{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Convolutional Wasserstein Barycenter example\n\n\nThis example is designed to illustrate how the Convolutional Wasserstein Barycenter\nfunction of POT works.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Author: Nicolas Courty <ncourty@irisa.fr>\n#\n# License: MIT License\n\n\nimport numpy as np\nimport pylab as pl\nimport ot"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Data preparation\n----------------\n\nThe four distributions are constructed from 4 simple images\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "f1 = 1 - pl.imread('../data/redcross.png')[:, :, 2]\nf2 = 1 - pl.imread('../data/duck.png')[:, :, 2]\nf3 = 1 - pl.imread('../data/heart.png')[:, :, 2]\nf4 = 1 - pl.imread('../data/tooth.png')[:, :, 2]\n\nA = []\nf1 = f1 / np.sum(f1)\nf2 = f2 / np.sum(f2)\nf3 = f3 / np.sum(f3)\nf4 = f4 / np.sum(f4)\nA.append(f1)\nA.append(f2)\nA.append(f3)\nA.append(f4)\nA = np.array(A)\n\nnb_images = 5\n\n# those are the four corners coordinates that will be interpolated by bilinear\n# interpolation\nv1 = np.array((1, 0, 0, 0))\nv2 = np.array((0, 1, 0, 0))\nv3 = np.array((0, 0, 1, 0))\nv4 = np.array((0, 0, 0, 1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Barycenter computation and visualization\n----------------------------------------\n\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(figsize=(10, 10))\npl.title('Convolutional Wasserstein Barycenters in POT')\ncm = 'Blues'\n# regularization parameter\nreg = 0.004\nfor i in range(nb_images):\n    for j in range(nb_images):\n        pl.subplot(nb_images, nb_images, i * nb_images + j + 1)\n        tx = float(i) / (nb_images - 1)\n        ty = float(j) / (nb_images - 1)\n\n        # weights are constructed by bilinear interpolation\n        tmp1 = (1 - tx) * v1 + tx * v2\n        tmp2 = (1 - tx) * v3 + tx * v4\n        weights = (1 - ty) * tmp1 + ty * tmp2\n\n        if i == 0 and j == 0:\n            pl.imshow(f1, cmap=cm)\n            pl.axis('off')\n        elif i == 0 and j == (nb_images - 1):\n            pl.imshow(f3, cmap=cm)\n            pl.axis('off')\n        elif i == (nb_images - 1) and j == 0:\n            pl.imshow(f2, cmap=cm)\n            pl.axis('off')\n        elif i == (nb_images - 1) and j == (nb_images - 1):\n            pl.imshow(f4, cmap=cm)\n            pl.axis('off')\n        else:\n            # call to barycenter computation\n            pl.imshow(ot.bregman.convolutional_barycenter2d(A, reg, weights), cmap=cm)\n            pl.axis('off')\npl.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.6.5"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}