如何在opencv中应用三点三角形渐变？

Question

假设我们有像 this one:

这样的 Delaunay 三角剖分

生产于 fillConvexPoly getVoronoiFacetList

里面有三角形可以通过getTriangleList获得。我想画德劳内三角剖分就像它是由像这样的三角形组成的平滑渐变图像：

如何在opencv中做这样的事情？

Answer 1

在 OpenCV 中，我认为没有现成的函数可以做到这一点。您将不得不遍历图像中的每个像素并计算重心（区域）插值。例如，参见 https://codeplea.com/triangular-interpolation

但是，在Python/Wand（基于ImageMagick）中，您可以按如下方式进行：

import numpy as np
from wand.image import Image
from wand.color import Color
from wand.drawing import Drawing
from wand.display import display

# define vertices of triangle
p1 = (250, 100)
p2 = (100, 400)
p3 = (400, 400)

# define barycentric colors and vertices
colors = {
    Color('RED'): p1,
    Color('GREEN1'): p2,
    Color('BLUE'): p3
}

# create black image
black = np.zeros([500, 500, 3], dtype=np.uint8)

with Image.from_array(black) as img:
    with img.clone() as mask:
        with Drawing() as draw:
            points = [p1, p2, p3]
            draw.fill_color = Color('white')
            draw.polygon(points)
            draw.draw(mask)
            img.sparse_color('barycentric', colors)
            img.composite_channel('all_channels', mask, 'multiply', 0, 0)   
            img.format = 'png'
            img.save(filename='barycentric_image.png')
            display(img)

结果：

Answer 2

这是 Python/OpenCV 中的方法，但它会比我之前介绍的 Python/Wand 版本慢，因为它必须在每个循环中求解线性最小二乘方程重心坐标的像素。

import cv2
import numpy as np

# References: 
# 
# https://math.stackexchange.com/questions/81178/help-with-cramers-rule-and-barycentric-coordinates

# create black background image
result = np.zeros((500,500,3), dtype=np.uint8)

# Specify (x,y) triangle vertices
a = (250,100)
b = (100,400)
c = (400,400)

# Specify colors
red = (0,0,255)
green = (0,255,0)
blue = (255,0,0)

# Make array of vertices
# ax bx cx
# ay by cy
#  1  1  1
triArr = np.asarray([a[0],b[0],c[0], a[1],b[1],c[1], 1,1,1]).reshape((3, 3))

# Get bounding box of the triangle
xleft = min(a[0], b[0], c[0])
xright = max(a[0], b[0], c[0])
ytop = min(a[1], b[1], c[1])
ybottom = max(a[1], b[1], c[1])

# loop over each pixel, compute barycentric coordinates and interpolate vertex colors
for y in range(ytop, ybottom):

    for x in range(xleft, xright):

        # Store the current point as a matrix
        p = np.array([[x], [y], [1]])

        # Solve for least squares solution to get barycentric coordinates
        (alpha, beta, gamma) = np.linalg.lstsq(triArr, p, rcond=-1)[0]

        # The point is inside the triangle if all the following conditions are met; otherwise outside the triangle
        if alpha > 0 and beta > 0 and gamma > 0:
            # do barycentric interpolation on colors
            color = (red*alpha + green*beta + blue*gamma)
            result[y,x] = color

# show results
cv2.imshow('result', result)
cv2.waitKey(0)
cv2.destroyAllWindows()

# save results
cv2.imwrite('barycentric_triange.png', result)

结果：

Answer 3

我修改了 of @fmw42 以利用矢量计算（np.linalg.lstsq 支持）并删除了 for 循环以获得更好的性能。

    #!/usr/bon/env python
    import cv2
    import numpy as np
    
    # create black background image
    result = np.zeros((500,500,3), dtype=np.uint8)
    
    # Specify (x,y) triangle vertices
    a = (250,100)
    b = (100,400)
    c = (400,400)
    
    # Specify colors
    red = np.array([0,0,255])
    green = np.array([0,255,0])
    blue = np.array([255,0,0])
    
    # Make array of vertices
    # ax bx cx
    # ay by cy
    #  1  1  1
    triArr = np.asarray([a[0],b[0],c[0], a[1],b[1],c[1], 1,1,1]).reshape((3, 3))
    
    # Get bounding box of the triangle
    xleft = min(a[0], b[0], c[0])
    xright = max(a[0], b[0], c[0])
    ytop = min(a[1], b[1], c[1])
    ybottom = max(a[1], b[1], c[1])
    
    # Build np arrays of coordinates of the bounding box
    xs = range(xleft, xright)
    ys = range(ytop, ybottom)
    xv, yv = np.meshgrid(xs, ys)
    xv = xv.flatten()
    yv = yv.flatten()
    
    # Compute all least-squares /
    p = np.array([xv, yv, [1] * len(xv)])
    alphas, betas, gammas = np.linalg.lstsq(triArr, p, rcond=-1)[0]
    
    # Apply mask for pixels within the triangle only
    mask = (alphas > 0) & (betas > 0) & (gammas > 0)
    alphas_m = alphas[mask]
    betas_m = betas[mask]
    gammas_m = gammas[mask]
    xv_m = xv[mask]
    yv_m = yv[mask]
    
    def mul(a, b) :
        # Multiply two vectors into a matrix
        return np.asmatrix(b).T @ np.asmatrix(a)
    
    # Compute and assign colors
    colors = mul(red, alphas_m) + mul(green, betas_m) + mul(blue, gammas_m)
    result[xv_m, yv_m] = colors
    
    # show results
    cv2.imshow('result', result)
    cv2.waitKey(0)
    cv2.destroyAllWindows()

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