![\"FMP\"](\"../data/FMP_Teaser_Cover.png\")
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"![\"AudioLabs\"](\"../data/Logo_AudioLabs_Long.png\"){kind=logo}
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"\n",
"\n",
"![\"C4\"](\"../data/C4_nav.png\")
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"\n", "Following Section 4.3.2 of [Müller, FMP, Springer 2015], we introduce in this notebook the concept of scape plots and apply them for visualizing the fitness of segments. These plots were originally introduced into the music processing area by Sapp and then applied for structure analysis by Müller and Jiang.\n", "\n", "
![\"FMP_C8_F19\"](\"../data/C4/FMP_C4_F19.png\")
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"\n",
"Given a triangular representation of all segments within $[1:N]$, the following example visually indicates the following sets of segments (see Exercise 4.12 of [Müller, FMP, Springer 2015]):\n",
"\n",
"(a) All segments having a minimal length above a given threshold $\\theta\\geq 0$![\"FMP_C4_E12.png\"](\"../data/C4/FMP_C4_E12.png\")
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Scape Plot\n",
"\n",
"The triangular representation can be used as a grid for visualizing a specific numeric property $\\varphi(\\alpha)\\in\\mathbb{R}$ that can be computed for all segments $\\alpha$. This property, for example, can be the fitness values as used for audio thumbnailing (see Section 4.3 of [Müller, FMP, Springer 2015]). Such a visual representation is also referred to as **scape plot** representation of the property. More precisely, we define a scape plot $\\Delta$ by setting \n",
"\n",
"\\begin{equation}\n",
"\\label{eq:AudioStru:Thumb:SPfitness}\n",
" \\Delta(c(\\alpha),|\\alpha|):=\\varphi(\\alpha)\n",
"\\end{equation}\n",
"\n",
"for segment $\\alpha$. As a toy example, we consider the function $\\varphi$ defined by $\\varphi(\\alpha):= (t-s+1)/N$ for $\\alpha=[s:t]$, which encodes the segment lengths relative to the total length $N$. In the following code cell, we provide a visualization function for plotting a scape plot representation of this function. \n",
"\n",
"N-square matrix SP as data structure to the store the segment-dependent property $\\varphi(\\alpha)\\in\\mathbb{R}$. We use the first dimension of SP to encode the length and the second one to encode the center. Since indexing in Python starts with index 0, one needs to be careful when interpreting the length dimension. In particular, the entry SP[length_minus_one, start] contains the information for the segment having length length_minus_one + 1 for length_minus_one = 0, ..., N-1. Furthermore, note that only the left-upper part (including the diagonal) of SP is used.\n",
"![\"FMP_C4_Teaser_Ann\"](\"../data/C4/FMP_C4_Teaser_Ann.png\")
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![\"C0\"](\"../data/C0_nav.png\") | \n",
" ![\"C1\"](\"../data/C1_nav.png\") | \n",
" ![\"C2\"](\"../data/C2_nav.png\") | \n",
" ![\"C3\"](\"../data/C3_nav.png\") | \n",
" | \n",
" ![\"C5\"](\"../data/C5_nav.png\") | \n",
" ![\"C6\"](\"../data/C6_nav.png\") | \n",
" ![\"C7\"](\"../data/C7_nav.png\") | \n",
" ![\"C8\"](\"../data/C8_nav.png\") | \n",
"