A simple augmented reality application

主要理解代码记录解决报错问题，具体内容有空补上。

相机矩阵转换成 OpenGL 格式

在 OpenGL 中主要使用 4x4 矩阵来表示转换，这个和 3x4 的相机矩阵不同。然而，OpenGL 中的 GL_PROJECTION 和 GL_MODELVIEW 是将相机矩阵分开来表示。其中 GL_PROJECTION 表示相机的内参数 K 矩阵；GL_MODELVIEW 表示物体和相机之间的转换关系，可以粗略地表示为 R 和 t 矩阵。

代码如下所示， K 表示校准后的相机内参数矩阵。

代码语言：javascript复制

from OpenGL.GL import *
from OpenGL.GLU import *
import pygame, pygame.image
from pygame.locals import *
from OpenGL.GLUT import *
import numpy as np
from scipy import linalg
import sys


def set_projection_from_camera(K):
    
    """
    Set view from a camera calibration matrix.
    """
    
    glMatrixMode(GL_PROJECTION)
    glLoadIdentity()
    
    fx = K[0, 0]
    fy = K[1, 1]
    # 计算以度为单位的垂直视野
    fovy = 2*np.arctan(0.5*height/fy)*180/np.pi
    # 纵横比
    aspect = (width*fy)/(height*fx)
    
    # define the near and far clipping planes
    near = 0.1
    far = 100.0
    
    # set perspective
    gluPerspective(fovy, aspect, near, far)
    glViewport(0, 0, width, height)

P = K[R|t]，所以 Rt = PK-1 得到。Rt 为下面代码的输入：

代码语言：javascript复制

def set_modelview_from_camera(Rt):
    
    """
    Set the model view matrix from camera pose.
    """
    glMatrixMode(GL_MODELVIEW)
    glLoadIdentity()
    
    # rotate teapot 90 deg around x-axis so that z-axis is up
    Rx = np.array([[1, 0, 0], [0, 0, -1], [0, 1, 0]])
    
    # set rotation to best approximation
    R = Rt[:, :3]
    U, S, V = linalg.svd(R)
    R = np.dot(U, V)
    R[0, :] = -R[0, :] # change sign of x-axis
    
    # set translation
    t = Rt[:, 3]
    
    # set 4*4 model view matrix
    M = np.eye(4)
    M[:3, :3] = np.dot(R, Rx)
    M[:3, 3] = t
    
    # transpose and flatten to grt column order
    M = M.T
    m = M.flatten()
    
    # replace model view with new matrix
    glLoadMatrixf(m)

将虚拟物体投放到图片上

代码语言：javascript复制

def draw_background(imname):
    
    """
    Draw background image using a quadrilateral.
    """
    
    # load backgound image (should be .bmp) to OpenGL texture
    bg_image = pygame.image.load(imname).convert()
    bg_data = pygame.image.tostring(bg_image, "RGBX", 1)
    
    glMatrixMode(GL_MODELVIEW)
    glLoadIdentity()
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)
    
    # bind the texture
    glEnable(GL_TEXTURE_2D)
    glBindTexture(GL_TEXTURE_2D, glGenTextures(1))
    glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width, height, 0, GL_RGBA, GL_UNSIGNED_BYTE, bg_data)
    glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST)
    glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST)
    
    # create quad to fill the whole window
    glBegin(GL_QUADS)
    glTexCoord2f(0.0, 0.0); glVertex3f(-1.0, -1.0, -1.0)
    glTexCoord2f(1.0, 0.0); glVertex3f( 1.0, -1.0, -1.0)
    glTexCoord2f(1.0, 1.0); glVertex3f( 1.0,  1.0, -1.0)
    glTexCoord2f(0.0, 1.0); glVertex3f(-1.0,  1.0, -1.0)
    glEnd()
    
    # clear the texture
    glDeleteTextures(1)

def draw_teapot(size):
    
    """
    Draw a red teapot at the origin.
    """
    glEnable(GL_LIGHTING) 
    glEnable(GL_LIGHT0) 
    glEnable(GL_DEPTH_TEST) 
    glClear(GL_DEPTH_BUFFER_BIT)
    
    # draw red teapot
    glMaterialfv(GL_FRONT,GL_AMBIENT,[0,0,0,0]) 
    glMaterialfv(GL_FRONT,GL_DIFFUSE,[0.5,0.0,0.0,0.0]) 
    glMaterialfv(GL_FRONT,GL_SPECULAR,[0.7,0.6,0.6,0.0]) 
    glMaterialf(GL_FRONT,GL_SHININESS,0.25*128.0) 
    glutSolidTeapot(size)

主代码：

代码语言：javascript复制

from OpenGL.GL import *
from OpenGL.GLU import *
from OpenGL.GLUT import *
import pygame, pygame.image
from pygame.locals import *
import pickle

width, height = 1000, 747

def setup():
    
    """
    Setup window and pygame environment.
    """
    
    pygame.init()
    pygame.display.set_mode((width, height), OPENGL | DOUBLEBUF)
    pygame.display.set_caption('OpenGL AR demo')
    
# load camera data
with open('ar_camera.pkl', 'rb') as f:
    K = pickle.load(f)
    Rt = pickle.load(f)
    
setup()
draw_background('./book_perspective.bmp')
set_projection_from_camera(K)
set_modelview_from_camera(Rt)
draw_teapot(0.05)

pygame.display.flip()
while True:
  for event in pygame.event.get():
    if event.type == pygame.QUIT:
       sys.exit()
       pygame.quit()
pygame.display.flip()

结果：

参考

[1]. Programming Computer Vision with Python

[2]. python照相机模型与增强现实

[3]. 【计算机视觉】照相机模型与增强现实

[4]. PyOpenGL Installation Notes for Windows

opengl api python

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A simple augmented reality application

相机矩阵转换成 OpenGL 格式

将虚拟物体投放到图片上

相关报错解决

参考