如何基於python實現單目三維重建詳解

2022-06-24 22:00:53

一、單目三維重建概述

客觀世界的物體是三維的，而我們用攝像機獲取的影象是二維的，但是我們可以通過二維影象感知目標的三維資訊。三維重建技術是以一定的方式處理影象進而得到計算機能夠識別的三維資訊，由此對目標進行分析。而單目三維重建則是根據單個攝像頭的運動來模擬雙目視覺，從而獲得物體在空間中的三維視覺資訊，其中，單目即指單個攝像頭。

二、實現過程

在對物體進行單目三維重建的過程中，相關執行環境如下：

matplotlib 3.3.4
numpy 1.19.5
opencv-contrib-python 3.4.2.16
opencv-python 3.4.2.16
pillow 8.2.0
python 3.6.2

其重建主要包含以下步驟：

（1）相機的標定

（2）影象特徵提取及匹配

（3）三維重建

接下來，我們來詳細看下每個步驟的具體實現：

（1）相機的標定

在我們日常生活中有很多相機，如手機上的相機、數碼相機及功能模組型相機等等，每一個相機的引數都是不同的，即相機拍出的照片的解析度、模式等。假設我們在進行物體三維重建的時候，事先並不知道我們相機的矩陣引數，那麼，我們就應當計算出相機的矩陣引數，這一個步驟就叫做相機的標定。相機標定的相關原理我就不介紹了，網上很多人都講解的挺詳細的。其標定的具體實現如下：

def camera_calibration(ImagePath):
    # 迴圈中斷
    criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
    # 棋盤格尺寸（棋盤格的交叉點的個數）
    row = 11
    column = 8
    
    objpoint = np.zeros((row * column, 3), np.float32)
    objpoint[:, :2] = np.mgrid[0:row, 0:column].T.reshape(-1, 2)

    objpoints = []  # 3d point in real world space
    imgpoints = []  # 2d points in image plane.

    batch_images = glob.glob(ImagePath + '/*.jpg')
    for i, fname in enumerate(batch_images):
        img = cv2.imread(batch_images[i])
        imgGray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        # find chess board corners
        ret, corners = cv2.findChessboardCorners(imgGray, (row, column), None)
        # if found, add object points, image points (after refining them)
        if ret:
            objpoints.append(objpoint)
            corners2 = cv2.cornerSubPix(imgGray, corners, (11, 11), (-1, -1), criteria)
            imgpoints.append(corners2)
            # Draw and display the corners
            img = cv2.drawChessboardCorners(img, (row, column), corners2, ret)
            cv2.imwrite('Checkerboard_Image/Temp_JPG/Temp_' + str(i) + '.jpg', img)

    print("成功提取:", len(batch_images), "張圖片角點！")
    ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, imgGray.shape[::-1], None, None)

其中，cv2.calibrateCamera函數求出的mtx矩陣即為K矩陣。

當修改好相應引數並完成標定後，我們可以輸出棋盤格的角點圖片來看看是否已成功提取棋盤格的角點，輸出角點圖如下：

圖1：棋盤格角點提取

（2）影象特徵提取及匹配

在整個三維重建的過程中，這一步是最為關鍵的，也是最為複雜的一步，圖片特徵提取的好壞決定了你最後的重建效果。
在圖片特徵點提取演演算法中，有三種演演算法較為常用，分別為：SIFT演演算法、SURF演演算法以及ORB演演算法。通過綜合分析對比，我們在這一步中採取SURF演演算法來對圖片的特徵點進行提取。三種演演算法的特徵點提取效果對比如果大家感興趣可以去網上搜來看下，在此就不逐一對比了。具體實現如下：

def epipolar_geometric(Images_Path, K):
    IMG = glob.glob(Images_Path)
    img1, img2 = cv2.imread(IMG[0]), cv2.imread(IMG[1])
    img1_gray = cv2.cvtColor(img1, cv2.COLOR_BGR2GRAY)
    img2_gray = cv2.cvtColor(img2, cv2.COLOR_BGR2GRAY)

    # Initiate SURF detector
    SURF = cv2.xfeatures2d_SURF.create()

    # compute keypoint & descriptions
    keypoint1, descriptor1 = SURF.detectAndCompute(img1_gray, None)
    keypoint2, descriptor2 = SURF.detectAndCompute(img2_gray, None)
    print("角點數量：", len(keypoint1), len(keypoint2))

    # Find point matches
    bf = cv2.BFMatcher(cv2.NORM_L2, crossCheck=True)
    matches = bf.match(descriptor1, descriptor2)
    print("匹配點數量：", len(matches))

    src_pts = np.asarray([keypoint1[m.queryIdx].pt for m in matches])
    dst_pts = np.asarray([keypoint2[m.trainIdx].pt for m in matches])
    # plot
    knn_image = cv2.drawMatches(img1_gray, keypoint1, img2_gray, keypoint2, matches[:-1], None, flags=2)
    image_ = Image.fromarray(np.uint8(knn_image))
    image_.save("MatchesImage.jpg")

    # Constrain matches to fit homography
    retval, mask = cv2.findHomography(src_pts, dst_pts, cv2.RANSAC, 100.0)

    # We select only inlier points
    points1 = src_pts[mask.ravel() == 1]
    points2 = dst_pts[mask.ravel() == 1]

找到的特徵點如下：

圖2：特徵點提取

（3）三維重建

我們找到圖片的特徵點並相互匹配後，則可以開始進行三維重建了，具體實現如下：

points1 = cart2hom(points1.T)
points2 = cart2hom(points2.T)
# plot
fig, ax = plt.subplots(1, 2)
ax[0].autoscale_view('tight')
ax[0].imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax[0].plot(points1[0], points1[1], 'r.')
ax[1].autoscale_view('tight')
ax[1].imshow(cv2.cvtColor(img2, cv2.COLOR_BGR2RGB))
ax[1].plot(points2[0], points2[1], 'r.')
plt.savefig('MatchesPoints.jpg')
fig.show()
# 

points1n = np.dot(np.linalg.inv(K), points1)
points2n = np.dot(np.linalg.inv(K), points2)
E = compute_essential_normalized(points1n, points2n)
print('Computed essential matrix:', (-E / E[0][1]))

P1 = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]])
P2s = compute_P_from_essential(E)

ind = -1
for i, P2 in enumerate(P2s):
    # Find the correct camera parameters
    d1 = reconstruct_one_point(points1n[:, 0], points2n[:, 0], P1, P2)
    # Convert P2 from camera view to world view
    P2_homogenous = np.linalg.inv(np.vstack([P2, [0, 0, 0, 1]]))
    d2 = np.dot(P2_homogenous[:3, :4], d1)
    if d1[2] > 0 and d2[2] > 0:
        ind = i

P2 = np.linalg.inv(np.vstack([P2s[ind], [0, 0, 0, 1]]))[:3, :4]
Points3D = linear_triangulation(points1n, points2n, P1, P2)

fig = plt.figure()
fig.suptitle('3D reconstructed', fontsize=16)
ax = fig.gca(projection='3d')
ax.plot(Points3D[0], Points3D[1], Points3D[2], 'b.')
ax.set_xlabel('x axis')
ax.set_ylabel('y axis')
ax.set_zlabel('z axis')
ax.view_init(elev=135, azim=90)
plt.savefig('Reconstruction.jpg')
plt.show()

其重建效果如下（效果一般）：

圖3：三維重建

三、結論

從重建的結果來看，單目三維重建效果一般，我認為可能與這幾方面因素有關：

（1）圖片拍攝形式。如果是進行單目三維重建任務，在拍攝圖片時最好保持平行移動相機，且最好正面拍攝，即不要斜著拍或特異角度進行拍攝；

（2）拍攝時周邊環境干擾。選取拍攝的地點最好保持單一，減少無關物體的干擾；

（3）拍攝光源問題。選取的拍照場地要保證合適的亮度（具體情況要試才知道你們的光源是否達標），還有就是移動相機的時候也要保證前一時刻和此時刻的光源一致性。

其實，單目三維重建的效果確實一般，就算將各方面情況都拉滿，可能得到的重建效果也不是特別好。或者我們可以考慮採用雙目三維重建，雙目三維重建效果肯定是要比單目的效果好的，在實現是也就麻煩一（億）點點，哈哈。其實也沒有多太多的操作，主要就是整兩個相機拍攝和標定兩個相機麻煩點，其他的都還好。

四、程式碼

本次實驗的全部程式碼如下：
GitHub：https://github.com/DeepVegChicken/Learning-3DReconstruction

import cv2
import json
import numpy as np
import glob
from PIL import Image
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False


def cart2hom(arr):
    """ Convert catesian to homogenous points by appending a row of 1s
    :param arr: array of shape (num_dimension x num_points)
    :returns: array of shape ((num_dimension+1) x num_points) 
    """
    if arr.ndim == 1:
        return np.hstack([arr, 1])
    return np.asarray(np.vstack([arr, np.ones(arr.shape[1])]))


def compute_P_from_essential(E):
    """ Compute the second camera matrix (assuming P1 = [I 0])
        from an essential matrix. E = [t]R
    :returns: list of 4 possible camera matrices.
    """
    U, S, V = np.linalg.svd(E)

    # Ensure rotation matrix are right-handed with positive determinant
    if np.linalg.det(np.dot(U, V)) < 0:
        V = -V

    # create 4 possible camera matrices (Hartley p 258)
    W = np.array([[0, -1, 0], [1, 0, 0], [0, 0, 1]])
    P2s = [np.vstack((np.dot(U, np.dot(W, V)).T, U[:, 2])).T,
           np.vstack((np.dot(U, np.dot(W, V)).T, -U[:, 2])).T,
           np.vstack((np.dot(U, np.dot(W.T, V)).T, U[:, 2])).T,
           np.vstack((np.dot(U, np.dot(W.T, V)).T, -U[:, 2])).T]

    return P2s


def correspondence_matrix(p1, p2):
    p1x, p1y = p1[:2]
    p2x, p2y = p2[:2]

    return np.array([
        p1x * p2x, p1x * p2y, p1x,
        p1y * p2x, p1y * p2y, p1y,
        p2x, p2y, np.ones(len(p1x))
    ]).T

    return np.array([
        p2x * p1x, p2x * p1y, p2x,
        p2y * p1x, p2y * p1y, p2y,
        p1x, p1y, np.ones(len(p1x))
    ]).T


def scale_and_translate_points(points):
    """ Scale and translate image points so that centroid of the points
        are at the origin and avg distance to the origin is equal to sqrt(2).
    :param points: array of homogenous point (3 x n)
    :returns: array of same input shape and its normalization matrix
    """
    x = points[0]
    y = points[1]
    center = points.mean(axis=1)  # mean of each row
    cx = x - center[0]  # center the points
    cy = y - center[1]
    dist = np.sqrt(np.power(cx, 2) + np.power(cy, 2))
    scale = np.sqrt(2) / dist.mean()
    norm3d = np.array([
        [scale, 0, -scale * center[0]],
        [0, scale, -scale * center[1]],
        [0, 0, 1]
    ])

    return np.dot(norm3d, points), norm3d


def compute_image_to_image_matrix(x1, x2, compute_essential=False):
    """ Compute the fundamental or essential matrix from corresponding points
        (x1, x2 3*n arrays) using the 8 point algorithm.
        Each row in the A matrix below is constructed as
        [x'*x, x'*y, x', y'*x, y'*y, y', x, y, 1]
    """
    A = correspondence_matrix(x1, x2)
    # compute linear least square solution
    U, S, V = np.linalg.svd(A)
    F = V[-1].reshape(3, 3)

    # constrain F. Make rank 2 by zeroing out last singular value
    U, S, V = np.linalg.svd(F)
    S[-1] = 0
    if compute_essential:
        S = [1, 1, 0]  # Force rank 2 and equal eigenvalues
    F = np.dot(U, np.dot(np.diag(S), V))

    return F


def compute_normalized_image_to_image_matrix(p1, p2, compute_essential=False):
    """ Computes the fundamental or essential matrix from corresponding points
        using the normalized 8 point algorithm.
    :input p1, p2: corresponding points with shape 3 x n
    :returns: fundamental or essential matrix with shape 3 x 3
    """
    n = p1.shape[1]
    if p2.shape[1] != n:
        raise ValueError('Number of points do not match.')

    # preprocess image coordinates
    p1n, T1 = scale_and_translate_points(p1)
    p2n, T2 = scale_and_translate_points(p2)

    # compute F or E with the coordinates
    F = compute_image_to_image_matrix(p1n, p2n, compute_essential)

    # reverse preprocessing of coordinates
    # We know that P1' E P2 = 0
    F = np.dot(T1.T, np.dot(F, T2))

    return F / F[2, 2]


def compute_fundamental_normalized(p1, p2):
    return compute_normalized_image_to_image_matrix(p1, p2)


def compute_essential_normalized(p1, p2):
    return compute_normalized_image_to_image_matrix(p1, p2, compute_essential=True)


def skew(x):
    """ Create a skew symmetric matrix *A* from a 3d vector *x*.
        Property: np.cross(A, v) == np.dot(x, v)
    :param x: 3d vector
    :returns: 3 x 3 skew symmetric matrix from *x*
    """
    return np.array([
        [0, -x[2], x[1]],
        [x[2], 0, -x[0]],
        [-x[1], x[0], 0]
    ])


def reconstruct_one_point(pt1, pt2, m1, m2):
    """
        pt1 and m1 * X are parallel and cross product = 0
        pt1 x m1 * X  =  pt2 x m2 * X  =  0
    """
    A = np.vstack([
        np.dot(skew(pt1), m1),
        np.dot(skew(pt2), m2)
    ])
    U, S, V = np.linalg.svd(A)
    P = np.ravel(V[-1, :4])

    return P / P[3]


def linear_triangulation(p1, p2, m1, m2):
    """
    Linear triangulation (Hartley ch 12.2 pg 312) to find the 3D point X
    where p1 = m1 * X and p2 = m2 * X. Solve AX = 0.
    :param p1, p2: 2D points in homo. or catesian coordinates. Shape (3 x n)
    :param m1, m2: Camera matrices associated with p1 and p2. Shape (3 x 4)
    :returns: 4 x n homogenous 3d triangulated points
    """
    num_points = p1.shape[1]
    res = np.ones((4, num_points))

    for i in range(num_points):
        A = np.asarray([
            (p1[0, i] * m1[2, :] - m1[0, :]),
            (p1[1, i] * m1[2, :] - m1[1, :]),
            (p2[0, i] * m2[2, :] - m2[0, :]),
            (p2[1, i] * m2[2, :] - m2[1, :])
        ])

        _, _, V = np.linalg.svd(A)
        X = V[-1, :4]
        res[:, i] = X / X[3]

    return res


def writetofile(dict, path):
    for index, item in enumerate(dict):
        dict[item] = np.array(dict[item])
        dict[item] = dict[item].tolist()
    js = json.dumps(dict)
    with open(path, 'w') as f:
        f.write(js)
        print("引數已成功儲存到檔案")


def readfromfile(path):
    with open(path, 'r') as f:
        js = f.read()
        mydict = json.loads(js)
    print("引數讀取成功")
    return mydict


def camera_calibration(SaveParamPath, ImagePath):
    # 迴圈中斷
    criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
    # 棋盤格尺寸
    row = 11
    column = 8
    objpoint = np.zeros((row * column, 3), np.float32)
    objpoint[:, :2] = np.mgrid[0:row, 0:column].T.reshape(-1, 2)

    objpoints = []  # 3d point in real world space
    imgpoints = []  # 2d points in image plane.
    batch_images = glob.glob(ImagePath + '/*.jpg')
    for i, fname in enumerate(batch_images):
        img = cv2.imread(batch_images[i])
        imgGray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
        # find chess board corners
        ret, corners = cv2.findChessboardCorners(imgGray, (row, column), None)
        # if found, add object points, image points (after refining them)
        if ret:
            objpoints.append(objpoint)
            corners2 = cv2.cornerSubPix(imgGray, corners, (11, 11), (-1, -1), criteria)
            imgpoints.append(corners2)
            # Draw and display the corners
            img = cv2.drawChessboardCorners(img, (row, column), corners2, ret)
            cv2.imwrite('Checkerboard_Image/Temp_JPG/Temp_' + str(i) + '.jpg', img)
    print("成功提取:", len(batch_images), "張圖片角點！")
    ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, imgGray.shape[::-1], None, None)
    dict = {'ret': ret, 'mtx': mtx, 'dist': dist, 'rvecs': rvecs, 'tvecs': tvecs}
    writetofile(dict, SaveParamPath)

    meanError = 0
    for i in range(len(objpoints)):
        imgpoints2, _ = cv2.projectPoints(objpoints[i], rvecs[i], tvecs[i], mtx, dist)
        error = cv2.norm(imgpoints[i], imgpoints2, cv2.NORM_L2) / len(imgpoints2)
        meanError += error
    print("total error: ", meanError / len(objpoints))


def epipolar_geometric(Images_Path, K):
    IMG = glob.glob(Images_Path)
    img1, img2 = cv2.imread(IMG[0]), cv2.imread(IMG[1])
    img1_gray = cv2.cvtColor(img1, cv2.COLOR_BGR2GRAY)
    img2_gray = cv2.cvtColor(img2, cv2.COLOR_BGR2GRAY)

    # Initiate SURF detector
    SURF = cv2.xfeatures2d_SURF.create()

    # compute keypoint & descriptions
    keypoint1, descriptor1 = SURF.detectAndCompute(img1_gray, None)
    keypoint2, descriptor2 = SURF.detectAndCompute(img2_gray, None)
    print("角點數量：", len(keypoint1), len(keypoint2))

    # Find point matches
    bf = cv2.BFMatcher(cv2.NORM_L2, crossCheck=True)
    matches = bf.match(descriptor1, descriptor2)
    print("匹配點數量：", len(matches))

    src_pts = np.asarray([keypoint1[m.queryIdx].pt for m in matches])
    dst_pts = np.asarray([keypoint2[m.trainIdx].pt for m in matches])
    # plot
    knn_image = cv2.drawMatches(img1_gray, keypoint1, img2_gray, keypoint2, matches[:-1], None, flags=2)
    image_ = Image.fromarray(np.uint8(knn_image))
    image_.save("MatchesImage.jpg")

    # Constrain matches to fit homography
    retval, mask = cv2.findHomography(src_pts, dst_pts, cv2.RANSAC, 100.0)

    # We select only inlier points
    points1 = src_pts[mask.ravel() == 1]
    points2 = dst_pts[mask.ravel() == 1]

    points1 = cart2hom(points1.T)
    points2 = cart2hom(points2.T)
    # plot
    fig, ax = plt.subplots(1, 2)
    ax[0].autoscale_view('tight')
    ax[0].imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
    ax[0].plot(points1[0], points1[1], 'r.')
    ax[1].autoscale_view('tight')
    ax[1].imshow(cv2.cvtColor(img2, cv2.COLOR_BGR2RGB))
    ax[1].plot(points2[0], points2[1], 'r.')
    plt.savefig('MatchesPoints.jpg')
    fig.show()
    # 

    points1n = np.dot(np.linalg.inv(K), points1)
    points2n = np.dot(np.linalg.inv(K), points2)
    E = compute_essential_normalized(points1n, points2n)
    print('Computed essential matrix:', (-E / E[0][1]))

    P1 = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]])
    P2s = compute_P_from_essential(E)

    ind = -1
    for i, P2 in enumerate(P2s):
        # Find the correct camera parameters
        d1 = reconstruct_one_point(points1n[:, 0], points2n[:, 0], P1, P2)
        # Convert P2 from camera view to world view
        P2_homogenous = np.linalg.inv(np.vstack([P2, [0, 0, 0, 1]]))
        d2 = np.dot(P2_homogenous[:3, :4], d1)
        if d1[2] > 0 and d2[2] > 0:
            ind = i

    P2 = np.linalg.inv(np.vstack([P2s[ind], [0, 0, 0, 1]]))[:3, :4]
    Points3D = linear_triangulation(points1n, points2n, P1, P2)

    return Points3D


def main():
    CameraParam_Path = 'CameraParam.txt'
    CheckerboardImage_Path = 'Checkerboard_Image'
    Images_Path = 'SubstitutionCalibration_Image/*.jpg'

    # 計算相機引數
    camera_calibration(CameraParam_Path, CheckerboardImage_Path)
    # 讀取相機引數
    config = readfromfile(CameraParam_Path)
    K = np.array(config['mtx'])
    # 計算3D點
    Points3D = epipolar_geometric(Images_Path, K)
    # 重建3D點
    fig = plt.figure()
    fig.suptitle('3D reconstructed', fontsize=16)
    ax = fig.gca(projection='3d')
    ax.plot(Points3D[0], Points3D[1], Points3D[2], 'b.')
    ax.set_xlabel('x axis')
    ax.set_ylabel('y axis')
    ax.set_zlabel('z axis')
    ax.view_init(elev=135, azim=90)
    plt.savefig('Reconstruction.jpg')
    plt.show()


if __name__ == '__main__':
    main()

總結

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如何基於python實現單目三維重建詳解

目錄

一、單目三維重建概述

二、實現過程

（1）相機的標定

（2）影象特徵提取及匹配

（3）三維重建

三、結論

四、程式碼

總結

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