OpenCV中已知矩形三条直线（角度与截距），能否推导第四条边？

我在OpenCV中检测具有已知尺寸的矩形，已编写可正常运行的代码用于检测四条边，但最远的边难以检测，常导致透视变换环节出现问题。

我的核心问题：从理论层面来说，已知三条直线（包含角度与截距）是否足以近似出第四条直线？（此前我已查阅资料，但未找到答案）

import numpy as np
import cv2
from sklearn.cluster import AgglomerativeClustering

# find intersection of lines
def line_intersect(m1, b1, m2, b2):

    if m1 == m2:
        print ("These lines are parallel!!!")
        return None

    x = int((b2 - b1) / (m1 - m2))

    y = int(m1 * x + b1)

    return [x,y]

# method specs
width_error = 10
height_error = 10
kernel_size = 7
kernel_dilate = np.ones((1, 1), 'uint8')
kernel = np.ones((5, 5), 'uint8')

# read and process image
img = cv2.imread('assets/game-frames/hard-m-2019-124-1200.jpg')
gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
blur_gray = cv2.GaussianBlur(gray,(kernel_size, kernel_size),0)
edges = cv2.Canny(blur_gray, 0, 100, apertureSize = 3)
dilate_img = cv2.dilate(edges, kernel_dilate, iterations=3)
closing = cv2.morphologyEx(dilate_img, cv2.MORPH_CLOSE, kernel)

# find hough lines
lines = cv2.HoughLinesP(closing, 2, np.pi/180, 100, minLineLength=20, maxLineGap=10)
lines_np = np.reshape(lines, (np.int32(lines.size/4), 4))
lines_np = lines_np[(lines_np[:, 2] - lines_np[:, 0]) != 0]
lines_np = np.c_[lines_np, (lines_np[:, 3] - lines_np[:, 1])/(lines_np[:, 2] - lines_np[:, 0])]
lines_np = np.c_[lines_np, np.sqrt((lines_np[:, 3] - lines_np[:, 1])**2 + (lines_np[:, 2] - lines_np[:, 0])**2)]

# find lengthwise lines
lengthwise_lines = lines_np[(abs(lines_np[:, 4]) < 3.5) & (abs(lines_np[:, 4]) > 1.20) & (lines_np[:, 5] > 100)]
if lengthwise_lines[:, 4].size < 2: print('No lengthwise lines!')
ward_length = AgglomerativeClustering(n_clusters = None, distance_threshold = 0.50, linkage = "ward").fit(abs(lengthwise_lines[:, 4].reshape(-1,1)))
lengthwise_lines = np.c_[lengthwise_lines, ward_length.labels_]
length_clusts = np.bincount(ward_length.labels_).argsort()[-2:]
lengthwise_lines = lengthwise_lines[np.isin(ward_length.labels_, length_clusts)]

# find extremities
x_max = np.max(lengthwise_lines[:,[0,2]].reshape(-1,1))
x_min = np.amin(lengthwise_lines[:,[0,2]])
y_coords = lengthwise_lines[:, [1, 3]].reshape(-1,1)
ward = AgglomerativeClustering(n_clusters = None, distance_threshold = 10, linkage = "ward").fit(y_coords)
want_clusts = np.bincount(ward.labels_).argsort()[-2:]
y_ext1 = np.median(y_coords[np.isin(ward.labels_, want_clusts[0])])
y_ext2 = np.median(y_coords[np.isin(ward.labels_, want_clusts[1])])
y_max = max(y_ext1, y_ext2)
y_min = min(y_ext1, y_ext2)

# find outer lengthwise lines
length_want = ward_length.labels_[np.isin(ward_length.labels_, length_clusts)][np.argmin(abs(lengthwise_lines[:,4]))]
lengthwise_lines = lengthwise_lines[lengthwise_lines[:, 6] == length_want]
lengthwise_lines = np.c_[lengthwise_lines, (lengthwise_lines[:,1] - (lengthwise_lines[:,4]*lengthwise_lines[:,0]))]
lengthwise_lines = np.c_[lengthwise_lines, ((np.max(lengthwise_lines[:,1]) - lengthwise_lines[:,5])/lengthwise_lines[:,4])]

# subset left and right outer lengthwise lines
l_left = lengthwise_lines[lengthwise_lines[:,4] < 0]
l_right = lengthwise_lines[lengthwise_lines[:,4] > 0]

# find top and bottom lines
widthwise_lines = lines_np[(abs(lines_np[:, 4]) < 0.10)]
widthwise_lines = np.c_[widthwise_lines, (widthwise_lines[:,1] - (widthwise_lines[:,4]*widthwise_lines[:,0]))]
bottom_lines = widthwise_lines[np.where((np.amin(widthwise_lines[:,[1,3]], axis = 1) >= y_min - height_error) & (np.amin(widthwise_lines[:,[1,3]], axis = 1) <= y_min + height_error) & (np.amin(widthwise_lines[:,[0,2]], axis = 1) >= x_min - width_error) & (np.amax(widthwise_lines[:,[0,2]], axis = 1) <= x_max + width_error))[0]]
top_lines = widthwise_lines[np.where((np.amax(widthwise_lines[:,[1,3]], axis = 1) >= y_max - height_error) & (np.amax(widthwise_lines[:,[1,3]], axis = 1) <= y_max + height_error) & (np.amin(widthwise_lines[:,[0,2]], axis = 1) >= x_min - width_error) & (np.amax(widthwise_lines[:,[0,2]], axis = 1) <= x_max + width_error))[0]]

# if no lines found for any border, stop
if top_lines.size == 0 or bottom_lines.size == 0 or l_left.size == 0 or l_right.size == 0: print('No Lengthwise lines!')

# take median of left outer lengthwise lines
l_left_b = np.median(l_left[:,7])
l_left_m = np.median(l_left[:,4])

# take median of right outer lengthwise lines
l_right_b = np.median(l_right[:,7])
l_right_m = np.median(l_right[:,4])

# take median of top widthwise lines
top_lines_b = np.median(top_lines[:,6])
top_lines_m = np.median(top_lines[:,4])

# take median of bottom widthwise lines
bottom_lines_b = np.median(bottom_lines[:,6])
bottom_lines_m = np.median(bottom_lines[:,4])

# find interesction of lines
int_pt1 = line_intersect(l_left_m, l_left_b, bottom_lines_m, bottom_lines_b)
int_pt2 = line_intersect(l_right_m, l_right_b, bottom_lines_m, bottom_lines_b)
int_pt3 = line_intersect(l_left_m, l_left_b, top_lines_m, top_lines_b)
int_pt4 = line_intersect(l_right_m, l_right_b, top_lines_m, top_lines_b)

# draw intersections
cv2.circle(img, int_pt1, 3, (0, 255, 0), -1)
cv2.circle(img, int_pt3, 3, (255, 255, 0), -1)
cv2.circle(img, int_pt2, 3, (0, 255, 0), -1)
cv2.circle(img, int_pt4, 3, (255, 255, 0), -1)

# show image
cv2.imshow('frame diff ', img)
cv2.waitKey(0)

内容的提问来源于stack exchange，提问作者spazznolo