0], det_i[:,1], 'kx')
        plt.grid()
        plt.axis('equal')

    #__3__
    plt.subplot(223)
    plt.title('Qualitative Estimates')

    for i, d in enumerate(detections):
        plt.text(d.c[0], d.c[1], str(i), fontsize=8, color='#999999')

    X, Y = det_i[:,0], det_i[:,1]
    U, V = undistortion[:,0], undistortion[:,1]
    plt.quiver(X, Y, U, -V, units='dots')
    # plt.quiver(X, Y, U, -V, angles='xy', scale_units='xy', scale=1) # plot exact
    plt.text( 0.5, 0, 'max observed distortion: %.2f px' % max_distortion, color='#CF4457', fontsize=10,
        horizontalalignment='center', verticalalignment='bottom', transform=plt.gca().transAxes)
    plt.gca().invert_yaxis()
    plt.axis('equal')

    #__4__
    plt.subplot(224)
    plt.title('Qualitative Undistortion')
    H, W = im.shape
    grid = np.array([[x, y] for y in xrange(0, H, 80) for x in xrange(0, W, 80)])
    predicted = model.predict(grid)
    X, Y = grid[:,0], grid[:,1]
    U, V = predicted[:,0], predicted[:,1]
    plt.quiver(X, Y, U, -V, units='dots')
    #plt.quiver(X, Y, U, -V, angles='xy', scale_units='xy', scale=1)) # plot exact
    plt.gca().invert_yaxis()
    plt.axis('equal')

    plt.tight_layout()
    plt.gcf().patch.set_facecolor('#dddddd')
    #plt.show()
    plt.savefig(filename + '.svg', bbox_inches='tight')


def main():
    import sys

    np.set_printoptions(precision=4, suppress=True)

    if len(sys.argv)==1:
        imfiles = ["/var/tmp/capture/070.png"]
    else:
        imfiles = sys.argv[1:]

    for filename in imfiles:
        process(filename)

if __name__ == '__main__':
    main()