docs(dist): add more scientific information on experimental results

README.rst

@@ -7,9 +7,9 @@ Description
 
 *color-matcher* enables color transfer across images which comes in handy for automatic color-grading
 of photographs, paintings and film sequences as well as light-field and stopmotion corrections. The methods behind
-the mappings are based on the approach from Reinhard *et al.*, an analytical solution to a Multi-Variate Gaussian
-Distribution (MVGD) transfer, the Monge-Kantorovich solution as proposed by Pitie *et al.* in conjunction with
-classical histogram matching.
+the mappings are based on the approach from Reinhard *et al.*, the Monge-Kantorovich Linearization (MKL) as proposed by
+Pitie *et al.* and our analytical solution to a Multi-Variate Gaussian Distribution (MVGD) transfer in conjunction with
+classical histogram matching. As shown below our HM-MVGD-HM compound outperforms existing methods.
 
 |release| |license| |build_github| |coverage| |pypi_total| |pypi|
 
@@ -50,10 +50,40 @@ Results
 
 |vspace|
 
+Experimental results
+====================
+
 |metric|
 
+The above diagram illustrates light-field color consistency from Wasserstein metric :math:`$W_1$` and histogram distance
+:math:`$D_2$` where low values indicate higher similarity between source :math:`$\mathbf{r}$` and target :math:`$\mathbf{z}$`.
+These distance metrics are computed as follows
+
+.. math::
+
+    W_1 = \int_{0}^{\infty} \left| F\left(\mathbf{r}^{(g)}\right) - F\left(\mathbf{z}^{(g)}\right) \right|_1 \, \mathrm{d}k
+
+    D_2 = \left\| f(\mathbf{r}) - f(\mathbf{z}) \right\|_2
+
+where :math:`$f(\cdot)$` and :math:`$F(\cdot)$` represent the Probability Density Function (PDF) and Cumulative Density Function (CDF), respectively.
+More detailed information can be found in `our IEEE paper <https://arxiv.org/pdf/2010.11687.pdf/>`__.
+
 |vspace|
 
+Citation
+--------
+
+.. code-block:: BibTeX
+
+    @article{hahne21:tip,
+        title={PlenoptiCam v1.0: A light-field imaging framework},
+        author={Christopher Hahne and Amar Aggoun},
+        journal={IEEE Transactions on Image Processing},
+        year={2021},
+        volume={31},
+        pages={1--15}
+    }
+
 Installation
 ------------
 
@@ -122,7 +152,7 @@ API Usage
 
 .. |metric| raw:: html
 
-    <img src="https://raw.githubusercontent.com/hahnec/color-matcher/develop/hist+wasser_dist.svg" max-width:"100%">
+    <img src="https://raw.githubusercontent.com/hahnec/color-matcher/develop/hist+wasser_dist.svg" max-width="100%" align="center">
 
 .. |src_photo| raw:: html
 
@@ -207,19 +237,9 @@ API Usage
 .. |binder| image:: https://img.shields.io/badge/launch-binder-579aca.svg?logo=data:image/png;base64,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
    :target: https://gesis.mybinder.org/binder/v2/gh/hahnec/color-matcher/3a85a06bb546fa6d4294c7fc241de9e3cce2b2e0?urlpath=lab%2Ftree%2F01_api_demo.ipynb
 
-Citation
---------
-
-.. code-block:: BibTeX
-
-    @article{hahne21:tip,
-        title={PlenoptiCam v1.0: A light-field imaging framework},
-        author={Christopher Hahne and Amar Aggoun},
-        journal={IEEE Transactions on Image Processing},
-        year={2021},
-        volume={31},
-        pages={1--15}
-    }
+.. |paper| image:: http://img.shields.io/badge/paper-arxiv.2010.11687-red.svg?style=flat-square
+    :target: https://arxiv.org/pdf/2010.11687.pdf
+    :alt: arXiv link
 
 Author
 ------