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\title[The Urban Observatory: Quantification of the Rebound Effect]{The Urban Observatory: Quantification of the Rebound Effect}


\author[Priyanshi Singh]{Priyanshi Singh$^{1}$\\
$^{1}$New York University (NYU)
}


\begin{document}

%\date{Accepted 1988 December 15. Received 1988 December 14; in original form 1988 October 11}

%\pagerange{\pageref{firstpage}--\pageref{lastpage}} \pubyear{2002}

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\label{firstpage}




%\begin{keywords}
%circumstellar matter -- infrared: stars.
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\section{Abstract}\label{abstract}

The rebound effect is described as the circumstance where gains through
implementation of energy efficient technologies are potentially offset
by increased usage patterns. Such an effect may have implications on
energy policy, business or building management and consumer behavior.
Consequently, this has been an important subject of scientific inquiry.
Previous research has examined whether there is an effect and what
methodologies best measure it. We seek to quantify the rebound effect by
introducing a new empirical methodology for observing and analyzing a
particular energy end use, lighting. We do~so by leveraging two areas of
research at the NYU Center for Urban Science and Progress Urban
Observatory, particularly identifying patterns in light usage with
broadband imaging and classifying light bulb types by their spectral
signature using hyperspectral imaging. We bring these work streams
together and integrate urban lightscape data with geospatial data for
the first time to address a research hypothesis as to whether there is a
significant variation in total lights on duration for efficient versus
non-efficient light technology. While a statistically significant
rebound effect was not found, we were able to establish an empirical
constraint on the amplitude of the rebound effect upon which to base
future scientific inquiry. We were also able to quantify light usage for
several light types as well as establish an analytical pipeline that
shows promise as a new avenue for empirical research into the rebound
effect.\\

\section{Introduction}\label{introduction}

New York City is known as the city that never sleeps, which perhaps is a
reason why energy consumption for residents in the New York State topped
1,115 trillion British Thermal Units (Btu) in 2015 \cite{BIBTEXIDe}~--
enough to produce approximately 327 billion kilowatt hours (kWh) of
electricity \cite{2017}. Energy consumption is a global concern,
as worldwide consumption is projected to increase by 48\% in 2040
compared to the 2012 levels \cite{BIBTEXID}. It is therefore no
surprise that significant focus is placed on energy efficiency with
substantial investment in both the public and private sectors. In 2016
the United States alone invested \$231 billion in energy efficiency
\cite{2017}. Such investments may include retail-focused
strategies for efficient lighting technologies, smart sensors for HVAC,
and better insulation materials for roofing, among others.\\

It is also no surprise that much attention has been given to
understanding the dynamics of energy efficiency and consumption, which
can be difficult to characterize. In as early as 1865, Jevon's
Paradox~stated ``when technological progress increases the efficiency
with which a resource is used, the rate of consumption of that resource
rises because of increased consumption and demand'' \cite{polimeni2012jevons}.
The modern term for this is the ``rebound effect.''\\

Unfortunately, not only are the dynamics of energy efficiency and
consumption complicated, but empirical data is sparse and existing
research can contain potential biases \cite{sorrell2007ukerc},
\cite{sorrell2009empirical}. Critics of research on the rebound effect claim that
it is widely overstated and can be a distraction from the cause of
conservation \cite{gillingham2013energy}. Indeed the field of energy efficiency
and economics has advanced greatly since Jevon first made his claim in
1865. For reasons explored in more detail later in this paper, it is
clear that the definitions of the rebound effect and the approaches to
measure it are quite varied and in need of more data as well as robust
constraints with which to frame scientific research, such as hypothesis
testing.\\

Fortunately, just as technological advancements are made in energy
efficiency, so too are advancements in scientific inquiry. Progress with
remote sensing instrumentation and technologies for collecting data,
greater computational resources, and statistical learning methods can be
brought to bear on issues such as the rebound effect. Indeed, the field
of urban informatics, defined as ``the study, design, and practice of
urban experiences across different urban contexts that are created by
new opportunities of real-time, ubiquitous technology and the
augmentation that mediates the physical and digital layers of people
networks and urban infrastructures,'' \cite{hinds2011proceedings} shows
tremendous promise for just this sort of inquiry.\\

We leverage advanced lightscape imaging survey methods pioneered by the
Urban Observatory (UO) at the New York University Center for Urban
Science and Progress (CUSP) to carry out the first empirical observation
of the rebound in Brooklyn, New York. Specifically, we determine if
significant variance in light use exists between users of conventional
and energy efficient technology. We developed and tested the methods in
the analytical pipeline required to carry out this analysis and have
collected 29 nights' worth of raw image data. We contribute to technical
methods of light source identification, classification, and integration
with existing records data as well as constructs an analytical pipeline
that can be used in other aspects of UO research.\textbf{\\
}\\

\section{Literature review and previous
research}\label{literature-review-and-previous-research}

\subsection{Rebound effect}\label{rebound-effect}

A key premise to the rebound effect is the implication that energy
efficiency has a price content, such that ``we may expect the energy
price reduction that increased efficiency entails to exert an upward
pressure on the demand for energy. This pressure will partly offset, and
may more than offset, the energy saving that results from improved
appliance efficiency''~\selectlanguage{english}\cite{khazzoom1980economic}.\\

\cite{Berkhout_2000}~provides a more thorough breakdown of the effect:\\

\begin{itemize}
\tightlist
\item
  technological progress makes equipment more energy efficient,
  therefore\\
\item
  less energy is needed to produce the same amount of product, using the
  same amount of equipment; however, not everything stays the same,
  therefore\\
\item
  the equipment has become more energy efficient, which causes the cost
  per unit of services of the equipment to fall, i.e. a price decrease,
  and\\
\item
  a price decrease normally leads to an increase in consumption,
  therefore\\
\item
  an increase in energy consumption may occur due to increased
  efficiency, which quantifies the rebound effect.\\
\end{itemize}

If the net usage of the product, such as lighting, is large enough then
the increase in energy consumption may actually exceed the energy saved
through efficiency completely, leading to an overall net increase in
consumption compared to non-efficient technology.\\

The rebound effect can be broadened to include macroeconomic as well as
microeconomic effects. These might include market-clearing price and
quantity adjustments and even transformational effects in energy
production and social conventions for energy use~\selectlanguage{english}\cite{A_Greening_2000}. We
remain focused on micro-economic behavior; however, it is worth noting
that even if direct rebound effects are small, an aggregated impact
could be non-trivial.\\

Empirical studies of the rebound effect generally fall into two
categories: quasi-experimental and econometric~\selectlanguage{english}\cite{sorrell2009empirical}.
Quasi-experimental studies attempt to directly measure the rebound
effect by comparing energy demand before and after adopted energy
efficient technology. This is done either by measuring the direct output
of the technology, such as heating or lighting, or the energy input,
such as fuel or electricity. In either case, obtaining direct
measurements is exceedingly difficult. Most studies surveyed used
within-group before-and-after comparisons instead of including a control
group~\selectlanguage{english}\cite{sorrell2009empirical}, which makes them prone to
bias~\selectlanguage{english}\cite{frondel2005evaluating},~\selectlanguage{english}\cite{meyer1995natural}. Since households must
opt-in to these studies, there is also a selection
bias~\selectlanguage{english}\cite{hartman1988self}. This is particularly problematic given two key
counterfactuals that must be assessed: what the energy use would have
been had the technology not been put in place, which is a measure of
energy savings; and subsequently, what the energy use would have been
had there not been a change in behavior, which is the rebound effect.\\

While engineering methods can help determine the energy saved through
efficient technology, without the ability to approximate a randomly
assigned controlled study or generate enough data, it is unlikely such
studies could produce a statistically valid result for the rebound
effect. For these reasons, econometric approaches are more common. They
use secondary data sources to estimate the rebound effect, typically by
estimating elasticities. Elasticity is the change in a particular
variable, such as energy demand, following a change in another, such as
energy efficiency, when all other variables are held
constant~\selectlanguage{english}\cite{sorrell2009empirical}. Several common definitions of the rebound
effect leverage energy efficiency, energy cost, and energy price
elasticity with regard to useful work and demand for
energy~\selectlanguage{english}\cite{sorrell2007ukerc}.\\

Elasticity by definition requires that all other variables be held
constant, opening these econometric approaches to bias and
confoundedness. For example, while a general assumption may be that
consumers react to a decrease in price by increasing consumption, it
could also be true that energy-conscious consumers would not increase
consumption despite cheaper energy. Alternatively, it is possible that
the perception of saving energy leads consumers using efficient
technology to feel more comfortable using more energy, independent of
cost or even demand for useful work. While investments in energy
efficiency do not necessarily translate into decreased energy
consumption (or vice versa), it is an indication that this is not a
straightforward matter and favors a more direct empirical inquiry into
actual usage behavior.\\

\subsection{Urban informatics and remote light
sensing}\label{urban-informatics-and-remote-light-sensing}

Observing light remotely can improve upon previous methodologies, such
as~by reducing selection bias and obtaining a sufficiently large and
varied sample size of both energy efficient lighting technology users
(treatment group) and non-users (control group) to allow for more robust
statistical assumptions, rather than before-and-after comparisons.
Integrating remote observations with the existing data can further
improve statistical assumptions by conditioning on these covariates,
such as income or building type.\\

Remote sensing allows direct independent observation of precisely when
and with what type of technology lights are used. The benefits of
measuring lighting use as it relates to urban characteristics have been
demonstrated, although some key challenges include lack of data,
particularly with more precise spatial resolution~\cite{hale2013mapping}.\\

A report on energy use in New York City suggested that improved lighting
technologies could greatly reduce overall energy consumption, estimating
that 13\% of the energy use within benchmarked buildings of all types in
New York City was used for lighting. However, that same study
acknowledged that this estimate was based on a survey of professional
auditors' assessments of lighting use by floor size and not directly
measured data~\cite{BIBTEXIDa}. Identifying a way to measure its use
directly could have a great benefit to better characterizing the impact
of investments in energy efficiency lighting technology. Previous
research by the UO has laid a foundation for such an inquiry.\\

The UO first provided light curve extraction from images of a city
lightscape~\cite{Dobler_2015}, identifying unique light sources from
broadband images of Manhattan and analyzing their light curves for major
``on'' and ``off'' transitions with a modified version of Canny's edge
detection approach~\cite{Canny_1986}. The UO's subsequent survey of
hyperspectral images of Manhattan used advanced imaging technology, a
single slit spectrograph with 872 spectral channels from 0.4--1.0
\selectlanguage{greek}μ\selectlanguage{english}m~\cite{Dobler_2016}. The resulting spectra were clustered into groups
with similar features in the wavelength domain and correlated with
spectra of known light sources. This method successfully classified 13
types of lighting used in the observation field and even proposed new
spectral templates of light classification. These efforts demonstrate
how an approach for quantifying the light use for specific lighting
technologies can be developed by calculating total ``on time duration''
for light sources based on their on and off transitions and comparing
these on times across lighting types.\\

We extend the previous UO studies with respect to urban lightscape
analysis in several ways. First, we add to the corpus of data with an
observation field of view that has less density and lower building
structure than Manhattan. This more common building typology facilitates
replication in other urban areas without Manhattan's unique profile.
Second, we integrate both broadband images and hyperspectral images,
which were previously analyzed separately, using these independent
imaging techniques to facilitate source identification and
classification. Third, we map these images with a three-dimensional
projection of the built-environment by leveraging photogrammetry
techniques. This allows for integration with public records, such as
building and socioeconomic and demographic (SED) data. Finally, this
research enhances, automates, and further validates several techniques
for image processing, particularly by:\\

\begin{itemize}
\tightlist
\item
  improving upon and automating methods for light source extraction and
  interpretation of light curves to isolate on and off transitions and
  lighting use behavior;\\
\item
  integrating both broadband images and hyperspectral
  images;~and\\[2\baselineskip]
\item
  projecting light sources onto a 3-dimensional LiDAR model of the
  cityscape to enable integration with Primary Land Use Tax Lot Output
  (PLUTO), which could be used to differentiate between residential and
  commercial buildings\\[2\baselineskip]
\end{itemize}

\section{Data Collection}\label{data-collection}

This project is founded upon primary data collection, which represents
an important contribution for the field of urban informatics as well as
provides insight into methods of instrumentation and raw image data
processing.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1-cameras/image1-cameras}
\caption{{\hypertarget{auto-label-caption-247766}{}
Figure 1. The hyperspectral camera (on the left) and the broadband
camera (on the~right) used to collect observed data.
\hypertarget{auto-label-caption-519800}{}
The cameras are shown here in the approximate orientation in which they
captured data from a field of view south of the CUSP facilities at 1
Metro Tech Center, Brooklyn.~%
}}
\end{center}
\end{figure}

\subsection{Broadband imaging}\label{auto-label-subsection-501188}

We began broadband image collection on the evening of June 25, 2017 and
continued through the evening of July 23, 2017 for a total of 29
consecutive nights of data. For each night during the observation
period, the broadband camera scanned the view shown in Figure 2 every 10
seconds from 9 pm to about 6 am, for a total of approximately 3,200
images per night. The raw images stored in the CUSP data facility are in
3-color (RGB) format with dimensions of 3072 x 4096 pixels. Each image
is a composite of 20 exposures of approximately 34 milliseconds (ms)
each for total exposure of approximately 680 ms per image. Each image
scan is approximately 12 Megabytes (Mb). If 3,200 scans are collected in
a given night at 12 Mbs per scan, about 38.4 Gigabytes (Gb) of data are
produced that night alone. Approximately 1.1 Terabytes (Tb) of data have
been collected from broadband image scans in the 29 night collection
period.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2-view/image2-view}
\caption{{\hypertarget{auto-label-caption-188423}{}
Figure 2. Approximate broadband imaging field of view over Southern
Brooklyn
A range of residential building types is visible, including the Gowanus
Houses public housing complex in the center of the view.
\hypertarget{auto-label-caption-417819}{}%
}}
\end{center}
\end{figure}

Aside from the challenges of collecting, processing and manipulating
such large datasets, the nighttime images have a low signal to noise
(S/N) ratio that makes analysis and classification of particular sources
difficult. Furthermore, the classification must rely upon unsupervised
techniques as labeling data through human-annotated ``ground truth''
methods is not practical. This not only makes light source
identification, classification, and on/off transition measurements
challenging, but renders traditional methods of algorithm evaluation
inadequate.\\

The broadband images in this research were used primarily to identify
specific light sources within the image plane, which were registered
with a shared frame of reference for the hyperspectral images and the
three-dimensional LiDAR model, and to measure the duration of lighting
use, particularly the total on time duration of a given source, which
constitutes the dependent variable of the research hypothesis.\\

\subsection{\texorpdfstring{Hyperspectral imaging\\
}{Hyperspectral imaging }}\label{hyperspectral-imaging}

Hyperspectral imaging (HSI) is a remote sensing technique through which
we collect high resolution spectral data that can be used for various
detection purposes.~Several scientific studies
\cite{Elvidge_2010},~\cite{Dobler_2016} relating to urban context in the
past used HSI for lighting type detection. The aforementioned
\cite{Dobler_2016}~describes a novel approach~adapted from astronomical
techniques to detect lighting types in an urban landscape using~a
hyperspectral sensor.~\cite{Dobler_2016} \selectlanguage{english}also described the nuances
associated with the post-processing of the hyperspectral scans to
extract the clean spectral information of various sources in the field
and subsequently the identification of lighting types. Adopting a
similar pipeline, this project uses the hyperspectral scans to match the
usage information of sources obtained through broadband imaging with the
corresponding lighting type, to measure the rebound characteristics
across the lighting types.\\

The UO has a~VNIR (Visible Near Infra Red) Hyperspectral Imager with a
spectral range of 395-1008 nm. It is a vertical slit aperture instrument
that collects a narrow beam of light that gets split by a prism into 848
hyperspectral channels with a spectral resolution of ~less than 1 nm
(Figure 3). It uses a horizontal pan mechanism to sweep through the
field of view and in our case takes \textasciitilde{}160 seconds to
capture one complete scan of our subject field. The digital output from
the camera is a raw file with 848 (number of spectral channels) x 1600
(pixel rows) x 3194 (pixel columns) dimensions. Each hyperspectral scan
is about \textasciitilde{}8.2 GB. The camera captured a set of 15
observations on the night of May 26, 2017, producing
\textasciitilde{}123 GB of data in one night. These scans were used to
identify the spectra of various light sources within the scene (Figure
4).~\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/10/10}
\caption{{\hypertarget{auto-label-caption-996245}{}
Figure 3. Relative Intensities of a light source across 848 wavelength
channels between 400-1000nm~%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/1/1}
\caption{{\hypertarget{auto-label-caption-720071}{}
Figure 4. 2D representation of a hyperspectral scan with light sources%
}}
\end{center}
\end{figure}

\subsection{LiDAR point cloud data}\label{lidar-point-cloud-data}

In addition to collecting broadband and hyperspectral data, we used
existing external data sources to identify physical locations of each
identified light source. Specifically, a LiDAR (Light Detection and
Ranging) scan collected by the private mapping company
\href{http://www.sanborn.com/lidar-case-study/}{Sanborn for the City
University of New York}served as the data source to map the topography
of the observed scene to image pixels. The LiDAR dataset is from 2010
and thus may not include buildings that were built in recent years.
However, establishing an analytical pipeline using the LiDAR data
ensures that the work can be easily replicated once the next dataset
becomes available (expected in fall 2017). The LiDAR data is segmented
into tiles that cover all five boroughs of NYC at a roughly 1 foot
spatial resolution. We selected the tiles containing the Brooklyn view
and rasterized them into a spatial grid, a matrix of cells organized
into rows and columns, where each cell contains elevation information
(Figure 4).\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Screen-Shot-2017-07-30-at-19.19.42/Screen-Shot-2017-07-30-at-19.19.42}
\caption{{\hypertarget{auto-label-caption-430125}{}
Figure 4. Rasterized LiDAR point cloud data of Brooklyn (left) and a
zoomed-in view of Brooklyn and Manhattan bridges (right)~ ~ ~ ~%
}}
\end{center}
\end{figure}

\section{Methodology}\label{auto-label-section-424261}

We propose a testable research hypothesis that there are observable
differences in the lighting use of users of energy efficient
technologies compared to users of non-efficient technology. The null
hypothesis states that there is no significant difference in total light
use---measured as the on time duration of light---between the users of
energy efficient lighting and users of non-energy efficient lighting.
Rejecting the null hypothesis would indicate a possible effect.~\\

\subsection{Source extraction}\label{source-extraction}

Prior to identifying light sources, we removed daylight images from the
dataset by taking the average luminosity of an entire image and omitting
any images with average light intensity greater than 0.5 (arbitrary)
light units above the mean of the entire night, which resulted in
omitting approximately 1,000 images, or 167 minutes of data from each
night for the final analysis. The resulted in 2,600 images per night
over a time period approximately from 9:16 pm in the evening to 4:30 am
the following morning.\\

Previous UO research relied on a manual method for extracting light
sources \cite{Dobler_2015}. To expand upon this, we used the time
dependence of individual pixels to determine which pixels can be
associated to the same source. The intuition is that a light turning on
or off would cause higher correlation in contiguous pixels, so highly
correlated neighboring pixels were grouped together as a light source.
While factors such as camera drift may increase correlation over time, a
sufficient threshold would filter these pixels out. Additionally,
integration with pixel spectra data will further filter out data not
likely to be a unique light source. As such, not only would this
technique automate the light extraction process, but reduces
preprocessing needed to clean noise.\\

To identify sources, we loaded images as a data cube of light intensity
values for each pixel over all images in time at 1 minute increments.
Each pixel time series was standardized by subtracting the mean from
each intensity value and dividing by the standard deviation. ~The
standardization was done for each night over 7 nights, June 25, 2017
through July 1, 2017, to produce an aggregated data cube of 3,031 images
(7 nights, 433 min a night) x 3072 pixel rows x 4096 pixel
columns.~Future work should also apply a Gaussian filter over these time
series to smooth patterns in the light curves.\\

The aggregated time-series vector of each pixel was multiplied and
averaged by the pixel to the right, \(< p_{ij} \cdot p_{ij+1} >\),~and below,
\(< p_{ij} \cdot p_{i+1j} >\), ~in order to identify correlation of light intensity
in time. Highly correlated pixels were considered components of the same
light source. We calculated the mean light intensity across pixels in
the light source, which we then used to extract the light curve of the
given light source. Figure 5 visualizes the steps to create the boolean
mask that identifies light sources.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/datacube/datacube}
\caption{{\hypertarget{auto-label-caption-133527}{}
Figure 5. Temporal correlation of pixels (Left) A datacube represents
time series of light intensity values for a pixel p at location (x, y)
throughout the images in time (t); (center) correlation coefficients of
neighboring pixel time series' are calculated; (right) highly correlated
pixels are grouped and labeled as a unique light source and their
location is preserved in a 2D boolean mask. ~ ~ ~~%
}}
\end{center}
\end{figure}

Each group of contiguous pixels in this boolean mask were given unique
labels that would be used to index individual light sources. With a
threshold of 0.60 correlation over observations from June 25 to July 1,
this method identified 6,870 possible light sources.\\

This technique performed well and indicates a promising new approach for
future research, though we recommend further improvements such as
including parallelization of the correlation algorithm to more
efficiently handle the large memory footprint of multiple weeks worth of
broadband imaging. Most important would be the introduction of a method
for ground-truthing, such as randomizing pixels to identify a minimum
noise threshold, or employing human-annotated labels.\\

\subsection{Light curve extraction and on/off transition
detection}\label{auto-label-subsection-285132}

The source extraction process preserved pixel location for light sources
in the original raw broadband images so that the light curves could be
extracted over all 29 nights of the observation period.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/single-lightcurve/single-lightcurve}
\caption{{\hypertarget{auto-label-caption-626559}{}
Figure 6. A single source light curve for a single night
\hypertarget{auto-label-caption-733325}{}
This light curve features a prominent ``off'' transition before
midnight. Not all light curves will have such clean transitions.%
}}
\end{center}
\end{figure}

On and off transitions were detected following the adopted Canny edge
detection method~\cite{Canny_1986}~that was used in earlier UO
work~\cite{Dobler_2015}. Noise was suppressed by convolving each light
curve with a Gaussian filter and taking the first derivative of the
result. The extrema of these derivatives indicate on and off
transitions. Following \cite{Dobler_2015}, we conducted robustness tests
to ensure a clear signal. First, the mean and variance of the signal
were tightened by removing values outside \(2\sigma\),
re-calculating~the mean and variance to ``clip'' the distribution; this
was iterated ten times. This adjusted distribution was used to identify
values outside \(10\sigma\)~which indicated possible transitions.
Second, the mean values for the 5 minute period before and after each
edge was calculated and correlated with the change in light intensity,
with a high correlation indicating that the transition exceed the
surrounding noise. We used only the on and off transitions that passed
these robustness tests in the final analysis. It is worth noting that of
the 196 light sources classified, only 7 failed to produce adequate
enough on and off transitions to calculate on time duration.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/onoff-steps/onoff-steps}
\caption{{\hypertarget{auto-label-caption-332635}{}
Figure 7. Key steps to detect on and off transitions
\hypertarget{auto-label-caption-489862}{}
The original light curve (top) is~smoothed with a Gaussian operator,
upon which the derivative is taken (2nd from top), from which extrema
are found in positive directions~to indicate~ ``on'' (3rd from the top),
and negative directions to indicate ``off'' (bottom). Not pictured are
the intermediary steps to amplify the transition and increase the signal
/ noise ratio.
\hypertarget{auto-label-caption-751950}{}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/june27-lightcurves/june27-lightcurves}
\caption{{\hypertarget{auto-label-caption-714736}{}
Figure 8. Light curves from June 27, 2017
\hypertarget{auto-label-caption-602152}{}
The left plot shows light curve intensities (normalized) as sorted by
the last off transition of the night. The right plot shows only light
sources classified by type (n = 196) on the same night, where some steep
drop-offs are visible indicating several sources turned off in around
the same time.%
}}
\end{center}
\end{figure}

We seek to understand light usage behavior, particular the lights on
duration. A quick examination of a particular set of light sources, the
Gowanus Houses, a New York City Housing Authority (NYCHA) complex,
revealed possible patterns in residential light usage over the course of
the 29 night observation period. The Gowanus Houses were visually
identified in the broadband image and sources within that area were
selected (n = 166).\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/All-ons-gowanus/image3-onoff-gow}
\caption{{\hypertarget{auto-label-caption-638617}{}
Figure 9. Nightly on and off transitions per 30 minutes for Gowanus
Houses
\hypertarget{auto-label-caption-700175}{}
The plots above show the patterns of on transitions for nights of the
week (top row) and off transitions (bottom row). The difference in on
distributions and off distributions is apparent on typical weekdays.
Distinct weekday vs weekend activity is visible as is anomalous activity
leading up to and during the Independence Day holiday on Tuesday, July
4.
\hypertarget{auto-label-caption-504417}{}%
}}
\end{center}
\end{figure}

\subsection{Lights on duration}\label{auto-label-subsection-217860}

Our dependent variable is the total lights on duration. This was
calculated for each unique light extracted from the broadband mask using
the time index of the on and off transitions. For a given light source,
for each night \(n \in N\) \selectlanguage{english}(N = 29), for each on or off tag per
night \(t \in T\), (T = the total on and off tags of a particular
night), the total duration for the source is:\\

\(=\sum_n^N\sum_t^Tn_t-n_{t-1},\text{if }n_t=\text{off}\text{ and }n_{t-1}=\text{on}\)\\

Some light curves may have multiple consecutive on transitions or
multiple consecutive off transitions, so a logical framework was
incorporated to preserve the previous state such that the above formula
aggregated the total on duration across such on and off transitions, as
illustrated in Figure 10. The assumption for this work being that
intermediate on and off transitions represented changes in light
intensity, but not a complete on and off transition. Such an example may
be a shade drawn, etc. Such edge cases can be complicated, and warrant
further improvements to the duration method.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/agg-onoff/agg-onoff}
\caption{{\hypertarget{auto-label-caption-470908}{}
Figure 10. Single light curve with multiple consecutive on and off
transitions
\hypertarget{auto-label-caption-234545}{}
Challenging cases appear when a light source has an off transition
followed by another off transition. Such transitions were assumed to be
variations of the same light source and the algorithm was designed to
aggregated all intermediary transitions as a total on time, as indicated
by the red arrows.
\hypertarget{auto-label-caption-544360}{}%
}}
\end{center}
\end{figure}

\subsection{Image registration of broadband and hyperspectral
sources}\label{image-registration-of-broadband-and-hyperspectral-sources}

Image registration is a process of overlaying two or more images of the
same scene taken at different times, from different viewpoints, and/or
by different sensors. The aim is to integrate information from multiple
observations of the same system.~For this project, the imaging devices
were deployed in interior locations. Thus, because the cameras were
perfectly stationary (e.g., there were no vibrations due to the wind as
there were
in~\href{http://www.sciencedirect.com/science/article/pii/S0306437915001167?via\%3Dihub}{Dobler
2015}\selectlanguage{english}) registration between images from the same camera was not
required. We verified that such offsets were \textless{}1 pixel from the
start time to end of our broadband and hyperspectral observations.
However, registration between the broadband and hyperspectral images was
necessary to associate individual sources.\\

In order to identify corresponding sources in both hyperspectral and
broadband imaging, for each labeled pixel in the broadband source mask,
the corresponding hyperspectral pixel was found by co-registering the
broadband and hyperspectral images.~Since the broadband images~have a
higher spatial resolution (3072 x 4096 pixels)~than hyperspectral images
(1600 x 3194 pixels), the pixel centroid locations were rescaled prior
to registration. The scaling factor was calculated by comparing the
distances between seven\textbf{~}scattered sources~in broadband and
hyperspectral images.~\\

~\\

The process of image registration typically includes two images: the
first, called the reference image, is considered the reference to which
the other images, called input images, are compared (Figure 11). The
objective of image registration is to bring the input image into
alignment with the reference image by applying a spatial transformation
to the input image. A spatial transformation maps locations in the
reference image to new locations in the input image. Determining the
spatial transformation parameters, mainly row offset, column offset and
vector rotation to bring the input image into alignment is the key to
the image registration process (Figure 12).~\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/reg-overlay-base/reg-overlay-base}
\caption{{\hypertarget{auto-label-caption-179042}{}
Figure 11. The figure shows the input image transparently overlaid on
the reference image. The displayed image is taken from
\href{http://http://www.johnloomis.org/ece564/notes/tform/image_reg/reg1/image_reg1.html}{Loomis,
John. (2009)}%
}}
\end{center}
\end{figure}

Image registration is a sequential process and it begins with extracting
sources from the input image and calculating quad of sources (4
sub-groups of sources) from the extracted sources by comparing the
distances between sources in the catalog and the ones identified in the
input image. Subsequently, relative angular separations of sources found
in the quad were tested with the constellation of sources in the catalog
and row offsets, column offset and the vector rotation was calculated
using rotation matrix from linear algebra (Figure 12). We used the
resulting parameters to spatially transform the input image in order to
bring it into alignment with the reference image (Figure 13).\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/rotation-offset-eq/rotation-offset-eq}
\caption{{\hypertarget{auto-label-caption-897395}{}
Figure 12. The figure shows rotation and offset matrix used to calculate
row offset, column offset, and vector rotation.~%
}}
\end{center}
\end{figure}

The diagram below represents the graphical illustration of the
process.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/flow1/flow1}
\caption{{\hypertarget{auto-label-caption-364434}{}
Figure 13. The figure shows graphical iIlustration of the image
registration process ~ ~ ~ ~%
}}
\end{center}
\end{figure}

As noted, the hyperspectral camera sweeps through the field of view and
the frame rate of the camera and pan rate of the pan/tilt mechanism are
not constant across~one complete scan, so the pixels in the scans are
not square or uniformly shaped. In order to compensate for this, another
scaling factor was calculated and aspect ratio of the hyperspectral
pixels was corrected accordingly. Subsequently, the column pixel
locations of sources in broadband were divided by this scaling factor in
order to scale them down to the pixel configuration of the
hyperspectral~image (Figure 14). After applying these scaling factors,
the broadband mask was registered onto the hyperspectral~mask by
calculating the row offset, column offset, and the vector rotation.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/bbtohsi/bbtohsi}
\caption{{\hypertarget{auto-label-caption-231482}{}
Figure 14. The figure shows the conversion of broadband mask (3072 x
4096 pixels, 6870 sources) to hyperspectral mask (1600 x 3194 pixels,
1265 sources)%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/pic1/pic1}
\caption{{\hypertarget{auto-label-caption-275756}{}
Figure 15. The registered broadband mask super-positioned on the
hyperspectral mask.
\hypertarget{auto-label-caption-537427}{}
The corresponding sources in both hyperspectral and broadband imaging
for each labeled pixel were identified. The red color indicates sources
not present in broadband but in hyperspectral, whereas the blue color
indicates sources present in broadband but not~hyperspectral. Purple
indicates sources that were present and aligned in both.~%
}}
\end{center}
\end{figure}

Due to the low spatial resolution of the hyperspectral images relative
to the broadband images, image registration distorted and shrank the
light source groups, so we removed all sources smaller than 20 pixels
from the broadband source list. This resulted in 1,265 sources in the
final mask with which to classify lighting types from the hyperspectral
images.\\

\subsection{Source type
identification}\label{source-type-identification}

Source type identification was accomplished using the hyperspectral
scans, in a~4 stage process as described below. The final lighting types
obtained from this process were eventually used for rebound analysis.\\

\textbf{Stage 1 - Stacking hyperspectral scans:} The hyperspectral scans
typically consist of detector noise~that obscures the spectral
information contained in it leading to low signal to noise ratio (Figure
16). In order to reduce the effect of noise and enhance the signal to
noise ratio, multiple hyperspectral scans are stacked together to
compute the mean spectral intensity for each pixel in each channel.
Since the detector noise is random, this process of computing the mean
intensity of multiple scans suppresses the noise. We collected 15
hyperspectral scans on May 26th, 2017 between 10-11PM, which were
stacked together for further analysis.~\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/original-1/original-1}
\caption{{\hypertarget{auto-label-caption-654144}{}
Figure 16. Spectrum of a pixel from raw hyperspectral scan having low
signal to noise ratio%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/stack-spectrum/stack-spectrum}
\caption{{\hypertarget{auto-label-caption-721195}{}
Figure 17. Spectrum of a pixel from stacked hyperspectral scans with
improved signal to noise ratio ~ ~ ~~%
}}
\end{center}
\end{figure}

\textbf{Stage 2 - Dark current suppression :} Dark current is another
type of instrument-based noise that was observed, which needed to be
cleaned to obtain the true spectra from the light sources. Unlike the
detector noise which is evenly distributed in all spectral channels,
dark current is unevenly distributed across the spectral dimension as
illustrated in the Figure 18 below. In order to compensate for this, we
adopted the 3-sigma clipping technique mentioned in \cite{Dobler_2016}.
3-sigma clipping is a process by which the median of each row/column of
the scan across each spectral channel is computed by masking the pixels
with intensities greater than 3 sigma with in channel multiple times
(n=10) and subtracting that median intensity~value from the respective
row/column of each channel. This process ensures that the unevenly
distributed noise gets suppressed and there by true source spectra are
obtained.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/dark-current/dark-current}
\caption{{\hypertarget{auto-label-caption-729867}{}
Figure 18. Mean spectrum of complete hyperspectral scan indicating dark
current in lower wavelength channels%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/clean-current/clean-current}
\caption{{\hypertarget{auto-label-caption-700308}{}
Figure 19. Mean spectrum of complete hyperspectral scan after cleaning
using 3 sigma clipping%
}}
\end{center}
\end{figure}

\textbf{Stage 3 - Extract mean spectrum for each source based on
registered source mask:}~In order to extract the characteristic spectra
for each of the lighting source in the broadband pipeline, we compute
the mean spectrum for each source across pixels comprising the light
source.\\

\textbf{Stage 4 - Correlate source spectra to lab spectra:} The final
clean source spectra obtained from the previous three stages was
correlated with lab spectra of known lighting types. National Oceanic
and Atmospheric Administration (NOAA) \cite{Elvidge_2007},
\selectlanguage{english}\cite{Elvidge_2010} has published a catalog of high resolution lab
spectra between the 100-2500nm spectral range for 43 lighting types
falling into 9 lighting categories i.e high pressure sodium, LED,
fluorescent, low pressure sodium, oil, metal halide, halogen,
incandescent and pressurized gas respectively. From this set of spectral
templates we identified 17 sufficiently distinct lighting types. We
then~correlated our source spectra with these 17 distinct NOAA spectral
templates. Each of the sources was labeled with the type of the lab
spectra template~with which they correlated the highest. It should be
noted that \selectlanguage{english}\cite{Dobler_2016}~also identified other new lighting types
through clustering techniques that were not categorized within the NOAA
catalog. Through this process, we were able to correlate and match 196
sources at a correlation threshold of 0.35. Figure 20 illustrates a few
source spectra and the corresponding lab spectra they were found to be
correlating with. Subsequently, the~bar chart in Figure 21 illustrates
the counts of different lighting types identified among the 196 sources
at 0.35 threshold.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Picture3/Picture3}
\caption{{\hypertarget{auto-label-caption-280243}{}
Figure 20. Source types detected for different lighting sources and the
corresponding lab spectra~ ~ ~ ~ ~ ~ ~~%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Picture1/Picture1}
\caption{{\hypertarget{auto-label-caption-941150}{}
Figure 21. Count of source types detected vs the lighting types%
}}
\end{center}
\end{figure}

\subsection{Point cloud data and image
integration}\label{auto-label-subsection-391040}

A key to estimating the rebound effect is understanding the interaction
between energy efficient lighting technologies and socioeconomic and
demographic (SED) characteristics of the underlying population that uses
these technologies. Previous, survey-based studies have concluded that,
in addition to physical characteristics of buildings, certain household
characteristics affect energy consumption \cite{jones2015socio}. In
particular, household income, age composition, and educational level
have a significant effect on energy consumption. Therefore, one can
expect the size of the rebound effect to vary for different SED groups
and building types.\\

To further explore this relationship, it is necessary to map observed
light sources and their corresponding lighting types to exact geographic
locations in the physical space. This would enable the extraction of
zoning types as well as SED characteristics of the underlying
populations that use the lighting technologies and exhibit on and off
patterns we observe in the scene. The process of obtaining SED
characteristics of the observed cityscape is a multi-step process
involving external datasets and such techniques as rasterization,
photogrammetry, and spatial joins.\\

Photogrammetry is the science of obtaining reliable information about
the properties of surfaces and objects without physical contact with the
objects \cite{schenk2005introduction} or, put simpler, is the science of obtaining
measurements from photographs. The relationship between coordinates in
an image plane (in two dimensions) and coordinates in an object space
(in three dimensions) can be modelled using mathematical models, namely
collinearity equations. In this work, we used collinearity equations to
model transformation from each pixel coordinates in the UO broadband
image to the x, y, and z coordinates in the physical space.~\\

The projection algorithm takes as inputs the image pixel coordinates as
well as seven parameters of the camera: x, y, and z location
coordinates, yaw, pitch, roll, and focus. In order to obtain the seven
camera parameters, we implement a camera optimization algorithm. This
algorithm takes as inputs image pixel coordinates of several unique
points of reference, called ``fiducial'' points, as well as their
corresponding coordinates in the LiDAR dataset, and~outputs the seven
degrees of freedom of the camera (Figure 22). To identify optimal camera
parameters, we chose eight fiducial points, which are well-spaced in the
image, including buildings close as well as far away from the camera. We
then identified the corresponding x, y, z coordinates of these points in
the LiDAR dataset (Figure 23). Both sets of fiducial points are
represented as red dots in Figures 22 and 23.~\\

We chose the initial parameters of the camera by an informed guess
(approximate camera location on the 19th floor of 1 Metro Tech Center
pointing south). These values are then used in the collinearity
equations along with the coordinates of the eight LiDAR fiducial points
to evaluate if the projected values are matching the pixel positions of
the fiducial points in the image. The mean squared error between the
fiducial points in the image and the projected LiDAR coordinates for
each point is minimized by adjusting the seven camera parameters using
gradient descent. This process is then iterated several times (with
different initial guesses) in order to obtain a minimum value for the
error term. The parameters corresponding to the function with the
minimum error value are chosen as camera parameters for the
photogrammetry. To visualize the goodness of fit of the chosen
parameters, we plotted projected fiducial points on the image as yellow
dots (Figure 22).\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/fit-fid-copy1/fit-fid-copy1}
\caption{{\hypertarget{auto-label-caption-454161}{}
Figure 22. Eight fiducial points identified in the image (red dots) and
projected LiDAR coordinates (yellow dots) used to optimize camera
parameters ~ ~ ~~%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Screen-Shot-2017-07-31-at-21.21.1/Screen-Shot-2017-07-31-at-21.21.1}
\caption{{\hypertarget{auto-label-caption-268361}{}
Figure 23. Eight fiducial points in the LiDAR dataset (in red). 1 Metro
Tech Center (in green) is included for perspective. ~ ~ ~ ~%
}}
\end{center}
\end{figure}

Once we optimized the camera parameters, we passed them along with the
image dimensions into the collinearity equations, which converted the
two-dimensional pixel coordinates into three-dimensional coordinates for
a given distance from the camera. This is done using a transformation
matrix containing the seven degrees of freedom of the camera and the
collinearity equations. The photogrammetry algorithm projects x, y and z
coordinates at one foot distance from the camera and checks whether at a
given location, there exists a point in the LiDAR dataset that has
higher elevation than the projected one. Of those points in space, the
algorithm then stores the points closest to the camera. The algorithm
returns three n-dimensional arrays as outputs: x and y coordinates of
projected points as well as the distance in feet between projected
points and the camera (Figure 24). The projected x and y coordinates
(latitude and longitude) then allow us to map every pixel to a
corresponding BBL using MapPLUTO shapefile for Brooklyn.~\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/ldr-proj/ldr-proj}
\caption{{\hypertarget{auto-label-caption-135588}{}
Figure 24. Distance between projected points and the camera. The color
coding goes from red to blue in a continuous cycle. Notable that
buildings that were built after 2010 are not included in the projection
(e.g. the closest building in the bottom right corner of the image). ~
~~
\hypertarget{auto-label-caption-535497}{}%
}}
\end{center}
\end{figure}

\section{Results and implications}\label{auto-label-section-661648}

\subsection{Results}\label{results}

Taken together, the separate work steams produced a dataset of light
sources classified by the lighting technology type and assigned features
of on/off transitions, total on duration, and geospatial location
coordinates that can be further integrated with SED data.~The original
source extraction identified 6,870 sources, further reduced to 1,265
after eliminating very small sources, of which 196 were classified with
known light bulb types--189 with clean enough on and off transitions
with which to calculate total duration of on time. Summary statistics
for these sources are as follows:\\\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
Source Type & Number Classified & Number with clean ``on time'' duration
& \vtop{\hbox{\strut Mean ``on time''}\hbox{\strut per
source~}\hbox{\strut all 29 nights (hrs)}} & \vtop{\hbox{\strut Mean
``on time''}\hbox{\strut per source~}\hbox{\strut per
night~(min)}}\tabularnewline
LED & 96 & 91 & 3.51 & 7.26 min / night\tabularnewline
Fluorescent & 51 & 50 & 3.61 & 7.48 min / night\tabularnewline
High Pressure Sodium & 22 & 21 & 4.17 & 8.62 min / night\tabularnewline
Metal Halide & 20 & 20 & 4.15 & 8.58 min / night\tabularnewline
Low Pressure Sodium & 6 & 6 & 3.83 & 7.92 min / night\tabularnewline
Quartz Halogen & 1 & 1 & 1.15 & 2.38 min / night\tabularnewline
All Types & 196 & 189 & 3.67 & 7.60 min / night\tabularnewline
\bottomrule
\end{longtable}

While only several light sources in the Gowanus Houses region were
classified by light type, there were 165 sources with clean on time
duration and summary statistics as follows:\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
& \vtop{\hbox{\strut Total Sources}\hbox{\strut (not just those
classified)}} & \vtop{\hbox{\strut Number with clean}\hbox{\strut ~``on
time'' duration}} & \vtop{\hbox{\strut Mean ``on time''}\hbox{\strut per
source}\hbox{\strut all 29 nights (hrs)}} & \vtop{\hbox{\strut Mean ``on
time''}\hbox{\strut per source}\hbox{\strut per night
(min)}}\tabularnewline
Gowanus Houses & 166 & 165 & 4.05 & 8.38 min / night\tabularnewline
\bottomrule
\end{longtable}

The sample size across all source types was deemed insufficient to do a
multi-class analysis of variance, but a histogram reveals that all types
show similar distributions of on time duration.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Hist-by-type/Hist-by-type}
\caption{{\hypertarget{auto-label-caption-503415}{}
Figure 25. Histogram of total duration per source for each light bulb
type (bin size=100)
\hypertarget{auto-label-caption-554570}{}
Duration was normalized across all sources for each night to produce
independent observations. While the sample size was small overall
(n=196), we can observe that the 5 types follow similar
distributions.~Quartz halogen was omitted with just 1 classified
source.%
}}
\end{center}
\end{figure}

\subsubsection{Statistical
analysis}\label{auto-label-subsubsection-831050}

The 188 classified light sources with clean durations (omitting the
quartz halogen source) were divided into a test group of ``efficient''
light types and a comparison group of ``non-efficient'' light types.
These assignments were based on a basic comparison of light output in
lumens per watt, a metric for light efficiency known as efficacy
\cite{He_1997}, \cite{thimijan1983photometric}. An arbitrary threshold was set
that bulbs with 40 lumens / watt efficacy or more were efficient
\cite{BIBTEXIDc}.~Metal halide and high pressure sodium lamps may have
relatively high source efficiency at the filament, but losses from
trapped light, covers and lenses, inefficient ballasts and high
operating temperatures mean these lamps typically operate at around 40
lumens / watt~\cite{BIBTEXIDd}\textbf{.~}As such, LED and fluorescent
lights were deemed efficient for the test group (n=141) and the
remaining types deemed non-efficient for the comparison group
(n=47).~The on time duration values were scaled across sources for each
given night and then aggregated across all 29 nights to produce
independent observation samples of total on time duration per source.\\

The null hypothesis states that: there is no significant difference
between total light use --- to be measured as the duration that a given
light is ``on'' --- for residents who use energy efficient lighting
compared to those who do not. Since the sample sizes vary (141 and 47)
and no probability distribution was specified, an Anderson-Darling
k-sample test \cite{anderson1952asymptotic}, \cite{Scholz_1987}, was conducted to
determine if the two samples were drawn from a single population. The
test failed to reject the null that the two distributions were
significantly different (test statistic of 0.7164, with
p\textgreater{}0.05).\\

It~is noted that a larger sample size is necessary to robustly test the
null hypothesis. A larger sample size would open up the opportunity to
use other nonparametric tests, such as the Kolmogorov-Smirnov, and
facilitate parameter estimation to support other tests. A histogram
reveals a similar distribution for these two groups as seen in Figure
27.\\\selectlanguage{english}
\begin{figure}
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Stat-hist/Stat-hist}
\caption{{\hypertarget{auto-label-caption-439663}{}
Figure 26. Histogram of total duration per source for the efficient and
non-efficient lighting groups (bin size = 100)
\hypertarget{auto-label-caption-982690}{}
The two groups demonstrated similar distributions of total on time
duration across all 29 observed nights.
\hypertarget{auto-label-caption-250635}{}%
}}
\end{center}
\end{figure}

\subsection{Implications}\label{auto-label-subsection-267417}

One of the goals of this work is to contribute a body of empirical
observations in an attempt to address some well-known challenges with
measuring the rebound effect. Quasi-experimental approaches are
vulnerable to selection bias, which can exacerbate conditions of
fairness \cite{sorrell2009empirical}. Subjects that are approached and consent to
participate in surveys or monitoring likely do not represent a random
sample of the population and can contribute to an
``interpretation-after-the-fact'' problem \cite{o2013being}~that
equates the results of a surveyed population with a larger population
and can misguide conclusions. Econometric approaches that use price
elasticity of demand, which were discussed earlier, make certain
assumptions about human behavior which may not be a true representation
of the real world.\\

The empirical approach to observing lighting use seeks to reduce the
selection bias or econometric methods by directly observing behavior
remotely. While this provides several advantages, caution should be
taken not to underestimate the level of bias in this approach, either,
particularly if data used in later studies. Even data that are
objectively and remotely collected may contain biases if observations
fail ``to represent different groups in accurate
proportions.''~\cite{barocas2016big}\\

This work seeks to map observed light sources to particular geographic
locations and integrate this new data with existing records, such as SED
information aggregated at the census tract level. Along with addressing
privacy concerns referenced later in this paper, aggregating light
sources to census tracts has several advantages. For example, it allows
for the conditioning of covariates, such as building type and
socioeconomic and demographic data, that can more fairly and accurately
define groups represented in the data. For example, one popular
statistical model, the potential outcome model created by Neyman and
further developed by Rubin \cite{rubin2005causal}, provides a framework with
which to make assumptions of unconfoundedness. This includes methods to
condition the treatment and control groups with covariates in order to
determine a propensity score that can more accurately weight these
covariates and isolate a treatment effect. For example, conditioning the
observed lighting behavior for a specific census tract by weighting the
proportion of income levels in the tract could address some of these
issues. Future work should leverage the techniques developed here to
assign covariates to observed light sources for such a purpose.\\

\section{Limitations}\label{auto-label-section-640486}

Similar limitations as discussed in previous UO research apply to this
project, among them that ``curtains, interior reflections and mixed
lighting type use can complicate the interpretation''
\cite{Dobler_2016}. In addition, certain limitations that are particular
to this capstone project should be kept in mind when interpreting
results. These include:\\

\begin{itemize}
\tightlist
\item
  Only North facing sources are captured. The field-of-view (FOV) of the
  images taken from a vantage-point in Downtown Brooklyn facing South
  exposes mostly the North-facing light sources of buildings. If there
  are any correlated aspects of facing North or downtown, those biases
  would be present in the data.\\
\item
  Far-field census tracts might be under-represented. Another aspect of
  the data collection methodology is the possibility of under
  representation of the census tracts that are present in the far-field~
  and over representation of census tracts in the near field, since more
  observable and distinct data sources may be visible. However, as noted
  earlier, it's also possible that the perspective of far-field light
  sources is more dense and causes them to be over-represented.
  Integrating sources with the built environment and aggregating to the
  census tract level should normalize this somewhat.\\
\item
  Shorter night duration in summer. The northern hemisphere experiences
  summer solstice in June, yielding longer daylight hours. This
  project's observations take place in and near June, so changes in
  lighting use due to longer days will clearly influence this data.
  Hence, the same analysis could lead to very different results in terms
  of rebound characteristics when performed in a different time of the
  year. Clearly describing the data collection methods and dates and
  normalizing for varying nighttime hours will address this.\\
\item
  Missing single-pixel light sources. The light sources were identified
  and extracted using an adjacent pixel correlation algorithm, so light
  sources smaller than the resolution of one pixel within the image
  would not get captured. While the broadband images have high
  resolution, this may become non-trivial with respect to the far-field
  sources, introducing another~ bias based on distance from the
  camera.\\
\end{itemize}

\subsection{Ethics and privacy
concerns}\label{auto-label-subsection-488353}

One of the broader objectives of the UO capstone project is to
contribute to a better understanding of the relationship between humans
and technology. The project aims to investigate whether the use of
energy efficient lighting produces a behavioral response which offsets
the beneficial effects of using that technology by collecting and
processing of thousands of images of the urban landscape in order to
identify light sources.\\

Since the camera view covers a large swath of the city, the project
cannot specify a well-defined group of participants or obtain consent
from all persons whose windows could potentially be captured in a UO
image; however, it is important to note that no Personally Identifiable
Information (PII) is obtained and the light exterior to buildings is in
the public domain, which does not require consent \cite{BIBTEXIDb}.~\\

After careful consideration, we concluded that identities cannot be
readily ascertained from the information collected by the UO.
Furthermore, individual identities cannot be ascertained after combining
observational data with publicly available socioeconomic and demographic
data because U.S. Census data are already de-identified and aggregated
to a census tract level.~\\

To better protect the privacy and restrict the data from public access,
the raw data are restricted (permission-based) within the CUSP data
facility.\\[2\baselineskip]

\section{Conclusion and future
research}\label{auto-label-section-164378}

This work put forth a novel approach to quantifying the rebound effect
and contributed in three general ways: with urban image detection, urban
informatics more broadly, and with respect to research into the rebound
effect.\\

\subsection{Urban image detection}\label{urban-image-detection}

Perhaps the most important contribution is establishment of an empirical
constraint on the amplitude of the rebound effect upon which to base
future scientific inquiry. Additionally, we developed an analytical
pipeline for observing and analyzing light use. The effectiveness of
previous techniques \cite{Dobler_2015}, \cite{Dobler_2016}~was further
validated and enhanced, and critically, the two previously separate work
streams, broadband light curve extraction and hyperspectral lighting
type classification, were brought together for the first time and
integrated with the 3-D LiDAR data projection to produce a completely
novel methodology for analyzing light use.\\

The work was technically challenging, particularly when seeking such a
heightened level of precision (exact light use for individual light
sources) while dealing with a low signal / noise ratio; however, the
benefit was a demonstrative success in quantifying light usage for
specific light types. Additional work to improve the methods used as
well as collect more data will surely increase the robustness of
statistical analyses. Furthermore, the ability to integrate light
sources with SED data vis-a-vis the 3-D projection technique opens an
entirely new avenue of inquiry.\\

\subsection{Rebound effect}\label{rebound-effect}

The rebound effect exemplifies some of the most challenging aspects of
applied science in that it seeks practical insights that can potentially
influence policy, business, and human behavior, yet must maintain the
integrity of scientific pursuit. This is particularly evident when
considering the issues of bias examined earlier. Bringing a new
empirical method to bear on the complex engineering, social, economic
dynamics of rebound effect is an important aspect of this work. For
example, characterizing sample populations for SED attributes, such as
income level, is crucial in developing robust statistical assumptions
and avoiding issues of bias our confoundedness, yet most research
utilizing such geo-specific data on behavior must rely upon sources like
the American Community Survey that produces data aggregated at the
census tract level and usually only every five years. Compared to this,
gaining insight into a specific light source as observed in arbitrarily
precise time units is a significant step forward.\\

This work also uses a methodology that should be easily replicated and
generalized for other geographical locations and, certainly most
tangibly, contributed a body of raw observed data that can be measured
in Terabytes and will hopefully encourage wider adoption of these
techniques by researchers investigating the rebound effect.\\

\subsection{\texorpdfstring{\\
Urban informatics\\
}{ Urban informatics }}\label{urban-informatics}

The pipeline described also reinforces the interdisciplinary nature and
creativity of the field of urban informatics. Previous UO research
leveraged astronomical techniques in a novel
way~\cite{Dobler_2015},~\cite{Dobler_2016}~as well as edge detection
techniques used for computer vision~\cite{Canny_1986}, which were key
components in our methodology. We also introduced photogrammetry as a
tool in the pipeline useful for 3-D projection. This research also
demonstrated how urban informatics can apply empirical methods to ever
broadening lines of inquiry, such as socio-economic issues. It speaks to
the power of urban instrumentation as a means to better understand
latent characteristics of the urban ecosystem, perhaps furthering the
claim that urban science holds a unique place in the scientific
realm~\cite{Bettencourt_2010}.\\

\section{Author contributions}\label{auto-label-section-755934}

Acknowledgements: Professor Gregory Dobler provided instrumental
guidance to the team and was actively involved in every step of the
process. The team would also like to acknowledge the wider UO team, in
particular Mohit Sharma and Andreas Karpf.\\

Daynan Crull: contributed much of the literature review on the rebound
effect as well as conducted the data processing and analysis within the
``broadband track'' of the analytical pipeline, including source
identification and extraction, light curve extraction, on/off edge
detection and (forthcoming) total light usage duration measurement.\\

Akshay Penmatcha:~contributed to the source type identification tasks in
the pipeline. Worked on the Hyperspectral imaging data to identify the
lighting source type. Used vectorized computations and correlation
techniques in order to accomplish the tasks.\\

Anastasia Shegay: worked on integrating image data with point cloud
data, which included applying photogrammetry techniques to convert
rasterized 3-dimensional x, y and z data to a 2-dimensional image
plane.~\\

Priyanshi Singh: Contributed in analyzing broadband images by performing
image registration, finding pixels deviations, and conversion of
broadband mask to HSI mask which makes use of registration techniques by
using Linear Algebra and rotation matrix computations.

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