insightface/utils/transform.py

import cv2
import math
import numpy as np
from skimage import transform as trans


def transform(data, center, output_size, scale, rotation):
    scale_ratio = scale
    rot = float(rotation) * np.pi / 180.0
    #translation = (output_size/2-center[0]*scale_ratio, output_size/2-center[1]*scale_ratio)
    t1 = trans.SimilarityTransform(scale=scale_ratio)
    cx = center[0] * scale_ratio
    cy = center[1] * scale_ratio
    t2 = trans.SimilarityTransform(translation=(-1 * cx, -1 * cy))
    t3 = trans.SimilarityTransform(rotation=rot)
    t4 = trans.SimilarityTransform(translation=(output_size / 2,
                                                output_size / 2))
    t = t1 + t2 + t3 + t4
    M = t.params[0:2]
    cropped = cv2.warpAffine(data,
                             M, (output_size, output_size),
                             borderValue=0.0)
    return cropped, M


def trans_points2d(pts, M):
    new_pts = np.zeros(shape=pts.shape, dtype=np.float32)
    for i in range(pts.shape[0]):
        pt = pts[i]
        new_pt = np.array([pt[0], pt[1], 1.], dtype=np.float32)
        new_pt = np.dot(M, new_pt)
        #print('new_pt', new_pt.shape, new_pt)
        new_pts[i] = new_pt[0:2]

    return new_pts


def trans_points3d(pts, M):
    scale = np.sqrt(M[0][0] * M[0][0] + M[0][1] * M[0][1])
    #print(scale)
    new_pts = np.zeros(shape=pts.shape, dtype=np.float32)
    for i in range(pts.shape[0]):
        pt = pts[i]
        new_pt = np.array([pt[0], pt[1], 1.], dtype=np.float32)
        new_pt = np.dot(M, new_pt)
        #print('new_pt', new_pt.shape, new_pt)
        new_pts[i][0:2] = new_pt[0:2]
        new_pts[i][2] = pts[i][2] * scale

    return new_pts


def trans_points(pts, M):
    if pts.shape[1] == 2:
        return trans_points2d(pts, M)
    else:
        return trans_points3d(pts, M)

def estimate_affine_matrix_3d23d(X, Y):
    ''' Using least-squares solution 
    Args:
        X: [n, 3]. 3d points(fixed)
        Y: [n, 3]. corresponding 3d points(moving). Y = PX
    Returns:
        P_Affine: (3, 4). Affine camera matrix (the third row is [0, 0, 0, 1]).
    '''
    X_homo = np.hstack((X, np.ones([X.shape[0],1]))) #n x 4
    P = np.linalg.lstsq(X_homo, Y)[0].T # Affine matrix. 3 x 4
    return P

def P2sRt(P):
    ''' decompositing camera matrix P
    Args: 
        P: (3, 4). Affine Camera Matrix.
    Returns:
        s: scale factor.
        R: (3, 3). rotation matrix.
        t: (3,). translation. 
    '''
    t = P[:, 3]
    R1 = P[0:1, :3]
    R2 = P[1:2, :3]
    s = (np.linalg.norm(R1) + np.linalg.norm(R2))/2.0
    r1 = R1/np.linalg.norm(R1)
    r2 = R2/np.linalg.norm(R2)
    r3 = np.cross(r1, r2)

    R = np.concatenate((r1, r2, r3), 0)
    return s, R, t

def matrix2angle(R):
    ''' get three Euler angles from Rotation Matrix
    Args:
        R: (3,3). rotation matrix
    Returns:
        x: pitch
        y: yaw
        z: roll
    '''
    sy = math.sqrt(R[0,0] * R[0,0] +  R[1,0] * R[1,0])
     
    singular = sy < 1e-6
 
    if  not singular :
        x = math.atan2(R[2,1] , R[2,2])
        y = math.atan2(-R[2,0], sy)
        z = math.atan2(R[1,0], R[0,0])
    else :
        x = math.atan2(-R[1,2], R[1,1])
        y = math.atan2(-R[2,0], sy)
        z = 0

    # rx, ry, rz = np.rad2deg(x), np.rad2deg(y), np.rad2deg(z)
    rx, ry, rz = x*180/np.pi, y*180/np.pi, z*180/np.pi
    return rx, ry, rz