another post

_posts/2024-07-21-fragmenting-the-tile-data.markdown

@@ -0,0 +1,69 @@
+---
+title: Fragmenting the tile data
+image: /img/subband_sizes_tiles1000.png
+description:
+---
+
+When looking at the data segment [CIS/COD
+images](/2024/04/03/learning-about-the-image-format.html) (i.e., the
+tiles) the byte sequence `0x63 0x6f 0x64` (ASCII: `cod`) appears
+several times and thus is conspicuous. According to [a wiki page
+describing a derived video
+codec](https://wiki.multimedia.cx/index.php/Lightning_Strike_Video_Codec)
+it marks the end of a "plane", a basic building blog of
+wavelet-compressed images. In this post we explore the distribution of
+these blocks.
+
+Let us start to analyse how many such parts we find in images for the
+different tile sizes:
+
+## 20 colour tiles of size 250x250
+
+| number of parts | frequency |
+|-----------------+-----------|
+|              39 |        17 |
+|              42 |         2 |
+|              48 |         1 |
+
+## 169 colour tiles of size 500x500
+
+| number of parts | frequency |
+|-----------------+-----------|
+|              36 |       162 |
+|              39 |         7 |
+
+## 2240 colour tiles of size 500x500
+
+| number of parts | frequency |
+|-----------------+-----------|
+|              36 |      2238 |
+|              37 |         1 |
+|              39 |         1 |
+
+## 24700 greyscale tiles of size 1000x1000
+
+| number of parts | frequency |
+|-----------------+-----------|
+|              13 |     24667 |
+|              14 |        33 |
+
+We can clearly see that most images of one tile size/type have the
+same number of parts: typically 36 for colour images and 13 for
+greyscale images (with the exception of the 250x250 overview images
+which have mainly 39 parts).
+
+Without going into further detail (yet) I can state that each part
+likely represents a "sub-band" of the wavelet decomposition which has
+a certain depth for each component (e.g., colour). The most simplest
+case are the greyscale tiles where we have 13 parts which would fit
+nicely to the following sub-band structure of depth 4:
+
+![13 sub-bands](/img/13subbands.png)
+
+(Given the depth *d*, the number of sub-bands can be computed as *3d +
+1*.)
+
+The following plot shows the size distribution of the components over
+all greyscale 1000x1000 tiles for each sub-band:
+
+![sub-band sizes for all 1000x1000 greyscale tiles](/img/subband_sizes_tiles1000.png)

src/Cod.ipynb

@@ -157,7 +157,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "84800e8e",
+   "id": "82fe4607",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -178,13 +178,7 @@
     "            sizes.append(i - lastpos)\n",
     "    return sizes\n",
     "\n",
-    "sizes = []\n",
-    "for t in Dsat.from_file(\"../dsatnord.mp\").tiles_zoom3.tiles:\n",
-    "    if len(t.data.planes) in [416, 880]: # skip small (\"empty\") tiles\n",
-    "        continue\n",
-    "    sizes.append(cod_sizes(t.data.planes))\n",
-    "                 \n",
-    "df = pd.DataFrame(sizes)\n",
+    "df = pd.DataFrame([cod_sizes(t.data.planes) for t in Dsat.from_file(\"../dsatnord.mp\").tiles_zoom3.tiles])\n",
     "\n",
     "ax = sns.violinplot(df, inner=None, split=False, log_scale=True, zorder=3, density_norm=\"count\", common_norm=True)\n",
     "plt.ylabel(\"size [bytes]\")\n",
@@ -199,7 +193,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4f5ae9b9",
+   "id": "05074bd2",
    "metadata": {},
    "outputs": [],
    "source": [