From 9789b0ee7f052c64b84f0c090de4250b3578e6db Mon Sep 17 00:00:00 2001
From: Orestis <orestis.malaspinas@pm.me>
Date: Mon, 28 Mar 2022 13:02:17 +0200
Subject: [PATCH] added image
---
slides/cours_20.md | 69 +++++++-
slides/figs/quad_img_simple_comp_avg.svg | 165 +++++++++++++++++++
slides/figs/quad_img_simple_comp_loss.svg | 161 ++++++++++++++++++
slides/graphviz/quad_img_simple_comp_avg.dot | 18 ++
4 files changed, 411 insertions(+), 2 deletions(-)
create mode 100644 slides/figs/quad_img_simple_comp_avg.svg
create mode 100644 slides/figs/quad_img_simple_comp_loss.svg
create mode 100644 slides/graphviz/quad_img_simple_comp_avg.dot
diff --git a/slides/cours_20.md b/slides/cours_20.md
index 0a0c51a..511ced6 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 0000000..2912f48
--- /dev/null
+++ b/slides/figs/quad_img_simple_comp_avg.svg
@@ -0,0 +1,165 @@
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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 0000000..c8972b1
--- /dev/null
+++ b/slides/figs/quad_img_simple_comp_loss.svg
@@ -0,0 +1,161 @@
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+<text text-anchor="middle" x="461" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">3</text>
+</g>
+<!-- id1->ig5 -->
+<g id="edge11" class="edge">
+<title>id1->ig5</title>
+<path fill="none" stroke="#000000" d="M405.0573,-74.7307C414.847,-64.803 427.7831,-51.6847 438.7497,-40.5637"/>
+<polygon fill="#000000" stroke="#000000" points="441.4351,-42.8252 445.9644,-33.2473 436.4508,-37.9102 441.4351,-42.8252"/>
+</g>
+<!-- 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 0000000..668fe9a
--- /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"]
+}
--
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