1，介紹
看到標題裏的兩個詞 Delaunay 三角剖分 和 Voronoi，估計第一次見到的小夥伴可能一臉懵(說的就是我自己)，爲了更直觀地認識這兩個概念，請看下圖：
左圖是上篇文章提到的 68個人臉特徵點標記，中圖是基於左圖的基礎上對 68個點進行 點與點之間形成 Delaunay 三角剖分(德勞內)，左圖是基於中間圖繪製的的 Voronoi Diagram (沃羅諾伊圖)
2，Delaunay 三角剖分
Delaunay 三角剖分算法命名那個來源於俄國數學家 Boris Delaunay，該方法目的是最大化三角剖分中三角形中最小角，目的是避免“極瘦“的三角形的出現
上方左圖與右圖的變換站示的就是 Delaunay 怎樣最大化最小角，左右兩圖是對於四個頂點的兩種不同的剖分方式；但左圖中 頂點 A、C 不在三角形 BCD、ABD 的外接圓內，使得 角 C 非常大
右圖對剖分形式有兩個方的 改動：1，B、D 座標右移；2，剖分線由 BD 變爲 AC ；最後使得剖分後的三角形不那麼”瘦“
3，Voronoi Diagram
Voronoi 命名同樣也是來源於一個 俄國數學家 Georgy Voronoy，有趣的是 Georgy Voronoy 是 Boris Delaunay 的博士導師
Voronoi 圖是基於 Delaunay 三角剖分創建，取 Delaunay 剖分的所有頂點，用線段連接相鄰三角形的外接圓心，構成一個區域，相鄰不同區域用不同顏色覆蓋；Voronoi 圖目前常用於凸邊形區域分割領域
從下面20個頂點組成的 Voronoi 圖種可以瞭解到，圖中相鄰點與點之間的距離是等長的
4，OpenCV 代碼實現
1，首先需要獲取人臉 68 個特徵點座標，並寫入 txt 文件，方便後面使用,這裏會用到的代碼
import dlib
import cv2
predictor_path = "E:/data_ceshi/shape_predictor_68_face_landmarks.dat"
png_path = "E:/data_ceshi/timg.jpg"
txt_path = "E:/data_ceshi/points.txt"
f = open(txt_path,'w+')
detector = dlib.get_frontal_face_detector()
#相撞
predicator = dlib.shape_predictor(predictor_path)
win = dlib.image_window()
img1 = cv2.imread(png_path)
dets = detector(img1,1)
print("Number of faces detected : {}".format(len(dets)))
for k,d in enumerate(dets):
print("Detection {} left:{} Top: {} Right {} Bottom {}".format(
k,d.left(),d.top(),d.right(),d.bottom()
))
lanmarks = [[p.x,p.y] for p in predicator(img1,d).parts()]
for idx,point in enumerate(lanmarks):
f.write(str(point[0]))
f.write("\t")
f.write(str(point[1]))
f.write('\n')
寫入後，txt 中格式如下
2，利用圖像大小創建一個矩形範圍( 因爲臉部特徵點都是圖中)，創建一個 Subdiv2D 實例(後面兩個圖的繪製都會用到這個類)，把點都插入創建的類中：
#Create an instance of Subdiv2d
subdiv = cv2.Subdiv2D(rect)
#Create an array of points
points = []
#Read in the points from a text file
with open("E:/data_ceshi/points.txt") as file:
for line in file:
x,y = line.split()
points.append((int(x),int(y)))
#Insert points into subdiv
for p in points:
subdiv.insert(p)
3，在原圖上繪製 Delaunay 三角剖分並預覽，這裏我加入了動畫效果 — 逐線段繪製(用了 for 循環)
#Draw delaunay triangles
def draw_delaunay(img,subdiv,delaunay_color):
trangleList = subdiv.getTriangleList()
size = img.shape
r = (0,0,size[1],size[0])
for t in trangleList:
pt1 = (t[0],t[1])
pt2 = (t[2],t[3])
pt3 = (t[4],t[5])
if (rect_contains(r,pt1) and rect_contains(r,pt2) and rect_contains(r,pt3)):
cv2.line(img,pt1,pt2,delaunay_color,1)
cv2.line(img,pt2,pt3,delaunay_color,1)
cv2.line(img,pt3,pt1,delaunay_color,1)
#Insert points into subdiv
for p in points:
subdiv.insert(p)
#Show animate
if animate:
img_copy = img_orig.copy()
#Draw delaunay triangles
draw_delaunay(img_copy,subdiv,(255,255,255))
cv2.imshow(win_delaunary,img_copy)
cv2.waitKey(100)
預覽效果如下：
4，最後繪製 Voronoi Diagram
def draw_voronoi(img,subdiv):
(facets,centers) = subdiv.getVoronoiFacetList([])
for i in range(0,len(facets)):
ifacet_arr = []
for f in facets[i]:
ifacet_arr.append(f)
ifacet = np.array(ifacet_arr,np.int)
color = (random.randint(0,255),random.randint(0,255),random.randint(0,255))
cv2.fillConvexPoly(img,ifacet,color)
ifacets = np.array([ifacet])
cv2.polylines(img,ifacets,True,(0,0,0),1)
cv2.circle(img,(centers[i][0],centers[i][1]),3,(0,0,0))
for p in points:
draw_point(img,p,(0,0,255))
#Allocate space for Voroni Diagram
img_voronoi = np.zeros(img.shape,dtype = img.dtype)
#Draw Voonoi diagram
draw_voronoi(img_voronoi,subdiv)
4，小總結
Delaunay 三角剖分對於第一次接觸的小夥伴來說可能還未完全理解，但這一剖分技術對於做人臉識別、融合、換臉是不可或缺的，本篇文章只是僅通過 OpenCV 的 Subdiv2D 函數下實現此功能，真正的識別技術要比這個複雜地多。
對於感興趣的小夥伴們，我的建議還是跟着提供的代碼敲一遍，完整代碼貼在下面：
import cv2
import numpy as np
import random
#Check if a point is insied a rectangle
def rect_contains(rect,point):
if point[0] <rect[0]:
return False
elif point[1]<rect[1]:
return False
elif point[0]>rect[2]:
return False
elif point[1] >rect[3]:
return False
return True
# Draw a point
def draw_point(img,p,color):
cv2.circle(img,p,2,color)
#Draw delaunay triangles
def draw_delaunay(img,subdiv,delaunay_color):
trangleList = subdiv.getTriangleList()
size = img.shape
r = (0,0,size[1],size[0])
for t in trangleList:
pt1 = (t[0],t[1])
pt2 = (t[2],t[3])
pt3 = (t[4],t[5])
if (rect_contains(r,pt1) and rect_contains(r,pt2) and rect_contains(r,pt3)):
cv2.line(img,pt1,pt2,delaunay_color,1)
cv2.line(img,pt2,pt3,delaunay_color,1)
cv2.line(img,pt3,pt1,delaunay_color,1)
# Draw voronoi diagram
def draw_voronoi(img,subdiv):
(facets,centers) = subdiv.getVoronoiFacetList([])
for i in range(0,len(facets)):
ifacet_arr = []
for f in facets[i]:
ifacet_arr.append(f)
ifacet = np.array(ifacet_arr,np.int)
color = (random.randint(0,255),random.randint(0,255),random.randint(0,255))
cv2.fillConvexPoly(img,ifacet,color)
ifacets = np.array([ifacet])
cv2.polylines(img,ifacets,True,(0,0,0),1)
cv2.circle(img,(centers[i][0],centers[i][1]),3,(0,0,0))
if __name__ == '__main__':
#Define window names;
win_delaunary = "Delaunay Triangulation"
win_voronoi = "Voronoi Diagram"
#Turn on animations while drawing triangles
animate = True
#Define colors for drawing
delaunary_color = (255,255,255)
points_color = (0,0,255)
#Read in the image
img_path = "E:/data_ceshi/timg.jpg"
img = cv2.imread(img_path)
#Keep a copy around
img_orig = img.copy()
#Rectangle to be used with Subdiv2D
size = img.shape
rect = (0,0,size[1],size[0])
#Create an instance of Subdiv2d
subdiv = cv2.Subdiv2D(rect)
#Create an array of points
points = []
#Read in the points from a text file
with open("E:/data_ceshi/points.txt") as file:
for line in file:
x,y = line.split()
points.append((int(x),int(y)))
#Insert points into subdiv
for p in points:
subdiv.insert(p)
#Show animate
if animate:
img_copy = img_orig.copy()
#Draw delaunay triangles
draw_delaunay(img_copy,subdiv,(255,255,255))
cv2.imshow(win_delaunary,img_copy)
cv2.waitKey(100)
#Draw delaunary triangles
draw_delaunay(img,subdiv,(255,255,255))
#Draw points
for p in points:
draw_point(img,p,(0,0,255))
#Allocate space for Voroni Diagram
img_voronoi = np.zeros(img.shape,dtype = img.dtype)
#Draw Voonoi diagram
draw_voronoi(img_voronoi,subdiv)
#Show results
cv2.imshow(win_delaunary,img)
cv2.imshow(win_voronoi,img_voronoi)
cv2.waitKey(0)
參考鏈接：
https://www.learnopencv.com/