README fixes.

[ci skip]

Author: hbldh

README.rst

@@ -18,21 +18,37 @@ Usage
 
     $ pip install pyefd
 
-Given a closed contour of a shape, this package can fit a 
-[Fourier series](https://en.wikipedia.org/wiki/Fourier_series) 
+Given a closed contour of a shape, generated by e.g. `scikit-image <http://scikit-image.org/>`_
+or `OpenCV <http://opencv.org/>`_, this package can fit a 
+`Fourier series <https://en.wikipedia.org/wiki/Fourier_series>`_
 approximating the shape of the contour::
 
     from pyefd import elliptic_fourier_descriptors
     coeffs = elliptic_fourier_descriptors(contour, order=10)
    
-The coefficients returned are the :math:`a_n`, :math:`b_n`, :math:`c_n` and :math:`d_n` of
-the following Fourier series representation of the shape:
+The coefficients returned are the `a_n`, `b_n`, `c_n` and `d_n` of
+the following Fourier series representation of the shape.
 
-.. math::
-    \begin{align*}
-        \hat{x}(t) & = A_0 + \sum_{n=1}^N\left( a_n \cos \frac{2n\pi t}{T} + b_n \sin \frac{2n\pi t}{T} \right)
-        \hat{y}(t) & = C_0 + \sum_{n=1}^N\left( c_n \cos \frac{2n\pi t}{T} + d_n \sin \frac{2n\pi t}{T} \right) 
-    \end{align*}
+The coefficients returned are by default normalized so that they are 
+rotation and size-invariant. This can be overridden by calling::
+
+    from pyefd import elliptic_fourier_descriptors
+    coeffs = elliptic_fourier_descriptors(contour, order=10, normalize=False)
+
+Normalization can also be done afterwards::
+
+    from pyefd import normalize_efd
+    coeffs = normalize_efd(coeffs)
+
+To use these as features, one can write a small wrapper function::
+
+    def efd_feature(contour):
+        coeffs = elliptic_fourier_descriptors(contour, order=10, normalize=True)
+        return coeffs.flatten()[3:]
+
+If the coefficients are normalized, then `coeffs[0, 0] = 1.0`, 
+`coeffs[0, 1] = 0.0` and `coeffs[0, 2] = 0.0`, so they can be disregarded when using
+the elliptic Fourier descriptors as features.
 
 See \[1\] for more technical details.
 
@@ -43,7 +59,7 @@ Run tests with::
 
     $ python setup.py test
 
-or with [Pytest](http://pytest.org/latest/)::
+or with `Pytest <http://pytest.org/latest/>`_::
 
     $ py.test tests.py
 
@@ -53,13 +69,14 @@ for testing.
 Documentation
 -------------
 
-See the [Github pages](http://hbldh.github.io/pyefd).
+See the `Github pages <http://hbldh.github.io/pyefd>`_.
 
 References
 ----------
 
-\[1\] [Frank P Kuhl, Charles R Giardina, Elliptic Fourier features of a closed contour, 
+\[1\] `Frank P Kuhl, Charles R Giardina, Elliptic Fourier features of a closed contour, 
 Computer Graphics and Image Processing, Volume 18, Issue 3, 1982, Pages 236-258, 
-ISSN 0146-664X, http://dx.doi.org/10.1016/0146-664X(82)90034-X.](http://www.sciencedirect.com/science/article/pii/0146664X8290034X)
+ISSN 0146-664X, http://dx.doi.org/10.1016/0146-664X(82)90034-X. <http://www.sci.utah.edu/~gerig/CS7960-S2010/handouts/Kuhl-Giardina-CGIP1982.pdf>`_
+
 
-\[2\] [LeCun et al. (1999): The MNIST Dataset Of Handwritten Digits](http://yann.lecun.com/exdb/mnist/)
+\[2\] `LeCun et al. (1999): The MNIST Dataset Of Handwritten Digits <http://yann.lecun.com/exdb/mnist/>`_