Develop Reference

Python OpenCV How to Apply Radial/Barrel Distortion?

A lot of questions about removing radial (or barrel) distortion, but how would I add it?
Visually, I want to take my input, which is presumed to be image (a), and distort it, to be like image (b):
And ideally I'd like a tunable parameter of some "radius" to control "how much distortion" I get. Based on what I want to do, it looks like I'd just need one parameter to control the 'radius of distortion' or whatever it would be called (correct me if I'm wrong).
How can I achieve this with OpenCV? I figure it must be possible because a lot of people try going the other way for things like this. I'm just not as familiar with the proper math operations and library calls to do it.
Any help much appreciated, cheers.

The program below creates barrel distortion
from wand.image import Image
import numpy as np
import cv2
with Image(filename='Path/to/Img/') as img:
print(img.size)
img.virtual_pixel = 'transparent'
img.distort('barrel', (0.1, 0.0, 0.0, 1.0)) # play around these values to create distortion
img.save(filename='filname.png')
# convert to opencv/numpy array format
img_opencv = np.array(img)
# display result with opencv
cv2.imshow("BARREL", img_opencv)
cv2.waitKey(0)
cv2.destroyAllWindows()

Here is one way to produce barrel or pincushion distortion in Python/OpenCV by creating the X and Y distortion maps and then using cv.remap() to do the warping.
Input:
import numpy as np
import cv2 as cv
import math
img = cv.imread('lena.jpg')
# grab the dimensions of the image
(h, w, _) = img.shape
# set up the x and y maps as float32
map_x = np.zeros((h, w), np.float32)
map_y = np.zeros((h, w), np.float32)
scale_x = 1
scale_y = 1
center_x = w/2
center_y = h/2
radius = w/2
#amount = -0.75 # negative values produce pincushion
amount = 0.75 # positive values produce barrel
# create map with the barrel pincushion distortion formula
for y in range(h):
delta_y = scale_y * (y - center_y)
for x in range(w):
# determine if pixel is within an ellipse
delta_x = scale_x * (x - center_x)
distance = delta_x * delta_x + delta_y * delta_y
if distance >= (radius * radius):
map_x[y, x] = x
map_y[y, x] = y
else:
factor = 1.0
if distance > 0.0:
factor = math.pow(math.sin(math.pi * math.sqrt(distance) / radius / 2), amount)
map_x[y, x] = factor * delta_x / scale_x + center_x
map_y[y, x] = factor * delta_y / scale_y + center_y
# do the remap
dst = cv.remap(img, map_x, map_y, cv.INTER_LINEAR)
# save the result
#cv.imwrite('lena_pincushion.jpg',dst)
cv.imwrite('lena_barrel.jpg',dst)
# show the result
cv.imshow('src', img)
cv.imshow('dst', dst)
cv.waitKey(0)
cv.destroyAllWindows()
Barrel (positive amount):
Pincushion (negative amount):

How do I divide a given image into 8 unique pie segments?

I am pretty new to Python and want to do the following: I want to divide the following image into 8 pie segments:
I want it to look something like this (I made this in PowerPoint):
The background should be black and the edge of the figure should have an unique color as well as each pie segment.
EDIT: I have written a code that divides the whole image in 8 segments:
from PIL import Image, ImageDraw
im=Image.open('C:/Users/20191881/Documents/OGO Beeldanalyse/Python/asymmetrie/rotation.png')
fill = 255
draw = ImageDraw.Draw(im)
draw.line((0,0) + im.size, fill)
draw.line((0, im.size[1], im.size[0], 0), fill)
draw.line((0.5*im.size[0],0, 0.5*im.size[0], im.size[1]), fill)
draw.line((0, 0.5*im.size[1], im.size[0], 0.5*im.size[1]), fill)
del draw
im.show()
The output gives:
The only thing that is left to do is to find a way to make each black segment inside the border an unique color and also give all the white edge segments an unique color.

Your code divides the image in eight parts, that's correct, but with respect to the image center, you don't get eight "angular equally" pie segments like you show in your sketch.
Here would be my solution, only using Pillow and the math module:
import math
from PIL import Image, ImageDraw
def segment_color(i_color, n_colors):
r = int((192 - 64) / (n_colors - 1) * i_color + 64)
g = int((224 - 128) / (n_colors - 1) * i_color + 128)
b = 255
return (r, g, b)
# Load image; generate ImageDraw
im = Image.open('path_to/vgdrD.png').convert('RGB')
draw = ImageDraw.Draw(im)
# Number of pie segments (must be an even number)
n = 8
# Replace (all-white) edge with defined edge color
edge_color = (255, 128, 0)
pixels = im.load()
for y in range(im.height):
for x in range(im.width):
if pixels[x, y] == (255, 255, 255):
pixels[x, y] = edge_color
# Draw lines with defined line color
line_color = (0, 255, 0)
d = min(im.width, im.height) - 10
center = (int(im.width/2), int(im.height)/2)
for i in range(int(n/2)):
angle = 360 / n * i
x1 = math.cos(angle/180*math.pi) * d/2 + center[0]
y1 = math.sin(angle/180*math.pi) * d/2 + center[1]
x2 = math.cos((180+angle)/180*math.pi) * d/2 + center[0]
y2 = math.sin((180+angle)/180*math.pi) * d/2 + center[1]
draw.line([(x1, y1), (x2, y2)], line_color)
# Fill pie segments with defined segment colors
for i in range(n):
angle = 360 / n * i + 360 / n / 2
x = math.cos(angle/180*math.pi) * 20 + center[0]
y = math.sin(angle/180*math.pi) * 20 + center[1]
ImageDraw.floodfill(im, (x, y), segment_color(i, n))
im.save(str(n) + '_pie.png')
For n = 8 pie segments, the following result is produced:
The first step is to replace all white pixels in the original image with the desired edge color. Of course, the assumption here is, that there are no other (white) pixels in the image. Also, this might be better done using NumPy and vectorized code, but I wanted to keep the solution Pillow-only.
Next step is to draw the (green) lines. Here, I calculate the proper coordinates of the lines' start and end using sin and cos.
The last step is to flood fill the pie segments' area, cf. ImageDraw.floodfill. Therefore, I calculate the seed points the same way as before, but add an angular shift to hit a point exactly within the pie segment.
As you can see, n is variable in my solution (n must be even):
Of course, there are limitations regarding the angular resolution, most due to the small image.
Hope that helps!
EDIT: Here's a modified version to also allow for individually colored edges.
import math
from PIL import Image, ImageDraw
def segment_color(i_color, n_colors):
r = int((192 - 64) / (n_colors - 1) * i_color + 64)
g = int((224 - 128) / (n_colors - 1) * i_color + 128)
b = 255
return (r, g, b)
def edge_color(i_color, n_colors):
r = 255
g = 255 - int((224 - 32) / (n_colors - 1) * i_color + 32)
b = 255 - int((192 - 16) / (n_colors - 1) * i_color + 16)
return (r, g, b)
# Load image; generate ImageDraw
im = Image.open('images/vgdrD.png').convert('RGB')
draw = ImageDraw.Draw(im)
center = (int(im.width/2), int(im.height)/2)
# Number of pie segments (must be an even number)
n = 8
# Replace (all-white) edge with defined edge color
max_len = im.width + im.height
im_pix = im.load()
for i in range(n):
mask = Image.new('L', im.size, 0)
mask_draw = ImageDraw.Draw(mask)
angle = 360 / n * i
x1 = math.cos(angle/180*math.pi) * max_len + center[0]
y1 = math.sin(angle/180*math.pi) * max_len + center[1]
angle = 360 / n * (i+1)
x2 = math.cos(angle/180*math.pi) * max_len + center[0]
y2 = math.sin(angle/180*math.pi) * max_len + center[1]
mask_draw.polygon([center, (x1, y1), (x2, y2)], 255)
mask_pix = mask.load()
for y in range(im.height):
for x in range(im.width):
if (im_pix[x, y] == (255, 255, 255)) & (mask_pix[x, y] == 255):
im_pix[x, y] = edge_color(i, n)
# Draw lines with defined line color
line_color = (0, 255, 0)
d = min(im.width, im.height) - 10
for i in range(int(n/2)):
angle = 360 / n * i
x1 = math.cos(angle/180*math.pi) * d/2 + center[0]
y1 = math.sin(angle/180*math.pi) * d/2 + center[1]
x2 = math.cos((180+angle)/180*math.pi) * d/2 + center[0]
y2 = math.sin((180+angle)/180*math.pi) * d/2 + center[1]
draw.line([(x1, y1), (x2, y2)], line_color)
# Fill pie segments with defined segment colors
for i in range(n):
angle = 360 / n * i + 360 / n / 2
x = math.cos(angle/180*math.pi) * 20 + center[0]
y = math.sin(angle/180*math.pi) * 20 + center[1]
ImageDraw.floodfill(im, (x, y), segment_color(i, n))
im.save(str(n) + '_pie.png')
Binary masks for each pie segment are created, and all white pixels only within that binary mask are replaced with a defined edge color.
Using NumPy still seems favorable, but I was curious to do that in Pillow only.

Image-Processing: Converting normal pictures into FishEye images with intrinsic matrix

I need to synthesize many FishEye images with different intrinsic matrices based on normal pictures. I am following the method mentioned in this paper.
Ideally, if the algorithm is correct, the ideal fish eye effect should look like this:
.
But when I used my algorithm to convert a picture
it looks like this
So below is my code's flow:
1. First, I read the raw image with cv2
def read_img(image):
img = ndimage.imread(image) #this would return a 4-d array: [R,G,B,255]
img_shape = img.shape
print(img_shape)
#get the pixel coordinate
w = img_shape[1] #the width
# print(w)
h= img_shape[0] #the height
# print(h)
uv_coord = []
for u in range(w):
for v in range(h):
uv_coord.append([float(u),float(v)]) #this records the coord in the fashion of [x1,y1],[x1, y2], [x1, y3]....
return np.array(uv_coord)
Then, based on the paper:
r(θ) = k1θ + k2θ^3 + k3θ^5 + k4θ^7, (1)
where Ks are the distorted coefficients
Given pixel coordinates (x,y) in the pinhole projection image, the corresponding image coordinates (x',y')in the fisheye can be computed as:
x'=r(θ) cos(ϕ), y' = r(θ) sin(ϕ), (2)
where ϕ = arctan((y − y0)/(x − x0)), and (x0, y0) are the coordinates of the principal point in the pinhole projection image.
And then the image coordinates (x',y') is converted into pixel coordinates (xf,yf): (xf, yf):
*xf = mu * x' + u0, yf = mv * y' + v0,* (3)
where (u0, v0) are the coordinates of the principle points in the fisheye, and mu, mv denote the number of pixels per unit distance in the horizontal and vertica directions. So I am guessing there are just from the intrinsic matrix [fx, fy] and u0 v0 are the [cx, cy].
def add_distortion(sourceUV, dmatrix,Kmatrix):
'''This function is programmed to remove the pixel of the given original image coords
input arguments:
dmatrix -- the intrinsic matrix [k1,k2,k3,k4] for tweaking purposes
Kmatrix -- [fx, fy, cx, cy, s]'''
u = sourceUV[:,0] #width in x
v = sourceUV[:,1] #height in y
rho = np.sqrt(u**2 + v**2)
#get theta
theta = np.arctan(rho,np.full_like(u,1))
# rho_mat = np.array([rho, rho**3, rho**5, rho**7])
rho_mat = np.array([theta,theta**3, theta**5, theta**7])
#get the: rho(theta) = k1*theta + k2*theta**3 + k3*theta**5 + k4*theta**7
rho_d = dmatrix#rho_mat
#get phi
phi = np.arctan2((v - Kmatrix[3]), (u - Kmatrix[2]))
xd = rho_d * np.cos(phi)
yd = rho_d * np.sin(phi)
#converting the coords from image plane back to pixel coords
ud = Kmatrix[0] * (xd + Kmatrix[4] * yd) + Kmatrix[2]
vd = Kmatrix[1] * yd + Kmatrix[3]
return np.column_stack((ud,vd))
Then after gaining the distorded coordinates, I perform moving pixels in this way, where I think the problem might be:
def main():
image_name = "original.png"
img = cv2.imread(image_name)
img = cv2.cvtColor(img, cv2.COLOR_RGB2BGR) #the cv2 read the image as BGR
w = img.shape[1]
h = img.shape[0]
uv_coord = read_img(image_name)
#for adding distortion
dmatrix = [-0.391942708316175,0.012746418822063 ,-0.001374061848026 ,0.005349692659231]
#the Intrinsic matrix of the original picture's
Kmatrix = np.array([9.842439e+02,9.808141e+02 , 1392/2, 2.331966e+02, 0.000000e+00])
# Kmatrix = np.array([2234.23470710156 ,2223.78349134123, 947.511596277837, 647.103139639432,-3.20443253476976]) #the distorted intrinsics
uv = add_distortion(uv_coord,dmatrix,Kmatrix)
i = 0
dstimg = np.zeros_like(img)
for x in range(w): #tthe coo
for y in range(h):
if i > (512 * 1392 -1):
break
xu = uv[i][0] #x, y1, y2, y3
yu = uv[i][1]
i +=1
# if new pixel is in bounds copy from source pixel to destination pixel
if 0 <= xu and xu < img.shape[1] and 0 <= yu and yu < img.shape[0]:
dstimg[int(yu)][int(xu)] = img[int(y)][int(x)]
img = Image.fromarray(dstimg, 'RGB')
img.save('my.png')
img.show()
However, this code does not perform in the way I want. Could you guys please help me with debugging it? I spent 3 days but I still could not see any problem with it. Thanks!!

Find [x,y] rotated coordinates locations in image [OpenCV / Python]

I want to rotate an image at several angles sequentially. I do that using cv2.getRotationMatrix2D and cv2.warpAffine. Having a pair of pixels coordinates [x,y], where x=cols, y=rows (in this case) I want to find their new coordinates in the rotated images.
I used the following slightly changed code courtesy of http://www.pyimagesearch.com/2017/01/02/rotate-images-correctly-with-opencv-and-python/ and the explanation from Affine Transformation to try to map the points in the rotated image : http://docs.opencv.org/2.4/doc/tutorials/imgproc/imgtrans/warp_affine/warp_affine.html.
The problem is my mapping or my rotation is wrong because the transformed calculated coordinates are wrong. (I tried to compute the corners manually for simple verification)
CODE:
def rotate_bound(image, angle):
# grab the dimensions of the image and then determine the
# center
(h, w) = image.shape[:2]
(cX, cY) = ((w-1) // 2.0, (h-1)// 2.0)
# grab the rotation matrix (applying the negative of the
# angle to rotate clockwise), then grab the sine and cosine
# (i.e., the rotation components of the matrix)
M = cv2.getRotationMatrix2D((cX, cY), -angle, 1.0)
cos = np.abs(M[0, 0])
sin = np.abs(M[0, 1])
# compute the new bounding dimensions of the image
nW = int((h * sin) + (w * cos))
nH = int((h * cos) + (w * sin))
print nW, nH
# adjust the rotation matrix to take into account translation
M[0, 2] += ((nW-1) / 2.0) - cX
M[1, 2] += ((nH-1) / 2.0) - cY
# perform the actual rotation and return the image
return M, cv2.warpAffine(image, M, (nW, nH))
#function that calculates the updated locations of the coordinates
#after rotation
def rotated_coord(points,M):
points = np.array(points)
ones = np.ones(shape=(len(points),1))
points_ones = np.concatenate((points,ones), axis=1)
transformed_pts = M.dot(points_ones.T).T
return transformed_pts
#READ IMAGE & CALL FCT
img = cv2.imread("Lenna.png")
points = np.array([[511, 511]])
#rotate by 90 angle for example
M, rotated = rotate_bound(img, 90)
#find out the new locations
transformed_pts = rotated_coord(points,M)
If I have for example the coordinates [511,511] I will obtain [-0.5, 511.50] ([col, row]) when I expect to obtain [0,511].
If I use instead the w // 2 a black border will be added on the image and my rotated updated coordinates will be off again.
Question: How can I find the correct location of a pair of pixels coordinates in a rotated image (by a certain angle) using Python ?

For this case of image rotation, where the image size changes after rotation and also the reference point, the transformation matrix has to be modified. The new with and height can be calculated using the following relations:
new.width = h*\sin(\theta) + w*\cos(\theta)
new.height = h*\cos(\theta) + w*\sin(\theta)
Since the image size changes, because of the black border that you might see, the coordinates of the rotation point (centre of the image) change too. Then it has to be taken into account in the transformation matrix.
I explain an example in my blog image rotation bounding box opencv
def rotate_box(bb, cx, cy, h, w):
new_bb = list(bb)
for i,coord in enumerate(bb):
# opencv calculates standard transformation matrix
M = cv2.getRotationMatrix2D((cx, cy), theta, 1.0)
# Grab the rotation components of the matrix)
cos = np.abs(M[0, 0])
sin = np.abs(M[0, 1])
# compute the new bounding dimensions of the image
nW = int((h * sin) + (w * cos))
nH = int((h * cos) + (w * sin))
# adjust the rotation matrix to take into account translation
M[0, 2] += (nW / 2) - cx
M[1, 2] += (nH / 2) - cy
# Prepare the vector to be transformed
v = [coord[0],coord[1],1]
# Perform the actual rotation and return the image
calculated = np.dot(M,v)
new_bb[i] = (calculated[0],calculated[1])
return new_bb
## Calculate the new bounding box coordinates
new_bb = {}
for i in bb1:
new_bb[i] = rotate_box(bb1[i], cx, cy, heigth, width)

The corresponding C++ code of the above mentioned Python code of # cristianpb, if someone is looking for a C++ code as like me:
// send the original angle i.e. don't transform it in radian
cv::Point2f rotatePointUsingTransformationMat(const cv::Point2f& inPoint, const cv::Point2f& center, const double& rotAngle)
{
cv::Mat rot = cv::getRotationMatrix2D(center, rotAngle, 1.0);
float cos = rot.at<double>(0,0);
float sin = rot.at<double>(0,1);
int newWidth = int( ((center.y*2)*sin) + ((center.x*2)*cos) );
int newHeight = int( ((center.y*2)*cos) + ((center.x*2)*sin) );
rot.at<double>(0,2) += newWidth/2.0 - center.x;
rot.at<double>(1,2) += newHeight/2.0 - center.y;
int v[3] = {static_cast<int>(inPoint.x),static_cast<int>(inPoint.y),1};
int mat3[2][1] = {{0},{0}};
for(int i=0; i<rot.rows; i++)
{
for(int j=0; j<= 0; j++)
{
int sum=0;
for(int k=0; k<3; k++)
{
sum = sum + rot.at<double>(i,k) * v[k];
}
mat3[i][j] = sum;
}
}
return Point2f(mat3[0][0],mat3[1][0]);
}

Open CV mapping patch to image

I have the following situation, in which I have an heightmap, and several patches extracted after an affine mapping from it, then I have applied a color mapping to the patch, and now what I need to do is to blend the patch onto the heightmap at the corrected coordinates. How can I do this? Following is the function I use to do the transformation, basically I will need the inverse.
def extract_patch(image, center, theta, width, height):
vx = (np.cos(theta), np.sin(theta))
vy = (-np.sin(theta), np.cos(theta))
sx = center[0] - vx[0] * (width / 2) - vy[0] * (height / 2)
sy = center[1] - vx[1] * (width / 2) - vy[1] * (height / 2)
mapping = np.array([[vx[0],vy[0], sx], [vx[1],vy[1], sy]])
return cv2.warpAffine(image, mapping, (width, height), flags = cv2.WARP_INVERSE_MAP, borderMode = cv2.BORDER_REPLICATE)