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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 | |
| 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 | |