多视角三维重建系统
下面我将实现一个完整的基于Python的多视角三维重建系统，包含特征提取与匹配、相机位姿估计、三维重建、优化和可视化等功能。
1. 环境准备与数据加载
首先安装必要的库：
pip install opencv-python opencv-contrib-python numpy matplotlib plotly scipy
python
import cv2
import numpy as np
import matplotlib.pyplot as plt
from scipy.sparse import lil_matrix
from scipy.optimize import least_squares
import os
from mpl_toolkits.mplot3d import Axes3D
import plotly.graph_objects as go
import time
from tqdm import tqdm
class MultiViewReconstruction:
def __init__(self, image_dir, focal_length=2000, principal_point=None):
"""
初始化多视角三维重建系统
参数:
image_dir: 图像目录路径
focal_length: 相机焦距(像素单位)
principal_point: 主点坐标(cx, cy), 默认为图像中心
"""
self.image_dir = image_dir
self.images = []
self.image_names = []
self.focal_length = focal_length
self.principal_point = principal_point
self.keypoints = []
self.descriptors = []
self.matches = {}
self.camera_poses = {} # 相机位姿字典 {image_id: (R, t)}
self.point_cloud = [] # 三维点云 [(x, y, z, r, g, b), ...]
self.point_visibility = {} # 点可见性 {point_id: [image_id1, image_id2, ...]}
# 加载图像
self._load_images()
# 如果没有指定主点，使用图像中心
if self.principal_point is None:
h, w = self.images[0].shape[:2]
self.principal_point = (w/2, h/2)
# 相机内参矩阵
self.K = np.array([
[self.focal_length, 0, self.principal_point[0]],
[0, self.focal_length, self.principal_point[1]],
[0, 0, 1]
])
def _load_images(self):
"""加载目录中的所有图像"""
print("Loading images...")
for img_name in sorted(os.listdir(self.image_dir)):
if img_name.lower().endswith(('.png', '.jpg', '.jpeg')):
img_path = os.path.join(self.image_dir, img_name)
img = cv2.imread(img_path)
if img is not None:
self.images.append(img)
self.image_names.append(img_name)
print(f"Loaded {len(self.images)} images.")2. 特征提取与匹配
python
def extract_features(self, method='SIFT', n_features=5000):
"""
从所有图像中提取特征点
参数:
method: 特征提取方法 ('SIFT', 'SURF', 'ORB')
n_features: 要提取的最大特征点数
"""
print(f"Extracting features using {method}...")
# 选择特征提取器
if method == 'SIFT':
detector = cv2.SIFT_create(nfeatures=n_features)
elif method == 'SURF':
detector = cv2.xfeatures2d.SURF_create(hessianThreshold=400)
elif method == 'ORB':
detector = cv2.ORB_create(nfeatures=n_features)
else:
raise ValueError(f"Unsupported feature method: {method}")
self.keypoints = []
self.descriptors = []
for img in tqdm(self.images):
# 转换为灰度图
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
# 检测特征点和计算描述子
kp, des = detector.detectAndCompute(gray, None)
self.keypoints.append(kp)
self.descriptors.append(des)
def match_features(self, method='FLANN', ratio_test=0.7):
"""
匹配不同图像之间的特征点
参数:
method: 匹配方法 ('FLANN' 或 'BF')
ratio_test: Lowe's ratio test的阈值
"""
print("Matching features between images...")
# 初始化匹配器
if method == 'FLANN':
if self.descriptors[0].dtype == np.uint8: # ORB描述子
flann_params = dict(algorithm=6, # FLANN_INDEX_LSH
table_number=6,
key_size=12,
multi_probe_level=1)
matcher = cv2.FlannBasedMatcher(flann_params, {})
else: # SIFT/SURF描述子
flann_params = dict(algorithm=1, trees=5) # FLANN_INDEX_KDTREE
matcher = cv2.FlannBasedMatcher(flann_params, {})
elif method == 'BF':
if self.descriptors[0].dtype == np.uint8: # ORB描述子
matcher = cv2.BFMatcher(cv2.NORM_HAMMING, crossCheck=False)
else: # SIFT/SURF描述子
matcher = cv2.BFMatcher(cv2.NORM_L2, crossCheck=False)
else:
raise ValueError(f"Unsupported matching method: {method}")
self.matches = {}
n_images = len(self.images)
# 匹配所有图像对
for i in tqdm(range(n_images)):
for j in range(i+1, n_images):
# 匹配描述子
matches = matcher.knnMatch(self.descriptors[i], self.descriptors[j], k=2)
# 应用Lowe's ratio test筛选好的匹配
good_matches = []
for m, n in matches:
if m.distance < ratio_test * n.distance:
good_matches.append(m)
if len(good_matches) > 20: # 只保留足够多的匹配对
self.matches[(i, j)] = good_matches
def visualize_matches(self, img_idx1, img_idx2):
"""可视化两个图像之间的匹配点"""
if (img_idx1, img_idx2) not in self.matches:
print(f"No matches found between image {img_idx1} and {img_idx2}")
return
img1 = self.images[img_idx1]
img2 = self.images[img_idx2]
matches = self.matches[(img_idx1, img_idx2)]
# 绘制匹配结果
matched_img = cv2.drawMatches(
img1, self.keypoints[img_idx1],
img2, self.keypoints[img_idx2],
matches, None,
flags=cv2.DrawMatchesFlags_NOT_DRAW_SINGLE_POINTS
)
plt.figure(figsize=(20, 10))
plt.imshow(cv2.cvtColor(matched_img, cv2.COLOR_BGR2RGB))
plt.title(f"Feature matches between image {img_idx1} and {img_idx2}")
plt.axis('off')
plt.show()3. 相机位姿估计与三维重建
python
def estimate_initial_pose(self):
"""估计初始相机位姿"""
print("Estimating initial camera poses...")
if not self.matches:
raise ValueError("No feature matches found. Run match_features() first.")
# 选择有最多匹配点的图像对作为初始对
best_pair = max(self.matches.keys(), key=lambda x: len(self.matches[x]))
img_idx1, img_idx2 = best_pair
matches = self.matches[best_pair]
# 获取匹配点的像素坐标
kp1 = self.keypoints[img_idx1]
kp2 = self.keypoints[img_idx2]
pts1 = np.float32([kp1[m.queryIdx].pt for m in matches])
pts2 = np.float32([kp2[m.trainIdx].pt for m in matches])
# 计算基础矩阵和本质矩阵
E, mask = cv2.findEssentialMat(pts1, pts2, self.K, method=cv2.RANSAC, prob=0.999, threshold=1.0)
# 从本质矩阵恢复相对位姿
_, R, t, mask = cv2.recoverPose(E, pts1, pts2, self.K, mask=mask)
# 设置第一个相机的位姿为世界坐标系
self.camera_poses[img_idx1] = (np.eye(3), np.zeros((3, 1))) # R, t
self.camera_poses[img_idx2] = (R, t)
# 三角测量初始点云
self._triangulate_initial_points(img_idx1, img_idx2)
# 逐步添加更多视图
self._incremental_sfm()
def _triangulate_initial_points(self, img_idx1, img_idx2):
"""三角测量初始点云"""
matches = self.matches[(img_idx1, img_idx2)]
kp1 = self.keypoints[img_idx1]
kp2 = self.keypoints[img_idx2]
# 获取匹配点的像素坐标
pts1 = np.float32([kp1[m.queryIdx].pt for m in matches])
pts2 = np.float32([kp2[m.trainIdx].pt for m in matches])
# 获取相机投影矩阵
R1, t1 = self.camera_poses[img_idx1]
R2, t2 = self.camera_poses[img_idx2]
P1 = np.dot(self.K, np.hstack((R1, t1)))
P2 = np.dot(self.K, np.hstack((R2, t2)))
# 三角测量
points_4d = cv2.triangulatePoints(P1, P2, pts1.T, pts2.T)
points_3d = points_4d[:3] / points_4d[3] # 齐次坐标转3D坐标
# 获取点的颜色
colors = []
img1 = self.images[img_idx1]
for pt in pts1:
x, y = int(round(pt[0])), int(round(pt[1]))
colors.append(img1[y, x][::-1]) # BGR转RGB
# 保存点云
for i in range(points_3d.shape[1]):
self.point_cloud.append((*points_3d[:, i], *colors[i]))
point_id = len(self.point_cloud) - 1
self.point_visibility[point_id] = [img_idx1, img_idx2]
def _incremental_sfm(self):
"""增量式运动恢复结构"""
print("Running incremental structure from motion...")
n_images = len(self.images)
registered_images = set(self.camera_poses.keys())
# 继续添加视图直到所有视图都注册
while len(registered_images) < n_images:
# 找到与已注册视图有最多匹配点的未注册视图
best_img = None
best_matches = 0
best_registered_img = None
best_matches_list = []
for unreg_img in set(range(n_images)) - registered_images:
for reg_img in registered_images:
pair = (min(unreg_img, reg_img), max(unreg_img, reg_img))
if pair in self.matches and len(self.matches[pair]) > best_matches:
best_matches = len(self.matches[pair])
best_img = unreg_img
best_registered_img = reg_img
best_matches_list = self.matches[pair]
if best_img is None:
print("No more images can be registered")
break
print(f"Registering image {best_img} using matches with image {best_registered_img}")
# 2D-3D对应关系
kp_reg = self.keypoints[best_registered_img]
kp_unreg = self.keypoints[best_img]
# 找到已重建的3D点
pts3d = []
pts2d = []
colors = []
for match in best_matches_list:
# 在已注册图像中找到对应的3D点
point_found = False
for point_id, img_list in self.point_visibility.items():
if best_registered_img in img_list:
# 检查是否是同一个特征点
img_pos = img_list.index(best_registered_img)
kp_idx = match.queryIdx if img_pos == 0 else match.trainIdx
# 这里简化处理，实际应该建立特征点与3D点的对应关系
# 为了简化，我们假设匹配是正确的
pts3d.append(self.point_cloud[point_id][:3])
pts2d.append(kp_unreg[match.trainIdx if img_pos == 0 else match.queryIdx].pt)
colors.append(self.point_cloud[point_id][3:6])
point_found = True
break
if not point_found:
continue
if len(pts3d) < 6:
print(f"Not enough 2D-3D correspondences for image {best_img}")
registered_images.add(best_img) # 标记为已注册但无法重建
continue
pts3d = np.array(pts3d, dtype=np.float32)
pts2d = np.array(pts2d, dtype=np.float32)
# 使用PnP算法估计新视图的相机位姿
_, rvec, tvec, inliers = cv2.solvePnPRansac(
pts3d, pts2d, self.K, None,
iterationsCount=1000,
reprojectionError=8.0,
confidence=0.99
)
# 转换旋转向量为旋转矩阵
R, _ = cv2.Rodrigues(rvec)
t = tvec
# 保存新视图的相机位姿
self.camera_poses[best_img] = (R, t)
registered_images.add(best_img)
# 三角测量新的点
self._triangulate_new_points(best_img, registered_images)
def _triangulate_new_points(self, new_img_idx, registered_images):
"""三角测量新的3D点"""
# 找到与新视图有匹配的已注册视图
for reg_img in registered_images:
if reg_img == new_img_idx:
continue
pair = (min(new_img_idx, reg_img), max(new_img_idx, reg_img))
if pair not in self.matches:
continue
matches = self.matches[pair]
kp_new = self.keypoints[new_img_idx]
kp_reg = self.keypoints[reg_img]
# 获取匹配点
pts_new = []
pts_reg = []
match_indices = []
for i, match in enumerate(matches):
# 检查这些匹配点是否已经存在于点云中
exists = False
for point_id, img_list in self.point_visibility.items():
if reg_img in img_list:
# 简化处理，实际应该建立特征点与3D点的对应关系
img_pos = img_list.index(reg_img)
kp_idx = match.queryIdx if img_pos == 0 else match.trainIdx
# 如果这个特征点已经有对应的3D点，跳过
exists = True
break
if not exists:
# 新点，准备三角测量
query_pt = kp_reg[match.queryIdx].pt
train_pt = kp_new[match.trainIdx].pt
pts_reg.append(query_pt)
pts_new.append(train_pt)
match_indices.append(i)
if len(pts_new) < 8:
continue
pts_new = np.float32(pts_new).T
pts_reg = np.float32(pts_reg).T
# 获取相机投影矩阵
R_reg, t_reg = self.camera_poses[reg_img]
R_new, t_new = self.camera_poses[new_img_idx]
P_reg = np.dot(self.K, np.hstack((R_reg, t_reg)))
P_new = np.dot(self.K, np.hstack((R_new, t_new)))
# 三角测量新点
points_4d = cv2.triangulatePoints(P_reg, P_new, pts_reg, pts_new)
points_3d = points_4d[:3] / points_4d[3] # 齐次坐标转3D坐标
# 检查点的深度是否为正(在两个相机前方)
valid_points = []
for i in range(points_3d.shape[1]):
point = points_3d[:, i]
# 在第一个相机坐标系下的深度
depth_reg = np.dot(R_reg, point) + t_reg.flatten()
# 在新相机坐标系下的深度
depth_new = np.dot(R_new, point) + t_new.flatten()
if depth_reg[2] > 0 and depth_new[2] > 0:
valid_points.append(i)
if not valid_points:
continue
# 获取点的颜色(取两个视图的平均)
img_new = self.images[new_img_idx]
img_reg = self.images[reg_img]
for i in valid_points:
match_idx = match_indices[i]
# 获取两个视图中的颜色
kp_new_idx = matches[match_idx].trainIdx
kp_reg_idx = matches[match_idx].queryIdx
x_new, y_new = map(int, map(round, kp_new[kp_new_idx].pt))
x_reg, y_reg = map(int, map(round, kp_reg[kp_reg_idx].pt))
color_new = img_new[y_new, x_new][::-1] # BGR转RGB
color_reg = img_reg[y_reg, x_reg][::-1]
avg_color = ((np.array(color_new) + np.array(color_reg)) / 2).astype(int)
# 添加到点云
self.point_cloud.append((*points_3d[:, i], *avg_color))
point_id = len(self.point_cloud) - 1
self.point_visibility[point_id] = [reg_img, new_img_idx]4. 光束法平差优化
python
def bundle_adjustment(self, n_iterations=10):
"""执行光束法平差优化相机位姿和3D点"""
print("Running bundle adjustment...")
if not self.camera_poses or not self.point_cloud:
raise ValueError("No camera poses or point cloud available")
# 准备数据
n_cameras = len(self.camera_poses)
n_points = len(self.point_cloud)
# 获取相机参数和点参数
camera_params = []
camera_indices = {img_idx: i for i, img_idx in enumerate(self.camera_poses.keys())}
for img_idx in self.camera_poses:
R, t = self.camera_poses[img_idx]
# 将旋转矩阵转换为旋转向量
rvec, _ = cv2.Rodrigues(R)
camera_params.extend([*rvec.flatten(), *t.flatten()])
camera_params = np.array(camera_params, dtype=np.float64)
points_3d = np.array([p[:3] for p in self.point_cloud], dtype=np.float64)
# 准备观测数据(2D点)
observations = []
camera_idx_for_obs = []
point_idx_for_obs = []
for point_id, img_list in self.point_visibility.items():
for img_idx in img_list:
# 找到这个点在图像中的位置
# 这里简化处理，实际应该建立特征点与3D点的对应关系
# 为了简化，我们假设点云中的点顺序与特征点顺序一致
kp_list = self.keypoints[img_idx]
for i, kp in enumerate(kp_list):
# 简化处理，实际应该使用更精确的匹配关系
if (img_idx, i) in [(img_idx, m.queryIdx) for m in self.matches.get((min(img_idx, other), max(img_idx, other)), [])
for other in self.camera_poses if (min(img_idx, other), max(img_idx, other)) in self.matches]:
observations.append(kp.pt)
camera_idx_for_obs.append(camera_indices[img_idx])
point_idx_for_obs.append(point_id)
break
observations = np.array(observations, dtype=np.float64)
# 优化函数
def fun(params, n_cameras, n_points, camera_indices, point_indices, observations):
"""计算残差"""
camera_params = params[:n_cameras * 6].reshape((n_cameras, 6))
points_3d = params[n_cameras * 6:].reshape((n_points, 3))
residuals = []
for i in range(len(observations)):
camera_idx = camera_indices[i]
point_idx = point_indices[i]
rvec = camera_params[camera_idx, :3]
tvec = camera_params[camera_idx, 3:6]
point = points_3d[point_idx]
# 投影点
projected, _ = cv2.projectPoints(
point.reshape(1, 1, 3),
rvec,
tvec,
self.K,
None
)
projected = projected.reshape(-1)
# 计算残差
residual = observations[i] - projected
residuals.extend(residual)
return np.array(residuals)
# 将参数合并为一个数组
x0 = np.hstack((camera_params.ravel(), points_3d.ravel()))
# 调用最小二乘优化
res = least_squares(
fun, x0,
jac='3-point',
method='trf',
max_nfev=n_iterations,
verbose=2,
args=(n_cameras, n_points, camera_idx_for_obs, point_idx_for_obs, observations)
)
# 更新优化后的参数
optimized_params = res.x
camera_params_opt = optimized_params[:n_cameras * 6].reshape((n_cameras, 6))
points_3d_opt = optimized_params[n_cameras * 6:].reshape((n_points, 3))
# 更新相机位姿
for i, img_idx in enumerate(self.camera_poses.keys()):
rvec = camera_params_opt[i, :3]
tvec = camera_params_opt[i, 3:6]
R, _ = cv2.Rodrigues(rvec)
t = tvec.reshape(3, 1)
self.camera_poses[img_idx] = (R, t)
# 更新点云
for i in range(n_points):
x, y, z = points_3d_opt[i]
r, g, b = self.point_cloud[i][3:6]
self.point_cloud[i] = (x, y, z, r, g, b)5. 可视化与结果展示
python
def visualize_point_cloud(self, method='matplotlib'):
"""可视化重建的点云"""
if not self.point_cloud:
print("No point cloud to visualize")
return
print("Visualizing point cloud...")
# 提取点坐标和颜色
points = np.array([p[:3] for p in self.point_cloud])
colors = np.array([p[3:6] for p in self.point_cloud]) / 255.0
if method == 'matplotlib':
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')
ax.scatter(
points[:, 0], points[:, 1], points[:, 2],
c=colors, s=1, alpha=0.6, marker='.'
)
# 绘制相机位置
for img_idx, (R, t) in self.camera_poses.items():
camera_center = -R.T @ t
ax.scatter(
camera_center[0], camera_center[1], camera_center[2],
c='red', s=50, marker='^'
)
ax.text(
camera_center[0], camera_center[1], camera_center[2],
f'Cam {img_idx}', color='black'
)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('Reconstructed 3D Point Cloud')
plt.show()
elif method == 'plotly':
fig = go.Figure()
# 添加点云
fig.add_trace(go.Scatter3d(
x=points[:, 0],
y=points[:, 1],
z=points[:, 2],
mode='markers',
marker=dict(
size=2,
color=colors,
opacity=0.8
),
name='Point Cloud'
))
# 添加相机
for img_idx, (R, t) in self.camera_poses.items():
camera_center = -R.T @ t
fig.add_trace(go.Scatter3d(
x=[camera_center[0]],
y=[camera_center[1]],
z=[camera_center[2]],
mode='markers+text',
marker=dict(
size=5,
color='red',
symbol='diamond'
),
text=f'Cam {img_idx}',
textposition="top center",
name=f'Camera {img_idx}'
))
fig.update_layout(
title='Reconstructed 3D Point Cloud',
scene=dict(
xaxis_title='X',
yaxis_title='Y',
zaxis_title='Z',
aspectmode='data'
),
margin=dict(l=0, r=0, b=0, t=0)
)
fig.show()
else:
raise ValueError(f"Unsupported visualization method: {method}")6. 完整流程示例
python
# 使用示例
if __name__ == "__main__":
# 初始化重建系统
image_dir = "path/to/your/images" # 替换为你的图像目录
reconstructor = MultiViewReconstruction(image_dir, focal_length=2000)
# 1. 特征提取
reconstructor.extract_features(method='SIFT')
# 2. 特征匹配
reconstructor.match_features(method='FLANN', ratio_test=0.7)
# 可视化一些匹配
reconstructor.visualize_matches(0, 1)
# 3. 相机位姿估计与三维重建
reconstructor.estimate_initial_pose()
# 4. 光束法平差优化
reconstructor.bundle_adjustment(n_iterations=20)
# 5. 可视化结果
reconstructor.visualize_point_cloud(method='plotly')系统说明
这个多视角三维重建系统实现了以下功能：
-
数据准备：加载多视角图像数据集，设置相机内参。
-
特征提取与匹配：
- 支持SIFT、SURF和ORB特征提取算法
- 使用FLANN或暴力匹配进行特征匹配
- 应用Lowe's ratio test筛选优质匹配
-
相机位姿估计：
- 从特征匹配计算本质矩阵
- 使用RANSAC去除异常值
- 恢复相机相对位姿
-
三维重建：
- 通过三角测量生成初始点云
- 增量式运动恢复结构逐步添加更多视图
- 处理新视图的注册和新增点的三角测量
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模型优化：
- 实现光束法平差(Bundle Adjustment)优化相机位姿和3D点
- 使用Scipy的最小二乘优化器
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可视化展示：
- 支持Matplotlib和Plotly两种可视化方式
- 显示点云和相机位置
技术要点
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特征选择：SIFT特征对旋转、尺度变化和光照变化具有较好的不变性。
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鲁棒估计：使用RANSAC算法处理匹配中的异常值。
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增量式重建：逐步添加视图，保证重建的稳定性。
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全局优化：光束法平差同时优化所有相机参数和3D点坐标，提高重建精度。
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效率优化：使用稀疏矩阵和高效的最小二乘算法处理大规模优化问题。
扩展方向
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稠密重建：在稀疏点云基础上进行稠密重建，获取更完整的表面。
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纹理映射：将原始图像纹理映射到重建的3D模型上。
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并行计算：利用GPU加速特征提取和匹配过程。
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实时重建：优化算法实现实时三维重建。
这个系统提供了多视角三维重建的基础框架，可以根据具体应用需求进行进一步扩展和优化。