Affine Transforms

translation.py

import numpy as np

def apply_transformations(transformations, data):
    # data =  T x K x 3 co-ordinates (2 for each point), or K x 3 points in case generate = True
    # transformations = T affine matrices 2 x 3 each (T x 2 x 3)
    K, _ = data.shape
    T, _, _ = transformations.shape  # T x 2 x 3 matrices
    data = np.broadcast_to(data, (T, K, 3))
    data = np.swapaxes(data, 1, 2)  # makes it T x 3 x K

    new_data = np.zeros([T, 2, K])

    for i in range(T):
        new_data[i, :, :] = transformations[i, :, :].dot(data[i, :, :])  # 2x3 x 3xK

    new_data = np.swapaxes(new_data, 1, 2)  # makes it T x K x 2
    new_data = np.append(new_data, np.ones([T, K, 1]), axis=2)

    return new_data


T = 30  # T different frames
K = 10  # K different points being tracked
translation_radius = 150  # pixels
rotation_radius = np.pi  # radians

if K > 10:
    raise Exception, 'Choose more colours'

# this is for display purposes
colour_seq = ['tab:blue', 'tab:orange', 'tab:green',
              'tab:red', 'tab:purple', 'tab:brown',
              'tab:pink', 'tab:gray', 'tab:olive', 'tab:cyan']


start_data = np.random.randint(0, 300, (K, 2))
start_data = np.append(start_data, np.ones([K,1]), axis=1) # convert to homogeneous co-ords

initial_translations = np.zeros([T, 2, 3])
initial_translations[:,0,0] = 1
initial_translations[:,1,1] = 1

for idx, tx in enumerate(range(-75, 75, 5)):
    initial_translations[idx, 0, 2] = tx
    # initial_translations[idx, 1, 2] = ty

initial_data = apply_transformations(initial_translations, start_data)

initial_data = initial_data.astype(np.float32)

from matplotlib import pyplot as plt


source = np.copy(initial_data).reshape(T, K, 3)

plt.figure(figsize=(8, 8))
for i in range(T):
    plt.scatter(x = source[i,:,0], y = source[i,:,1],c =colour_seq, s=60)
plt.title('Translated Points')
plt.xlim(0, 300)
plt.ylim(300, 0)

plt.show()