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slides/cours_20.md
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...@@ -83,13 +83,13 @@ Son équivalent tri-dimensionnel est l'octree (chaque nœud a 8 enfants ou aucun ...@@ -83,13 +83,13 @@ Son équivalent tri-dimensionnel est l'octree (chaque nœud a 8 enfants ou aucun
## Comment représenter l'image ## Comment représenter l'image
![Image noir/blanc.](figs/board_blacked_parts.svg) ![Image noir/blanc (0/1).](figs/board_blacked_parts.svg)
:::: ::::
:::: {.column width=70%} :::: {.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) { ...@@ -788,5 +788,70 @@ bool last_value(node *qt, int *val) {
*val = info; *val = info;
return true; 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?
![](figs/quad_img_simple.svg)
. . .
## Arbre compressé
![](figs/quad_img_simple_comp_loss.svg)
# 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 $\theta=0.5$?
. . .
![Arbre compressé.](figs/quad_img_simple_comp_avg.svg)
slides/figs/quad_img_simple_comp_avg.svg 0 → 100644
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<title>id1-&gt;id5</title>
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<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
slides/graphviz/quad_img_simple_comp_avg.dot 0 → 100644
+ 18
− 0
View file @ 9789b0ee
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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