RepNet/eval_functions.py at master · CaptainMe-AI/RepNet · GitHub

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import numpy as np


def procrustes(X, Y, scaling=True, reflection='best'):
    """
    Reimplementation of MATLAB's `procrustes` function to Numpy.

    """

    n, m = X.shape
    ny, my = Y.shape

    muX = X.mean(0)
    muY = Y.mean(0)

    X0 = X - muX
    Y0 = Y - muY

    ssX = (X0**2.).sum()
    ssY = (Y0**2.).sum()

    # centred Frobenius norm
    normX = np.sqrt(ssX)
    normY = np.sqrt(ssY)

    # scale to equal (unit) norm
    X0 /= normX
    Y0 /= normY

    if my < m:
        Y0 = np.concatenate((Y0, np.zeros(n, m-my)),0)

    # optimum rotation matrix of Y
    A = np.dot(X0.T, Y0)
    U,s,Vt = np.linalg.svd(A,full_matrices=False)
    V = Vt.T
    T = np.dot(V, U.T)

    if reflection is not 'best':

        # does the current solution use a reflection?
        have_reflection = np.linalg.det(T) < 0

        # if that's not what was specified, force another reflection
        if reflection != have_reflection:
            V[:,-1] *= -1
            s[-1] *= -1
            T = np.dot(V, U.T)

    traceTA = s.sum()

    if scaling:

        # optimum scaling of Y
        b = traceTA * normX / normY

        # standarised distance between X and b*Y*T + c
        d = 1 - traceTA**2

        # transformed coords
        Z = normX*traceTA*np.dot(Y0, T) + muX

    else:
        b = 1
        d = 1 + ssY/ssX - 2 * traceTA * normY / normX
        Z = normY*np.dot(Y0, T) + muX

    # transformation matrix
    if my < m:
        T = T[:my,:]
    c = muX - b*np.dot(muY, T)

    #transformation values
    tform = {'rotation':T, 'scale':b, 'translation':c}

    return d, Z, tform


def err_3dpe(p_ref, p):
    import numpy as np

    # reshape pose if necessary
    if p.shape[0] == 1:
        p = p.reshape(3, int(p.shape[1]/3))

    if p_ref.shape[0] == 1:
        p_ref = p_ref.reshape(3, int(p_ref.shape[1]/3))

    d, Z, tform = procrustes(p_ref.T, p.T)

    Z = Z.T

    sum_dist = 0

    for i in range(p.shape[1]):
        sum_dist += np.linalg.norm(Z[:, i]-p_ref[:, i], 2)

    err = np.sum(sum_dist) / Z.shape[1]

    return err