solutions week 7

d67c97e3 · Vedrana Andersen Dahl · ee51d512 · d67c97e3 · d67c97e3 · d67c97e3
Commit d67c97e3 authored 2 weeks ago by Vedrana Andersen Dahl
--- a/Week07/QUIZ_week7_solution.ipynb
+++ b/Week07/QUIZ_week7_solution.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "608c7b2a",
+   "metadata": {},
+   "source": [
+    "# QUIZ WEEK 7 SOLUTION"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "fc7238e9",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[2 0 1 1 2 1]\n",
+      "line_cost =  22\n",
+      "zero_cost =  19\n",
+      "two_cost =  10\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np \n",
+    "import matplotlib.pyplot as plt\n",
+    "import slgbuilder\n",
+    "\n",
+    "I = np.array([[6, 1, 5, 4, 5, 7],\n",
+    "    [2, 7, 2, 3, 4, 1],\n",
+    "    [1, 5, 7, 4, 2, 6],\n",
+    "    [5, 2, 3, 5, 4, 3],\n",
+    "    [2, 4, 3, 6, 7, 7]])\n",
+    "\n",
+    "line_cost = I[3].sum()  # index 3 corresponds to z=2\n",
+    "zero_cost = I.sum(axis = 1).min()\n",
+    "\n",
+    "k = I.argmin(axis = 0)\n",
+    "print(k)  # check that change is never larger than 3\n",
+    "\n",
+    "two_cost = I.min(axis = 0).sum()\n",
+    "\n",
+    "print(f'{line_cost =  }')\n",
+    "print(f'{zero_cost =  }')\n",
+    "print(f'{two_cost =  }')\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "94b1d764",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Just checing that solution using slgbuilder is giving the same result\n",
+    "layer = slgbuilder.GraphObject(I.astype(int))\n",
+    "np.bool = bool\n",
+    "np.int = int\n",
+    "helper = slgbuilder.MaxflowBuilder()\n",
+    "helper.add_object(layer)\n",
+    "helper.add_layered_boundary_cost()\n",
+    "helper.add_layered_smoothness(delta=3, wrap=False)\n",
+    "helper.solve()\n",
+    "segmentation = helper.what_segments(layer)\n",
+    "segmentation_line = segmentation.sum(axis=0) - 1\n",
+    "c = (I[segmentation_line, np.arange(segmentation.shape[1])]).sum()\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "ax.imshow(I)\n",
+    "ax.plot(segmentation_line, 'r')\n",
+    "ax.set_title(f'two_cost={c}')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "76b75526",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.10.9"
+  },
+  "vscode": {
+   "interpreter": {
+    "hash": "864c54ae2c00d287136c49aec72343cc9457da9cff5129afc5c16bdd0f87f600"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
+%% Cell type:markdown id:608c7b2a tags:
+
+# QUIZ WEEK 7 SOLUTION
+
+%% Cell type:code id:fc7238e9 tags:
+
+``` python
+import numpy as np
+import matplotlib.pyplot as plt
+import slgbuilder
+
+I = np.array([[6, 1, 5, 4, 5, 7],
+    [2, 7, 2, 3, 4, 1],
+    [1, 5, 7, 4, 2, 6],
+    [5, 2, 3, 5, 4, 3],
+    [2, 4, 3, 6, 7, 7]])
+
+line_cost = I[3].sum()  # index 3 corresponds to z=2
+zero_cost = I.sum(axis = 1).min()
+
+k = I.argmin(axis = 0)
+print(k)  # check that change is never larger than 3
+
+two_cost = I.min(axis = 0).sum()
+
+print(f'{line_cost =  }')
+print(f'{zero_cost =  }')
+print(f'{two_cost =  }')
+```
+
+%% Output
+
+    [2 0 1 1 2 1]
+    line_cost =  22
+    zero_cost =  19
+    two_cost =  10
+
+%% Cell type:code id:94b1d764 tags:
+
+``` python
+# Just checing that solution using slgbuilder is giving the same result
+layer = slgbuilder.GraphObject(I.astype(int))
+np.bool = bool
+np.int = int
+helper = slgbuilder.MaxflowBuilder()
+helper.add_object(layer)
+helper.add_layered_boundary_cost()
+helper.add_layered_smoothness(delta=3, wrap=False)
+helper.solve()
+segmentation = helper.what_segments(layer)
+segmentation_line = segmentation.sum(axis=0) - 1
+c = (I[segmentation_line, np.arange(segmentation.shape[1])]).sum()
+
+fig, ax = plt.subplots()
+ax.imshow(I)
+ax.plot(segmentation_line, 'r')
+ax.set_title(f'two_cost={c}')
+plt.show()
+```
+
+%% Output
+
+
+
+%% Cell type:code id:76b75526 tags:
+
+``` python
+```
--- a/Week07/dental_solution.ipynb
+++ b/Week07/dental_solution.ipynb
--- a/Week07/limeshone_solution.ipynb
+++ b/Week07/limeshone_solution.ipynb