diff --git a/slides/cours_20.md b/slides/cours_20.md
index 0a0c51a70e387e43fa93ed6d52811d2128bf5ca5..511ced6860b3167aaf43cee5af2a4b7687cb8e44 100644
--- a/slides/cours_20.md
+++ b/slides/cours_20.md
@@ -83,13 +83,13 @@ Son équivalent tri-dimensionnel est l'octree (chaque nœud a 8 enfants ou aucun
## Comment représenter l'image
-
+
::::
:::: {.column width=70%}
-## Sous la forme d'un arbre quaternaire?
+## Sous la forme d'un arbre quaternaire (5min, matrix)?
. . .
@@ -788,5 +788,70 @@ bool last_value(node *qt, int *val) {
*val = info;
return true;
}
+```
+
+
+# Compression avec perte (1/N)
+
+## Idée générale
+* Regrouper les pixels par valeur sous certaines conditions
+
+```
+ SG=0 | SD=1 SG=0 | SD=1
+ 21 | 12 | 4 | 3 21 | 12 | 4
+ 9 | 7 | 4 | 4 9 | 7 |
+----------------- => ------------------
+ 1 | 1 | 0 | 31 1 | 0 | 31
+ 2 | 1 | 3 | 27 | 3 | 27
+ IG=2 | ID=3 IG=2 | ID=3
```
+
+* On enlève si l'écart à la moyenne est "petit"?
+
+# Compression avec perte (2/N)
+
+## Que devient l'arbre suivant si l'écart est petit?
+
+
+
+. . .
+
+## Arbre compressé
+
+
+
+# Compression avec perte (3/N)
+
+## Comment mesurer l'écart à la moyenne?
+
+. . .
+
+* Avec l'écart-type
+
+\begin{equation*}
+\mu = \frac{1}{4}\sum_{i=0}^{3} p[i],\quad \sigma = \sqrt{\frac{1}{N}\sum_{i=0}^3 (\mu-p[i])
+^2}
+\end{equation*}
+
+## Que devient l'algorithme?
+
+. . .
+
+* Si $\sigma<\theta$, $\theta$ est la **tolérance**:
+ * Remplacer la valeur du pixel par la moyenne eds enfants.
+ * Remonter les valeurs dans l'arbre.
+
+## Quelle influence de la valeur de $\theta$ sur la compression?
+
+. . .
+
+* Plus $\theta$ est grand, plus l'image sera compressée.
+
+# Compression avec perte (4/N)
+
+## Que devient l'arbre avec $\theta=0.5$?
+
+. . .
+
+
diff --git a/slides/figs/quad_img_simple_comp_avg.svg b/slides/figs/quad_img_simple_comp_avg.svg
new file mode 100644
index 0000000000000000000000000000000000000000..2912f485a2ed5ebd7794c57dde69618566c89f63
--- /dev/null
+++ b/slides/figs/quad_img_simple_comp_avg.svg
@@ -0,0 +1,165 @@
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+</g>
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+<title>0->id1</title>
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+</g>
+<!-- sg1->sg2 -->
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+</g>
+<!-- sg1->sd2 -->
+<g id="edge6" class="edge">
+<title>sg1->sd2</title>
+<path fill="none" stroke="#000000" d="M144.144,-76.8394C135.8231,-65.9941 126.067,-53.2783 117.7574,-42.4479"/>
+<polygon fill="#000000" stroke="#000000" points="120.3226,-40.0414 111.4585,-34.238 114.7689,-44.3024 120.3226,-40.0414"/>
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+<!-- ig2 -->
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+<title>ig2</title>
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+</g>
+<!-- sg1->ig2 -->
+<g id="edge7" class="edge">
+<title>sg1->ig2</title>
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+<polygon fill="#000000" stroke="#000000" points="171.7659,-46.6751 169.2366,-36.3866 164.7979,-46.0067 171.7659,-46.6751"/>
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\ No newline at end of file
diff --git a/slides/figs/quad_img_simple_comp_loss.svg b/slides/figs/quad_img_simple_comp_loss.svg
new file mode 100644
index 0000000000000000000000000000000000000000..c8972b12117d86a3a25eca49a3f7e3a01765b456
--- /dev/null
+++ b/slides/figs/quad_img_simple_comp_loss.svg
@@ -0,0 +1,161 @@
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+<!-- id5 -->
+<g id="node13" class="node">
+<title>id5</title>
+<ellipse fill="none" stroke="#000000" cx="533" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="533" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">27</text>
+</g>
+<!-- id1->id5 -->
+<g id="edge12" class="edge">
+<title>id1->id5</title>
+<path fill="none" stroke="#000000" d="M411.7186,-79.0647C435.7614,-66.9593 474.713,-47.3473 501.968,-33.6245"/>
+<polygon fill="#000000" stroke="#000000" points="503.7192,-36.6614 511.077,-29.0382 500.5712,-30.4092 503.7192,-36.6614"/>
+</g>
+</g>
+</svg>
\ No newline at end of file
diff --git a/slides/graphviz/quad_img_simple_comp_avg.dot b/slides/graphviz/quad_img_simple_comp_avg.dot
new file mode 100644
index 0000000000000000000000000000000000000000..668fe9a7a9ccd00fb973e778f41e93c6af4e8ee5
--- /dev/null
+++ b/slides/graphviz/quad_img_simple_comp_avg.dot
@@ -0,0 +1,18 @@
+digraph G {
+ 0 [label=" "]
+ sg1 [label="12.25\n 5.36"]
+ sd1 [label="3.75\n 0.43"]
+ ig1 [label="1.25\n 0.43"]
+ id1 [label="15.25\n 13.86"]
+ sg2 [label="21"]
+ sd2 [label="12"]
+ ig2 [label="9"]
+ id2 [label="7"]
+ sg5 [label="0"]
+ sd5 [label="31"]
+ ig5 [label="3"]
+ id5 [label="27"]
+ 0->{sg1, sd1, ig1, id1} [quadtree = "normal"]
+ sg1->{sg2, sd2, ig2, id2} [quadtree = "normal"]
+ id1->{sg5, sd5, ig5, id5} [quadtree = "normal"]
+}