Python: Show cartesian image in polar plot

Question

Description:

I have this data represented in a cartesian coordinate system with 256 columns and 640 rows. Each column represents an angle, theta, from -65 deg to 65 deg. Each row represents a range, r, from 0 to 20 m.

An example is given below:

With the following code I try to make a grid and transform each pixel location to the location it would have on a polar grid:

def polar_image(image, bearings):

    (h,w) = image.shape

    x_max = (np.ceil(np.sin(np.deg2rad(np.max(bearings)))*h)*2+1).astype(int)
    y_max = (np.ceil(np.cos(np.deg2rad(np.min(np.abs(bearings))))*h)+1).astype(int)

    blank = np.zeros((y_max,x_max,1), np.uint8)

    for i in range(w):
        for j in range(h):
            X = (np.sin(np.deg2rad( bearings[i]))*j)

            Y = (-np.cos(np.deg2rad(bearings[i]))*j)

            blank[(Y+h).astype(int),(X+562).astype(int)] = image[h-1-j,w-1-i]


    return blank

This returns an image as below:

Questions:

This is sort of what I actually want to achieve except from two things:

1) there seem to be some artifacts in the new image and also the mapping seems a bit coarse.

Does someone have a suggestion on how to interpolate to get rid of this?

2) The image remains in a Cartesian representation, meaning that I don't have any polar gridlines, nor can I visualize intervals of range/angle.

Anybody know how to visualize the polar grids with axis ticks in theta and range?

Answer 1

You can use pyplot.pcolormesh() to plot the converted mesh:

import numpy as np
import pylab as pl
img = pl.imread("c:/tmp/Wnov4.png")
angle_max = np.deg2rad(65)
h, w = img.shape
angle, r = np.mgrid[-angle_max:angle_max:h*1j, 0:20:w*1j]
x = r * np.sin(angle)
y = r * np.cos(angle)

fig, ax = pl.subplots()
ax.set_aspect("equal")
pl.pcolormesh(x, y, img, cmap="gray");

or you can use the remap() in OpenCV to convert it to a new image:

import cv2
import numpy as np
from PIL import Image
img = cv2.imread(r"c:/tmp/Wnov4.png", cv2.IMREAD_GRAYSCALE)
angle_max = np.deg2rad(65)
r_max = 20
x = np.linspace(-20, 20, 800)
y = np.linspace(20, 0, 400)
y, x = np.ix_(y, x)
r = np.hypot(x, y)
a = np.arctan2(x, y)

map_x = r / r_max * img.shape[1]
map_y = a / (2 * angle_max) * img.shape[0] + img.shape[0] * 0.5

img2 = cv2.remap(img, map_x.astype(np.float32), map_y.astype(np.float32), cv2.INTER_CUBIC)
Image.fromarray(img2)