Merge branch 'main' of https://github.com/cpge-itc/itc2

cpge-itc · Nov 13, 2023 · ffccc3c · ffccc3c
2 parents 6e3a3e0 + 5473564
commit ffccc3c
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diff --git a/_toc.yml b/_toc.yml
@@ -37,5 +37,5 @@ parts:
       file: algo/prog_dyn/td/matrice_prog_dyn.pdf
     - tp: algo/prog_dyn/tp/tp1/tp_prog_dyn.ipynb
     - tp: algo/prog_dyn/tp/tp2/tp_sac_dos.ipynb
-    - tp: algo/prog_dyn/seam_carving/seam_carving.ipynb
+    - cor: algo/prog_dyn/seam_carving/seam_carving.ipynb
 root: intro
diff --git a/files/dl/algo/prog_dyn/seam_carving/seam_carving.ipynb b/files/dl/algo/prog_dyn/seam_carving/seam_carving.ipynb
@@ -124,6 +124,35 @@
     "**Question** : Écrire une fonction `matrice_gradient(m)` qui renvoie `g` à partir de `m`. On pourra utiliser, au choix, une liste de listes ou un tableau `numpy` (en utilisant, par exemple, `np.zeros((..., ...))` pour créer `g`). On pourra utiliser `abs` pour la valeur absolue."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "tags": [
+     "cor"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def matrice_gradient(m):\n",
+    "    n, k = np.shape(m)\n",
+    "    g = np.zeros((n, k))\n",
+    "    g[0][0] = abs(m[1][0] - m[0][0]) + abs(m[0][1] - m[0][0])\n",
+    "    g[n-1][k-1] = abs(m[n-1][k-1] - m[n-2][k-1]) + abs(m[n-1][k-1] - m[n-1][k-2])\n",
+    "    g[0][k-1] = abs(m[1][k-1] - m[0][k-1]) + abs(m[0][k-1] - m[0][k-2])\n",
+    "    g[n-1][0] = abs(m[n-1][0] - m[n-2][0]) + abs(m[n-1][1] - m[n-1][0])\n",
+    "    for i in range(1, n-1):\n",
+    "        g[i][0] = abs(m[i+1][0] - m[i-1][0]) + abs(m[i][1] - m[i][0])\n",
+    "        g[i][k-1] = abs(m[i+1][k-1] - m[i-1][k-1]) + abs(m[i][k-1] - m[i][k-2])\n",
+    "    for j in range(1, k-1):\n",
+    "        g[0][j] = abs(m[1][j] - m[0][j]) + abs(m[0][j+1] - m[0][j-1])\n",
+    "        g[n-1][j] = abs(m[n-1][j] - m[n-2][j]) + abs(m[n-1][j+1] - m[n-1][j-1])\n",
+    "    for i in range(1, n-1):\n",
+    "        for j in range(1, k-1):\n",
+    "            g[i][j] = abs(m[i+1][j] - m[i-1][j]) + abs(m[i][j+1] - m[i][j-1])\n",
+    "    return g"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 4,
@@ -206,6 +235,28 @@
     "    return np.array(m2) # conversion en matrice numpy"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "tags": [
+     "cor"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def enlever_chemin(m, c):\n",
+    "    n, p = np.shape(m)\n",
+    "    m2 = []\n",
+    "    for i in range(n):\n",
+    "        l = []\n",
+    "        for j in range(p):\n",
+    "            if j != c[i]:\n",
+    "                l.append(m[i][j])\n",
+    "        m2.append(l)\n",
+    "    return np.array(m2)"
+   ]
+  },
   {
    "attachments": {},
    "cell_type": "markdown",
@@ -233,6 +284,27 @@
     "**Question** : Écrire une fonction `dp_chemin(g)` qui renvoie une matrice `d` de même dimension que `g` telle que `d[i][j]` est l'énergie minimum d'un chemin depuis le haut de l'image jusqu'à un pixel `i, j`."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "tags": [
+     "cor"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def dp_chemin(g):\n",
+    "    d = np.zeros(g.shape)\n",
+    "    d[0] = g[0]\n",
+    "    for i in range(1, g.shape[0]):\n",
+    "        d[i, 0] = g[i, 0] + min(d[i-1, 0], d[i-1, 1])\n",
+    "        d[i, -1] = g[i, -1] + min(d[i-1, -1], d[i-1, -2])\n",
+    "        for j in range(1, g.shape[1]-1):\n",
+    "            d[i, j] = g[i, j] + min(d[i-1, j-1], d[i-1, j], d[i-1, j+1])\n",
+    "    return d"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 9,
@@ -272,6 +344,24 @@
     "**Question** : Écrire une fonction `min_energie_bas(d)` qui renvoie le numéro de colonne `j` du pixel de la dernière ligne d'énergie minimale, c'est-à-dire tel que `d[n - 1][j]` est minimal, où `d` est la matrice renvoyée par la fonction `dp_chemin(m)` et `n` est le nombre de lignes de `d`."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "tags": [
+     "cor"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def min_energie_bas(d):\n",
+    "    j_mini = 0 # indice du minimum de d sur la dernière ligne\n",
+    "    for j in range(1, d.shape[1]):\n",
+    "        if d[-1, j] < d[-1, j_mini]:\n",
+    "            j_mini = j\n",
+    "    return j_mini"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 11,
@@ -317,6 +407,29 @@
     "    return c[::-1] # pour inverser c"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "tags": [
+     "cor"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def min_chemin(m):\n",
+    "    d = dp_chemin(matrice_gradient(m))\n",
+    "    c = [min_energie_bas(d)]\n",
+    "    for i in range(len(m) - 2, -1, -1):\n",
+    "        j = c[-1]\n",
+    "        mini = j\n",
+    "        for k in range(j - 1, j + 2):\n",
+    "            if k >= 0 and k < len(d[i]) and d[i, k] < d[i, j]:\n",
+    "                mini = k\n",
+    "        c.append(mini)\n",
+    "    return c[::-1] # pour inverser c"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 14,
@@ -362,6 +475,23 @@
     "- Enlever le chemin `c` de `m`"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "tags": [
+     "cor"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def seam_carving(m, n):\n",
+    "    for i in range(n):\n",
+    "        c = min_chemin(m)\n",
+    "        m = enlever_chemin(m, c)\n",
+    "    return m"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 16,