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main.tex
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\documentclass[%
aspectratio=169,
9pt,
USenglish,
titlegraphic, % store custom image to .images/titlegraphic
affiliationintitlepagehead,
%progressbar,
affiliation,
]{beamer}
\usetheme{TUM}
\input{preamble.tex}
\usetikzlibrary{external}
\tikzexternalize[prefix=tikz/]
\tikzexternalize
\tikzexternaldisable
\usepackage{tummath}
\setbeamertemplate{blocks}[rounded][shadow=false]
\usepackage{appendixnumberbeamer}
% \end{itemize}
%
% Research Scope
% \begin{itemize}
% \item Imbalance of Raster and Label Data
% \item Analogies to NLP
% \item Sequence modeling
% \end{itemize}
%
% Research Projects
% \begin{itemize}
% \item Crop Classification with Multi-temporal Land Cover Classification
% \item Early Classificaiton of Time Series
% \end{itemize}
%
%
%\end{frame}
\title{BreizhCrops}
\subtitle{A Satellite Time Series Dataset for Crop Type Identification}
\author[M. Rußwurm, S. Lefèvre, M. Körner]{Marc Rußwurm,\footnotemark[1] Sébastien Lefèvre,\footnotemark[2] Marco Körner\footnotemark[1]}
\institute[TUM]{Technical Univ. of Munich, Remote Sensing Technology \footnotemark[1] \\
IRISA-Obelix, University of South Brittany\footnotemark[2]}
\date{June 14th 2019, Time Series Workshop ICML 2019}
\begin{document}
\begin{frame}[t]
\titlepage
\end{frame}
{\setbeamercolor{background canvas}{bg=tumbluedark}
\begin{frame}[plain]
\vfill
\Huge\color{white}
\begin{center}
We challenge the Time Series Community
\end{center}
\vfill
\end{frame}
}
{\setbeamercolor{background canvas}{bg=white}
\begin{frame}[plain]
\vfill
\Huge\color{tumbluedark}
\begin{center}
with a real-world time series dataset $\mathcal{D} = (\M{X},\V{y})^i$ \\
\vspace{1em}
\visible<2->{of satellite observations $\M{X} = (\V{x}_1^T,\V{x}_2^T,\dots,\V{x}_N^T)$} \\
\vspace{1em}
\visible<3->{vegetation classes $\V{y} = (y_\text{corn},y_\text{meadow},\dots)$}
\end{center}
\vfill
\end{frame}
}
{\setbeamercolor{background canvas}{bg=black}
\begin{frame}[plain]
\vfill
\Huge\color{white}
\begin{center}
\begin{columns}
\column{.5\textwidth}
\vspace{7em}
\hfill
Earth Observation
\column{.5\textwidth}
\includegraphics[width=5cm]{images/epic1}
%\includegraphics[width=7cm]{images/fdl}
\end{columns}
\end{center}
\vfill
\end{frame}
}
%
\begin{frame}
\frametitle{Optical Satellites}
\begin{columns}
\column{.5\textwidth}
\begin{itemize}[itemsep=.5em]
\item<1-> Sensor measures \textbf{Digital Numbers} $\text{DN}(\lambda)$ for each wavelength $\lambda$.
\item<2-> \textbf{Digital Numbers} are normalized to \textbf{Radiance}
$L(\lambda), \left[\frac{W}{\text{sr}m^2}\right]$ by gain and offset calibration.
\item<3-> Radiance is normalized to \textbf{top-of-atmosphere reflectance} $\rho(\lambda)$
% \item<4-> \textbf{Bottom-of-atmosphere reflectances} are reconstructed using a functional model of the atmosphere.
\end{itemize}
% Radiance $R_\lambda$ from measured Digital Numbers via calibrated gain $\alpha$ and offset $\beta$
% \begin{equation*}
% L_\lambda = \alpha \text{DN}_\lambda + \beta, \left[\frac{W}{\text{sr}m^1}\right]
% \end{equation*}
%
% top-of-atmosphere reflectance $\rho_\lambda$ as normalized Radiance $R_\lambda$ with solar
% \begin{equation*}
% \rho_\lambda = \frac{L_\lambda}{\cos(\varphi_\text{sun})}
% \frac{
% \pi d^2
% }
% {
% E_\text{sun}(\lambda)
% }
% \end{equation*}
%
% \vspace{1em}
%
% \begin{itemize}
% \item measured radiance $L(\lambda)$
% \item solar irradiance $E_\text{sun}(\lambda)$
% \item solar zenith angle $\varphi_\text{sun}$
% \item squared Earth-Sun distance $d$ in AU
% \end{itemize}
\column{.5\textwidth}
\begin{tikzpicture}
% \draw [black,dotted, fill=tumbluelight,domain=110:70] plot ({13*cos(\x)}, {13*sin(\x)-12.8});
\draw [fill=tumivory,domain=110:70] plot ({10*cos(\x)}, {10*sin(\x)-10});
% \draw [fill=tumbluelight,domain=110:70] plot ({12*cos(\x)}f, {12*sin(\x)-10});
\node(sun) at (-2,2) {\includegraphics[width=10mm]{images/icons/sun}};
\node[rotate=130,anchor=center](sat) at (2,2) {\includegraphics[width=10mm]{images/icons/sat2}};
\node(px) at ({10*cos(90)}, {10*sin(90)-10.1}){
\begin{tikzpicture}[xscale=.5,yscale=.25]
\draw[fill=tumbluelight] (0,0) -- (1,0) -- (2,1) -- (1,1) -- (0,0);
\end{tikzpicture}
%\includegraphics[width=5mm]{images/icons/house}
};
\draw[-stealth] (sun) -- node[midway,sloped]{\wave} (px);
\draw[-stealth] (px) -- node[midway,sloped]{\wave} (sat);
\visible<3->{\draw[-stealth] (sun) -- node[midway,sloped]{\wave} (sat);
\draw[draw=tumgray] (px) -- node[at end,left]{$\varphi_\text{sun}$} ++(0,1.4);
\draw [draw=tumgray, domain=130:90] plot ({1*cos(\x)}, {1*sin(\x)});
}
\node[above=.5em of sun]{$E_\text{sun}(\lambda)$};
\visible<1>{\node[above=4em of sat]{$DN(\lambda)$};}
\visible<2>{\node[above=4em of sat]{$L(\lambda)$};}
\visible<3>{\node[above=4em of sat]{$\rho_\text{toa}(\lambda)$};}
% \visible<4>{\node[above=4em of sat]{$\rho_\text{boa}(\lambda)$};}
% \draw[red] (0,0) sin (1,2);
\end{tikzpicture}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Acquired in regular time intervals}
\framesubtitle{Sentinel 2 Satellite}
% \includemovie[
% poster,
% text={\small(Loading Circle-m-increase3.mp4)}
% ]{6cm}{6cm}{images/s2orbits.mp4}
%
% \movie{loaded}{images/s2orbits.avi}
\begin{columns}
\column{.5\textwidth}
\Large
\begin{itemize}
\item<1-> polar sun-synchronous orbit
\item<2-> single orbit circa 100 minutes
\item<3-> revisit same location after 5 days
\item<4-> acquisition stripe of 290km width
\item<5-> 13 spectral bands
\item<6-> ground resolution 10-60m
\item<7-> global coverage and free of charge
\end{itemize}
\column{.5\textwidth}
% \only<1>{\includegraphics[width=\textwidth]{images/s2orbits/1}}
% \only<2>{\includegraphics[width=\textwidth]{images/s2orbits/2}}
% \only<3>{\includegraphics[width=\textwidth]{images/s2orbits/3}}
\only<1>{\includegraphics[width=\textwidth]{images/s2orbits/14}}
\only<2>{\includegraphics[width=\textwidth]{images/s2orbits/19}}
\only<3>{\includegraphics[width=\textwidth]{images/s2orbits/24}}
\only<4>{\includegraphics[width=\textwidth]{images/s2orbits/35}}
\only<5>{\includegraphics[width=\textwidth]{images/s2orbits/36}}
\only<6>{\includegraphics[width=\textwidth]{images/s2orbits/37}}
\only<7>{\includegraphics[width=\textwidth]{images/s2orbits/48}}
\tiny\url{https://www.esa.int/spaceinvideos/Videos/2016/08/Sentinel-2_global_coverage}
\end{columns}
\end{frame}
%
%
%{\setbeamercolor{background canvas}{bg=tumblack}
% \begin{frame}[plain]
%
% \vfill
% \Huge\color{white}
% \begin{center}
% \begin{columns}
% \column{.5\textwidth}
% \vspace{7em}
%
% \hfill
% Satellite Data Take-away
% \column{.5\textwidth}
%
%
% %% \includegraphics[width=5cm]{images/epic1}
% % \includegraphics[width=7cm]{images/fdl}
% \end{columns}
% \end{center}
%
% \vfill
%\end{frame}
%}
{\setbeamercolor{background canvas}{bg=tumbluedark}
\begin{frame}[plain]
\vfill
\Huge\color{white}
\begin{center}
\begin{columns}
\column{.5\textwidth}
\vspace{7em}
\hfill
Vegetation Modeling
\column{.5\textwidth}
\includegraphics[width=\textwidth]{images/Large1954_cerial_growth_stages_white}
%% \includegraphics[width=5cm]{images/epic1}
% \includegraphics[width=7cm]{images/fdl}
\end{columns}
\small\raggedleft(Large et al., 1954)
\end{center}
\vfill
\end{frame}
}
\newcommand{\rastergrid}{
\begin{tikzpicture}
% each layer
\begin{scope}[scale=2]
% raster size
\def\d{0.7}
% distance layer
\def\s{\d*5}
\foreach \i in {1,...,6}
{
\begin{scope}[
yshift=\s*\i,every node/.append style={
yslant=0.5,xslant=-1},yslant=0.5,xslant=-1
]
%\draw[step=3.33mm] (0,0) grid (1,1);
%\fill[black,fill opacity=.9] (0.333,0.333) rectangle (0.333,0.333);
\foreach \row in {0,...,2}{
\foreach \col in {0,...,2}{
\draw[tumblack, fill=tumblue!\pdfuniformdeviate 40,fill opacity=1,rounded corners=1] (\col*\d/3,\row*\d/3) rectangle (\col*\d/3+\d/3, \row*\d/3+\d/3);
% \draw[black, fill=black!\pdfuniformdeviate 40,fill opacity=1,rounded corners=1] (\col*\d/3,\row*\d/3) rectangle (\col*\d/3+\d/3, \row*\d/3+\d/3);
}
}
%\draw[step=3.33mm] (0,0) grid (1,1);
%\fill[white,fill opacity=.9] (0,0) rectangle (1,1);
\end{scope}
}
\end{scope}
\end{tikzpicture}
}
%\begin{frame}
%\frametitle{Spectral Band}
%\end{frame}
\begin{frame}
\frametitle{Multi-temporal Vegetation Modeling}
\begin{columns}
\column{.5\textwidth}
\begin{tikzpicture}
\node[] at (0,0){\includegraphics[width=\textwidth]{images/Large1954_cerial_growth_stages}};
% \draw[step=1.0,black,thin, fill=none] (-2,-2) grid (2,2);
\visible<-1>{\draw [fill=white, draw=none, opacity=0.8] (-0.8,-3) rectangle (2,2.5);}
\visible<-2>{\draw [fill=white, draw=none, opacity=0.8] (2,-3) rectangle (5,2.5);}
\visible<1>{\node[rotate=190] at (-2.5,1.5){\includegraphics[width=15mm]{images/icons/sat2}};}
\visible<2>{\node[rotate=225] at (-2.5,1.5){\includegraphics[width=15mm]{images/icons/sat2}};}
\visible<3->{\node[rotate=260] at (-2.5,1.5){\includegraphics[width=15mm]{images/icons/sat2}};}
% \visible<4->{\node at (-1.5,1.4) {\includegraphics[width=10mm]{images/cloud}};
% }
\end{tikzpicture}
\column{.5\textwidth}
{\Large
\only<1>{
\begin{equation*}
f_\text{vegetation}(\V{X}_t)
\end{equation*}
}
\only<2>{
\begin{equation*}
f_\text{vegetation}(\V{X}_t,\V{X}_{t+1})
\end{equation*}
}
\only<3>{
\begin{equation*}
f_\text{vegetation}(\V{X}_t,\V{X}_{t+1},\V{X}_{t+2})
\end{equation*}
}
}
\vspace{2em}
\visible<1->{\includegraphics[width=.22\textwidth]{images/s2grid/1}}
\visible<2->{\includegraphics[width=.22\textwidth]{images/s2grid/2}}
\visible<3->{\includegraphics[width=.22\textwidth]{images/s2grid/3}}
% \visible<4->{\includegraphics[width=.22\textwidth]{images/s2grid/4}}
\vspace{1em}
{\small
Large, E. C. (1954). Growth stages in cereals illustration of the Feekes scale. Plant pathology, 3(4), 128-129.
}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Problem Definition}
\Large
\centering\begin{tikzpicture}[node distance=0em]
\visible<2->{\node(y){\V{y}};}
\visible<2->{\node[right=of y](equals){$=$};}
\node[right=of equals](f){$f_\text{vegetation}$};
\visible<1->{\node[right=of f](x){$(\V{X}_t,\V{X}_{t+1},\V{X}_{t+2})$};}
\end{tikzpicture}
\vspace{1em}
\raggedright
\begin{description}\setlength\itemsep{1em}
\item[\color{tumblue}Problem:]<1-> \textbf{unsupervised learning} of a vegetation model \textbf{is difficult}
\item[\color{tumblue}Solution:]<2-> re-framing as \textbf{supervised classification} of crop type labels
\item[\color{tumblue}Intuition:]<3-> A \textbf{supervised classification model} must \textbf{internalize} a learned \textbf{discriminative model} for the \textbf{vegetation}
\end{description}
\end{frame}
\input{images/input.tikz}
\begin{frame}
\frametitle{Crop Type Labels in Europe}
\begin{columns}
\column{.5\textwidth}
\Large
\begin{description}\setlength\itemsep{1em}
\item[\color{tumblue}collected] yearly within European \textbf{Common Agricultural Policy} (CAP)
\item[\color{tumblue}declared] by Farmers at \textbf{crop subsidy} applications
\item[\color{tumblue}today] slowly made publicly available (on a national basis)
\item[\color{tumblue}in future] further harmonized within \textbf{Europe's INSPIRE} directive
\end{description}
\column{.5\textwidth}
\includegraphics[width=\textwidth]{images/europe_data2}
\end{columns}
\end{frame}
{\setbeamercolor{background canvas}{bg=tumbluedark}
\begin{frame}[plain]
\vfill
\Huge\color{white}
\begin{center}
\begin{columns}
\column{.5\textwidth}
\vspace{7em}
\hfill
The Dataset
\column{.5\textwidth}
\includegraphics[width=\textwidth]{images/map/breizh_white}
%% \includegraphics[width=5cm]{images/epic1}
% \includegraphics[width=7cm]{images/fdl}
\end{columns}
\small\raggedleft Field Parcel Coverage in Brittany
\end{center}
\vfill
\end{frame}
}
\begin{frame}
\frametitle{Organization}
\begin{columns}
\column{.5\textwidth}
\only<1>{
\emph{Nomenclature des unités territoriales statistiques (NUTS)} as European standard of administrative Boundaries.
\begin{description}
\item[NUTS-0] countries
\item[NUTS-1] states
\item[NUTS-2] districts
\item[NUTS-3] municipalities
\end{description}%NUTS-0 countries, NUTS-1 states, NUTS-2 districts, NUTS-3 municipalities. Add-on: All European Statistics (Eurostats) are collected in these administrative divisions.
}
\only<2>{
Field Parcels
\begin{tabular}{lrrr}
\toprule
Departements & NUTS-3 & Parcels & Size \\
\cmidrule(lr){1-1}\cmidrule(lr){2-2}\cmidrule(lr){3-3}\cmidrule(lr){4-4}
% \midrule
\color{frh04color}\textbf{Morbihan} & FRH04 & 158522 & 4.3 Gb\\
\color{tumgraydark}\textbf{Côtes-d’Armor} & FRH01 & 221095 & 6.7 Gb \\
\color{frh02color}\textbf{Finistère} & FRH02 & 180565 & 6.2 Gb \\
\color{frh03color}\textbf{Ille-et-Vilaine} & FRH03 & 207993 & 6.8 Gb\\
\\
\midrule
Brittany & FRH0 & 768175\\
\bottomrule
\end{tabular}
}
\vspace{1em}
we suggest a spatially distinct train/test split via these partitions. \\
\vspace{1em}
\textbf{Bonus:} Eurostat statistics are gathered on NUTS boundaries.
\column{.5\textwidth}
\includegraphics[width=.9\textwidth]{images/map/regions}
NUTS-3 regions within Brittany, France
\end{columns}
\end{frame}
\input{images/example.tikz}
\begin{frame}
\frametitle{Corn Example}
\examplecorn
\end{frame}
%
%\begin{frame}
%\frametitle{Examples}
%\centering
%%\externalize{beispiel}{%
%\begin{tikzpicture}[node distance=.1em]
%% \visible<1>{
%% \node[font=\huge](veg) at (0,0){Vegetationsmodell};
%% \node[right=0em of veg](input){$\left(\satimage{1},\satimage{1},\satimage{3}\right)$};
%% }
%\node[font=\huge, label=$f$](equals){$\leftarrow$};
%% \visible<2>{\node[right=0em of equals](input){\timeseries{input.csv}};}
%\visible<1>{
% \node[right=0em of equals](input){\timeseries{prep74526670.csv}};}
%
%\visible<2>{\node[right=0em of equals](input){\timeseries{prep77770412.csv}};}
%
%\visible<1>{\node[left= of equals, font=\huge](probas){meadows};}
%\visible<2>{\node[left= of equals, font=\huge](probas){corn};}
%
%
%\end{tikzpicture}%
%%}
%\end{frame}
{\setbeamercolor{background canvas}{bg=tumbluedark}
\begin{frame}[plain]
\vfill
\Huge\color{white}
\begin{center}
\begin{columns}
\column{.5\textwidth}
\vspace{7em}
\hfill
Baseline Results
\column{.5\textwidth}
% \includegraphics[width=5cm]{images/epic1}
%\includegraphics[width=7cm]{images/fdl}
\end{columns}
\end{center}
\vfill
\end{frame}
}
\input{images/confmat.tikz}
\begin{frame}
\frametitle{Two Baseline Models}
\Large
Inspired by Models used in NLP, we implemented a \textbf{multi-layer LSTM} and a \textbf{(minified) Transformer encoder}.
\vspace{1em}
\normalsize
% \begin{table*}[b]
% \caption{Accuracy metrics for the Multi-layer bidirectional LSTM \cite{hochreiter1997long} and the Transformer-Encoder \cite{Vaswani:transformer}.}
% \label{tab:accuracies}
% \centering
\begin{tabular}{lrrrrrrr}
\toprule
baseline & accuracy & $\kappa$ & mean f1 & mean precision & mean recall \\
\cmidrule(lr){1-1}\cmidrule(lr){2-2}\cmidrule(lr){3-3}\cmidrule(lr){4-4}\cmidrule(lr){5-5}\cmidrule(lr){6-6}\cmidrule(lr){7-7}
Transformer {\small (Vaswani et al., 2017)} & \textbf{0.69} & \textbf{0.63} & 0.57 & {0.60} & 0.56 \\
LSTM {\small (Hochreiter and Schmidhuber, 1997)} & 0.68 & 0.62 & \textbf{0.59} & \textbf{0.63} & \textbf{0.58} \\
\bottomrule
\end{tabular}
\vspace{1em}
\Large
\textbf{Takeaway:}
\begin{itemize}
\item Models perform quite similar
\item Potential for improvement
\item well-defined classes accurately classified
\item broadly defined classes systematically confused
\end{itemize}
% \end{table*}
\end{frame}
\begin{frame}
\frametitle{Results}
\framesubtitle{LSTM Model}
\small
\begin{columns}
\column{.5\textwidth}
\begin{tabular}{rlcccc}
\toprule
\textbf{\#} & \textbf{crop type} & \textbf{prec.} & \textbf{rec.} & \textbf{$f_1$} & \textbf{\#samples} \\
\cmidrule(lr){1-1}\cmidrule(lr){2-2}\cmidrule(lr){3-3}\cmidrule(lr){4-4}\cmidrule(lr){5-5}\cmidrule(lr){6-6}
%\midrule
1 & barley & 90 & 86 & 88 & 4982 \\
2 & wheat & 83 & 95 & 89 & 13850 \\
3 & corn & 93 & \textbf{96} & 94 & 25059 \\
4 & fodder & 51 & 34 & 41 & 3449 \\
5 & fallow & 30 & 2 & 4 & 3863 \\
6 & misc. & 50 & 49 & 49 & 12499 \\
7 & orchards & 21 & 7 & 10 & 391 \\
8 & cereals & 74 & 47 & 57 & 4645 \\
9 & perm. meadows & 51 & 47 & 49 & 20966 \\
10 & protein crops & 42 & 61 & 50 & 498 \\
11 & rapeseed & \textbf{96} & 94 & \textbf{95} & 2664 \\
12 & temp. meadows & 56 & 68 & 62 & 29977 \\
13 & vegetables & 86 & 69 & 76 & 3114 \\
& & & & & \\
& & \textbf{63} & \textbf{58} & \textbf{59} & 125957 \\
\bottomrule
\end{tabular}
\column{.5\textwidth}
\confmat{images/data/BreizhCrops_rnn/npy/confmat_flat.csv}{3}{1}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Summary}
\Large
\begin{columns}[t]
\column{.5\textwidth}
\visible<1->{
% \textbf{Impact}
% \vspace{1em}
%
% \begin{description}[itemsep=.5em]
% \item large scale \textbf{real-world dataset}
% \item effectively \textbf{unlimited data} (spatially and temporally)
% \item \textbf{assessing generalization} over large regions
% \item potential for further \textbf{vegetation characteristics} (drought indicator, early classification, crop yield)
% \end{description}
\textbf{Summary}
\vspace{1em}
\begin{itemize}[itemsep=.5em]
\item<1-> we gathered, compiled, harmonized a \textbf{large supervised classification dataset} (20 Gb of data) for crop type mapping
\item<2-> we \textbf{prove the feasibility} of classification with two deep neural network classifiers (LSTM and Transformer)
\item<3-> baslines \textbf{leave potential} \textbf{for improvement} by future research
\end{itemize}
}
\column{.5\textwidth}
\textbf{Challenges}
\vspace{1em}
\begin{description}[itemsep=.5em]
\item<4-> \textbf{Imbalanced} class \textbf{labels}
\item<5-> Classes with \textbf{similar characteristics}
\item<6-> Non-Gaussian noise induced by \textbf{clouds}
\item<7-> \textbf{Regional} \textbf{variations} in the class distributions
\item<8-> \textbf{Spatial} \textbf{autocorrelation}
\item<9-> \textbf{Irregular} temporal \textbf{sampling} distance
\item<10-> \textbf{Variable} \textbf{sequence} length
\end{description}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Takeaway and Feedback}
\Large
We hope to have given an \textbf{overview over the problem space} of multi-temporal \textbf{Earth observation}.
\vspace{2em}
We warmly welcome \textbf{feedback and suggestions} as questions or as discussion at the poster
\end{frame}
%
%\begin{frame}
% \frametitle{Summary}
%
% \Large
%
% \begin{itemize}[itemsep=.5em]
% \item<1-> we gathered, compiled, harmonized a \textbf{large supervised classification dataset} (20 Gb of data) for crop type mapping
% \item<2-> it poses a series of \textbf{real-world challenges} to the time series researchers.
% \item<3-> it is structured \textbf{following administrative boundaries} and \textbf{can be augmented} by \textbf{more regions} or \textbf{additional statistical data} from Eurostat.
% \item<4-> we \textbf{prove the feasibility} of classification with two deep neural network classifiers
% \item<5-> results form a \textbf{baseline}, but \textbf{leave potential} \textbf{for improvement} by future research
% \item<6-> we \textbf{publish dataset}, and \textbf{source code} to the baseline models on \textbf{Github}
% \end{itemize}
%
%
%\end{frame}
\begin{frame}
\frametitle{Thank you}
\centering
\includegraphics[width=3cm]{images/qrcode}
\Large\textbf{github.com/TUM-LMF/BreizhCrops}
\Large
lmf.bgu.tum.de/vision
twitter.com/MarcCoru
\end{frame}
\appendix
{\setbeamercolor{background canvas}{bg=tumbluedark}
\begin{frame}[plain]
\vfill
\Huge\color{white}
\begin{center}
\begin{columns}
\column{.5\textwidth}
\vspace{7em}
\hfill
Backup slides...
\column{.5\textwidth}
% \includegraphics[width=5cm]{images/epic1}
%\includegraphics[width=7cm]{images/fdl}
\end{columns}
\end{center}
\vfill
\end{frame}
}
{\setbeamercolor{background canvas}{bg=tumbluedark}
\begin{frame}[plain]
\vfill
\Huge\color{white}
\begin{center}
\begin{columns}
\column{.5\textwidth}
\vspace{7em}
\hfill
Challenges
\column{.5\textwidth}
% \includegraphics[width=5cm]{images/epic1}
%\includegraphics[width=7cm]{images/fdl}
\end{columns}
\end{center}
\vfill
\end{frame}
}
\begin{frame}
\frametitle{Challenge 1: Clouds adding a positive bias}
\includegraphics[width=2cm]{images/s2grid/1}
\includegraphics[width=2cm]{images/s2grid/2}
\includegraphics[width=2cm]{images/s2grid/3}
\includegraphics[width=2cm]{images/s2grid/4}
%\input{images/example.tikz}
\examplecorn
\end{frame}
\begin{frame}
\frametitle{Challenge : Imbalanced class labels}
\input{images/partition_histograms.tikz}
\end{frame}
\begin{frame}
\frametitle{Challenge: Classes with similar characteristics}
Multi-Layer RNN baseline
\begin{columns}
\column{.5\textwidth}
\textbf{Precision}
\confmat{images/data/BreizhCrops_rnn/npy/confmat_flat.csv}{3}{1}
\column{.5\textwidth}
\textbf{Recall}
\confmat{images/data/BreizhCrops_rnn/npy/confmat_flat.csv}{4}{1}
\end{columns}
\end{frame}
%
%\begin{frame}
%\frametitle{Transformer baseline}
%
%\input{images/confmat.tikz}
%
%\begin{columns}
%
%\column{.5\textwidth}
%\confmat{images/data/BreizhCrops_transformer/npy/confmat_flat.csv}{3}{1}
%
%\column{.5\textwidth}
%\confmat{images/data/BreizhCrops_transformer/npy/confmat_flat.csv}{4}{1}
%
%\end{columns}
%
%\end{frame}
\begin{frame}
\frametitle{Challenge: Irregular sampling distance.}
\includegraphics[width=\textwidth]{images/days_between_acquisitions}
\end{frame}
\begin{frame}
\frametitle{Challenge: Variable sequence length}
\includegraphics[width=\textwidth]{images/sequencelengths}
\end{frame}
\begin{frame}
\frametitle{Challenge: Regional variations in the class distributions}
\begin{tikzpicture}
\node(o){\includegraphics[width=2.5cm]{images/orchards}};
\coordinate[yshift=2.55cm](co2) at (o);
\draw ($ (co2)+(-1cm,0) $) -- ($ (co2)+(1cm,0) $) node[name=labblue, pos=1.1, anchor=west]{1224 parcels};
\coordinate[yshift=-.43cm](co) at (o);
\draw ($ (co)+(-1cm,0) $) -- ($ (co)+(1cm,0) $) node[name=laborange, pos=1.1, anchor=west]{350 parcels};
\node[right=4cm of o](regions){\includegraphics[width=8cm]{images/map/regions}};
\draw (laborange) -- ($ (regions)+(-2cm,.5cm) $);
\draw (labblue) -- ($ (regions)+(3cm,0cm) $);
\end{tikzpicture}
\end{frame}
\begin{frame}
\frametitle{Spatial autocorrelation}
\includegraphics[width=11cm]{images/map/breizh}
\end{frame}
{\setbeamercolor{background canvas}{bg=tumbluedark}
\begin{frame}[plain]
\vfill
\Huge\color{white}
\begin{center}
\begin{columns}
\column{.5\textwidth}
\vspace{7em}
\hfill
Summary and Outlook
\column{.5\textwidth}
% \includegraphics[width=5cm]{images/epic1}
%\includegraphics[width=7cm]{images/fdl}
\end{columns}
\end{center}
\vfill
\end{frame}
}
\begin{frame}
\frametitle{Scaling up}
\includegraphics[width=5cm]{images/EuroCrops}
\includegraphics[width=5cm]{images/France}
\includegraphics[width=4cm]{images/Bavaria}
\end{frame}
\begin{frame}
\frametitle{Supported by Google Research Credits}
\includegraphics[width=.3\textwidth]{images/google_research_credits}
\includegraphics[width=.3\textwidth]{images/google}
\includegraphics[width=.2\textwidth]{images/earth-engine-logo}
%\includegraphics[width=3cm]{images/250px-Google-Cloud-Storage-Logo}
%\includegraphics[width=3cm]{images/Google_Compute_Engine_logo}
%\includegraphics[width=3cm]{images/google_cloud_sql}
\end{frame}
\newcommand{\myvec}[1]{\ensuremath{\begin{pmatrix}#1\end{pmatrix}}}
\begin{frame}
\frametitle{Spatial and Temporal Discretization}
\begin{columns}
\column{.5\textwidth}
{
\begin{equation*}
\V{x}_t = \myvec{\rho_{\lambda_1} \\ \rho_{\lambda_2} \\ \dots \\ \rho_{\lambda_n}}
\end{equation*}
}
Spectral reflectance of \textbf{spectral bands} disctretized on a \textbf{spatial grid}. Each grid cell is georeferenced by its Longitude $\Lambda$ and Latitude $\Phi$.
Acquisitions in regular \textbf{temporal intervals}.
\column{.5\textwidth}
\begin{tikzpicture}
% \node(a){\includegraphics[width=3cm]{images/s2grid/1}};
% \draw[step=1cm,gray,very thin] (-2,-2) grid (6,6);
\draw [fill=tumivory,domain=110:70] plot ({11*cos(\x)}, {11*sin(\x)-8.5});
\begin{scope}[scale=1]
% raster size
\def\d{1}
% distance layer
\def\s{\d*50}
\node at (-1.7,2.4){$t_{i-1}$};
\node at (-1.7,4.2){$t_i$};
\node at (-1.7,6){$t_{i-1}$};
\node at (1,1.9){$\Lambda$};
\node at (-1,1.9){$\Phi$};
% \draw[step=1.0,black,thin] (-2,0) grid (2,5);
\foreach \i in {1,...,3}
{
\begin{scope}[
yshift=\s*\i,every node/.append style={
yslant=0.5,xslant=-1},yslant=0.5,xslant=-1,scale=0.35
]
%\draw[step=3.33mm] (0,0) grid (1,1);