4_2_houghTransform.py

import sys
import numpy
import matplotlib.pyplot as plt


def apply_hough_transformation(data, num_dims, alpha_values):
    """
    Maps data points to parameter functions.
    :param data:
    :param num_dims:
    :param alpha_values:
    :return: List of nd-arrays (data points <-> rows, paramter function values <-> columns).
    """
    parameter_function_values = []

    # Apply Hough transformations on each point.
    for data_point in data:
        delta = numpy.zeros([1, len(alpha_values[0])])

        # Iterate over point's attributes.
        for i in range(0, num_dims):
            pi_sinus_alpha = numpy.ones([1, len(alpha_values[0])])
            # Iterate over sinus values.
            for j in range(0, i):
                pi_sinus_alpha *= numpy.sin(alpha_values[j])

            delta += data_point[i] * pi_sinus_alpha * numpy.cos(alpha_values[i])

        parameter_function_values.append(delta)

    return parameter_function_values

data = numpy.array([[1, 2], [2, 3], [3, 4], [4, 5], [6, 7], [7, 2], [1, 5]])

num_points = len(data)
num_dims = len(data[0])
alpha_values = [numpy.arange(start=0, stop=360 * numpy.pi / 180, step=0.1) for i in range(0, num_dims)]

fig, subplots = plt.subplots(1, 2, sharex=False, sharey=False, squeeze=False)

subplots[0, 0].scatter(data[:, 0:1], data[:, 1:2])
subplots[0, 0].grid(True)
subplots[0, 0].set_ylim(0, 10)
subplots[0, 0].set_xlim(0, 10)
subplots[0, 1].set_ylabel("$\delta$")
subplots[0, 1].set_xlabel("$\\alpha\:in\:^{\circ}$")
subplots[0, 1].grid(True)

# Calculate and plot Hough transform.
for index, param_function_value in enumerate(apply_hough_transformation(data, num_dims, alpha_values)):
    subplots[0, 1].plot(alpha_values[0] * 180 / numpy.pi, param_function_value.T, label="${f_p}_" + str(index + 1) + "$")[0]

subplots[0, 1].legend(bbox_to_anchor=(1.01, 1), loc=2, borderaxespad=0.)

# fig.tight_layout();
plt.show()