ccg_transform_exmp_1.py

import cv2
import numpy as np


# constructing an image with a frame in the center
img = np.zeros([255, 255], dtype=np.int)
img[64:192, 64] = np.ones([128], dtype=np.int) * 255
img[64:192, 192] = np.ones([128], dtype=np.int) * 255
img[64, 64:192] = np.ones([128], dtype=np.int) * 255
img[192, 64:192] = np.ones([128], dtype=np.int) * 255
cv2.imwrite('orig.png', img)


# complex transformation
def transform(z):
    result = 0
    for t in np.linspace(0.0, 1.0, 100):
        ratio = np.exp(-t)
        phi = 2 * np.pi * t
        w = np.cos(phi) + np.sin(phi) * 1j
        result += ratio * w * z / 12.5
    return result

# transform image
def grid_sample(img, w):
    t1 = np.zeros(w.shape, dtype=np.int)
    t2 = np.zeros(w.shape, dtype=np.int)
    grid = (128 + 128j) + 128 * w

    tx = np.round(np.real(grid)).astype(np.int)
    ty = np.round(np.imag(grid)).astype(np.int)
    t1[ty, tx] = img

    tx = np.round(np.real(grid) + 0.5).astype(np.int)
    ty = np.round(np.imag(grid) + 0.5).astype(np.int)
    t2[ty, tx] = img

    return np.max(np.array([t1, t2]), axis=0)


# apply transformation
def apply(img, trans):
    x, y = np.meshgrid(np.linspace(-1.0, 1.0, 255), np.linspace(-1.0, 1.0, 255))
    z = x + 1j * y
    img = img + grid_sample(img, trans(z))
    img = img + grid_sample(img, trans(z))
    img = img + grid_sample(img, trans(z))
    img = img + grid_sample(img, trans(z))
    img = img + grid_sample(img, trans(z))
    img = img + grid_sample(img, trans(z))
    img = img + grid_sample(img, trans(z))
    img = img + grid_sample(img, trans(z))
    return img


cv2.imwrite('result.png', apply(img, transform))