"""
===============================
Using geometric transformations
===============================

In this example, we will see how to use geometric transformations in the context
of image processing.
"""

from __future__ import print_function

import math
import numpy as np
import matplotlib.pyplot as plt

from skimage import data
from skimage import transform as tf

######################################################################
# Basics
# ======
#
# Several different geometric transformation types are supported: similarity,
# affine, projective and polynomial.
#
# Geometric transformations can either be created using the explicit
# parameters (e.g. scale, shear, rotation and translation) or the
# transformation matrix:
#
# First we create a transformation using explicit parameters:

tform = tf.SimilarityTransform(scale=1, rotation=math.pi/2,
                               translation=(0, 1))
print(tform.params)

######################################################################
# Alternatively you can define a transformation by the transformation matrix
# itself:

matrix = tform.params.copy()
matrix[1, 2] = 2
tform2 = tf.SimilarityTransform(matrix)

######################################################################
# These transformation objects can then be used to apply forward and inverse
# coordinate transformations between the source and destination coordinate
# systems:

coord = [1, 0]
print(tform2(coord))
print(tform2.inverse(tform(coord)))

######################################################################
# Image warping
# =============
#
# Geometric transformations can also be used to warp images:

text = data.text()

tform = tf.SimilarityTransform(scale=1, rotation=math.pi/4,
                               translation=(text.shape[0]/2, -100))

rotated = tf.warp(text, tform)
back_rotated = tf.warp(rotated, tform.inverse)

fig, ax = plt.subplots(nrows=3)

ax[0].imshow(text, cmap=plt.cm.gray)
ax[1].imshow(rotated, cmap=plt.cm.gray)
ax[2].imshow(back_rotated, cmap=plt.cm.gray)

for a in ax:
    a.axis('off')

plt.tight_layout()

######################################################################
# Parameter estimation
# ====================
#
# In addition to the basic functionality mentioned above you can also
# estimate the parameters of a geometric transformation using the least-
# squares method.
#
# This can amongst other things be used for image registration or
# rectification, where you have a set of control points or
# homologous/corresponding points in two images.
#
# Let's assume we want to recognize letters on a photograph which was not
# taken from the front but at a certain angle. In the simplest case of a
# plane paper surface the letters are projectively distorted. Simple matching
# algorithms would not be able to match such symbols. One solution to this
# problem would be to warp the image so that the distortion is removed and
# then apply a matching algorithm:

text = data.text()

src = np.array([[0, 0], [0, 50], [300, 50], [300, 0]])
dst = np.array([[155, 15], [65, 40], [260, 130], [360, 95]])

tform3 = tf.ProjectiveTransform()
tform3.estimate(src, dst)
warped = tf.warp(text, tform3, output_shape=(50, 300))

fig, ax = plt.subplots(nrows=2, figsize=(8, 3))

ax[0].imshow(text, cmap=plt.cm.gray)
ax[0].plot(dst[:, 0], dst[:, 1], '.r')
ax[1].imshow(warped, cmap=plt.cm.gray)

for a in ax:
    a.axis('off')

plt.tight_layout()