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# -*- coding: utf-8 -*-
# Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. (MPG) is
# holder of all proprietary rights on this computer program.
# You can only use this computer program if you have closed
# a license agreement with MPG or you get the right to use the computer
# program from someone who is authorized to grant you that right.
# Any use of the computer program without a valid license is prohibited and
# liable to prosecution.
#
# Copyright©2019 Max-Planck-Gesellschaft zur Förderung
# der Wissenschaften e.V. (MPG). acting on behalf of its Max Planck Institute
# for Intelligent Systems. All rights reserved.
#
# Contact: ps-license@tuebingen.mpg.de
import cv2
import numpy as np
from .glm import ortho
class Camera:
def __init__(self, width=1600, height=1200):
# Focal Length
# equivalent 50mm
focal = np.sqrt(width * width + height * height)
self.focal_x = focal
self.focal_y = focal
# Principal Point Offset
self.principal_x = width / 2
self.principal_y = height / 2
# Axis Skew
self.skew = 0
# Image Size
self.width = width
self.height = height
self.near = 1
self.far = 10
# Camera Center
self.center = np.array([0, 0, 1.6])
self.direction = np.array([0, 0, -1])
self.right = np.array([1, 0, 0])
self.up = np.array([0, 1, 0])
self.ortho_ratio = None
def sanity_check(self):
self.center = self.center.reshape([-1])
self.direction = self.direction.reshape([-1])
self.right = self.right.reshape([-1])
self.up = self.up.reshape([-1])
assert len(self.center) == 3
assert len(self.direction) == 3
assert len(self.right) == 3
assert len(self.up) == 3
@staticmethod
def normalize_vector(v):
v_norm = np.linalg.norm(v)
return v if v_norm == 0 else v / v_norm
def get_real_z_value(self, z):
z_near = self.near
z_far = self.far
z_n = 2.0 * z - 1.0
z_e = 2.0 * z_near * z_far / (z_far + z_near - z_n * (z_far - z_near))
return z_e
def get_rotation_matrix(self):
rot_mat = np.eye(3)
s = self.right
s = self.normalize_vector(s)
rot_mat[0, :] = s
u = self.up
u = self.normalize_vector(u)
rot_mat[1, :] = -u
rot_mat[2, :] = self.normalize_vector(self.direction)
return rot_mat
def get_translation_vector(self):
rot_mat = self.get_rotation_matrix()
trans = -np.dot(rot_mat, self.center)
return trans
def get_intrinsic_matrix(self):
int_mat = np.eye(3)
int_mat[0, 0] = self.focal_x
int_mat[1, 1] = self.focal_y
int_mat[0, 1] = self.skew
int_mat[0, 2] = self.principal_x
int_mat[1, 2] = self.principal_y
return int_mat
def get_projection_matrix(self):
ext_mat = self.get_extrinsic_matrix()
int_mat = self.get_intrinsic_matrix()
return np.matmul(int_mat, ext_mat)
def get_extrinsic_matrix(self):
rot_mat = self.get_rotation_matrix()
int_mat = self.get_intrinsic_matrix()
trans = self.get_translation_vector()
extrinsic = np.eye(4)
extrinsic[:3, :3] = rot_mat
extrinsic[:3, 3] = trans
return extrinsic[:3, :]
def set_rotation_matrix(self, rot_mat):
self.direction = rot_mat[2, :]
self.up = -rot_mat[1, :]
self.right = rot_mat[0, :]
def set_intrinsic_matrix(self, int_mat):
self.focal_x = int_mat[0, 0]
self.focal_y = int_mat[1, 1]
self.skew = int_mat[0, 1]
self.principal_x = int_mat[0, 2]
self.principal_y = int_mat[1, 2]
def set_projection_matrix(self, proj_mat):
res = cv2.decomposeProjectionMatrix(proj_mat)
int_mat, rot_mat, camera_center_homo = res[0], res[1], res[2]
camera_center = camera_center_homo[0:3] / camera_center_homo[3]
camera_center = camera_center.reshape(-1)
int_mat = int_mat / int_mat[2][2]
self.set_intrinsic_matrix(int_mat)
self.set_rotation_matrix(rot_mat)
self.center = camera_center
self.sanity_check()
def get_gl_matrix(self):
z_near = self.near
z_far = self.far
rot_mat = self.get_rotation_matrix()
int_mat = self.get_intrinsic_matrix()
trans = self.get_translation_vector()
extrinsic = np.eye(4)
extrinsic[:3, :3] = rot_mat
extrinsic[:3, 3] = trans
axis_adj = np.eye(4)
axis_adj[2, 2] = -1
axis_adj[1, 1] = -1
model_view = np.matmul(axis_adj, extrinsic)
projective = np.zeros([4, 4])
projective[:2, :2] = int_mat[:2, :2]
projective[:2, 2:3] = -int_mat[:2, 2:3]
projective[3, 2] = -1
projective[2, 2] = (z_near + z_far)
projective[2, 3] = (z_near * z_far)
if self.ortho_ratio is None:
ndc = ortho(0, self.width, 0, self.height, z_near, z_far)
perspective = np.matmul(ndc, projective)
else:
perspective = ortho(-self.width * self.ortho_ratio / 2,
self.width * self.ortho_ratio / 2,
-self.height * self.ortho_ratio / 2,
self.height * self.ortho_ratio / 2, z_near,
z_far)
return perspective, model_view
def KRT_from_P(proj_mat, normalize_K=True):
res = cv2.decomposeProjectionMatrix(proj_mat)
K, Rot, camera_center_homog = res[0], res[1], res[2]
camera_center = camera_center_homog[0:3] / camera_center_homog[3]
trans = -Rot.dot(camera_center)
if normalize_K:
K = K / K[2][2]
return K, Rot, trans
def MVP_from_P(proj_mat, width, height, near=0.1, far=10000):
'''
Convert OpenCV camera calibration matrix to OpenGL projection and model view matrix
:param proj_mat: OpenCV camera projeciton matrix
:param width: Image width
:param height: Image height
:param near: Z near value
:param far: Z far value
:return: OpenGL projection matrix and model view matrix
'''
res = cv2.decomposeProjectionMatrix(proj_mat)
K, Rot, camera_center_homog = res[0], res[1], res[2]
camera_center = camera_center_homog[0:3] / camera_center_homog[3]
trans = -Rot.dot(camera_center)
K = K / K[2][2]
extrinsic = np.eye(4)
extrinsic[:3, :3] = Rot
extrinsic[:3, 3:4] = trans
axis_adj = np.eye(4)
axis_adj[2, 2] = -1
axis_adj[1, 1] = -1
model_view = np.matmul(axis_adj, extrinsic)
zFar = far
zNear = near
projective = np.zeros([4, 4])
projective[:2, :2] = K[:2, :2]
projective[:2, 2:3] = -K[:2, 2:3]
projective[3, 2] = -1
projective[2, 2] = (zNear + zFar)
projective[2, 3] = (zNear * zFar)
ndc = ortho(0, width, 0, height, zNear, zFar)
perspective = np.matmul(ndc, projective)
return perspective, model_view
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