faceswap/lib/umeyama.py

#!/usr/bin/env python3
""" Umeyama for Faceswap

    License (Modified BSD)
    Copyright (C) 2011, the scikit-image team 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 skimage 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 AUTHOR ''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 AUTHOR 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
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    umeyama function from scikit-image/skimage/transform/_geometric.py
"""
import numpy as np

MEAN_FACE_X = np.array([
    0.000213256, 0.0752622, 0.18113, 0.29077, 0.393397, 0.586856, 0.689483,
    0.799124, 0.904991, 0.98004, 0.490127, 0.490127, 0.490127, 0.490127,
    0.36688, 0.426036, 0.490127, 0.554217, 0.613373, 0.121737, 0.187122,
    0.265825, 0.334606, 0.260918, 0.182743, 0.645647, 0.714428, 0.793132,
    0.858516, 0.79751, 0.719335, 0.254149, 0.340985, 0.428858, 0.490127,
    .551395, 0.639268, 0.726104, 0.642159, 0.556721, 0.490127, 0.423532,
    0.338094, 0.290379, 0.428096, 0.490127, 0.552157, 0.689874, 0.553364,
    0.490127, 0.42689])

MEAN_FACE_Y = np.array([
    0.106454, 0.038915, 0.0187482, 0.0344891, 0.0773906, 0.0773906, 0.0344891,
    0.0187482, 0.038915, 0.106454, 0.203352, 0.307009, 0.409805, 0.515625,
    0.587326, 0.609345, 0.628106, 0.609345, 0.587326, 0.216423, 0.178758,
    0.179852, 0.231733, 0.245099, 0.244077, 0.231733, 0.179852, 0.178758,
    0.216423, 0.244077, 0.245099, 0.780233, 0.745405, 0.727388, 0.742578,
    0.727388, 0.745405, 0.780233, 0.864805, 0.902192, 0.909281, 0.902192,
    0.864805, 0.784792, 0.778746, 0.785343, 0.778746, 0.784792, 0.824182,
    0.831803, 0.824182])


def umeyama(src, estimate_scale, dst=None):
    """Estimate N-D similarity transformation with or without scaling.
    Parameters
    ----------
    src : (M, N) array
        Source coordinates.
    dst : (M, N) array
        Destination coordinates.
    estimate_scale : bool
        Whether to estimate scaling factor.
    Returns
    -------
    T : (N + 1, N + 1)
        The homogeneous similarity transformation matrix. The matrix contains
        NaN values only if the problem is not well-conditioned.
    References
    ----------
    .. [1] "Least-squares estimation of transformation parameters between two
            point patterns", Shinji Umeyama, PAMI 1991, DOI: 10.1109/34.88573
    """
    if dst is None:
        dst = np.stack([MEAN_FACE_X, MEAN_FACE_Y], axis=1)

    num = src.shape[0]
    dim = src.shape[1]

    # Compute mean of src and dst.
    src_mean = src.mean(axis=0)
    dst_mean = dst.mean(axis=0)

    # Subtract mean from src and dst.
    src_demean = src - src_mean
    dst_demean = dst - dst_mean

    # Eq. (38).
    A = np.dot(dst_demean.T, src_demean) / num

    # Eq. (39).
    d = np.ones((dim,), dtype=np.double)
    if np.linalg.det(A) < 0:
        d[dim - 1] = -1

    T = np.eye(dim + 1, dtype=np.double)

    U, S, V = np.linalg.svd(A)

    # Eq. (40) and (43).
    rank = np.linalg.matrix_rank(A)
    if rank == 0:
        return np.nan * T
    elif rank == dim - 1:
        if np.linalg.det(U) * np.linalg.det(V) > 0:
            T[:dim, :dim] = np.dot(U, V)
        else:
            s = d[dim - 1]
            d[dim - 1] = -1
            T[:dim, :dim] = np.dot(U, np.dot(np.diag(d), V))
            d[dim - 1] = s
    else:
        T[:dim, :dim] = np.dot(U, np.dot(np.diag(d), V.T))

    if estimate_scale:
        # Eq. (41) and (42).
        scale = 1.0 / src_demean.var(axis=0).sum() * np.dot(S, d)
    else:
        scale = 1.0

    T[:dim, dim] = dst_mean - scale * np.dot(T[:dim, :dim], src_mean.T)
    T[:dim, :dim] *= scale

    return T