# Favelas 4D: Scalable methods for morphology analysis of informal settlements
using terrestrial laser scanning data

Arianna Salazar Miranda Correspondence<EMAIL_ADDRESS>Senseable City Lab,
Department of Urban Studies and Planning, Massachusetts Institute of
Technology  Guangyu Du  Senseable City Lab, Department of Urban Studies and
Planning, Massachusetts Institute of Technology  Claire Gorman  Senseable City
Lab, Department of Urban Studies and Planning, Massachusetts Institute of
Technology  Fabio Duarte  Senseable City Lab, Department of Urban Studies and
Planning, Massachusetts Institute of Technology  Pontíficia Universidade
Católica do Paraná, Curitiba, Brazil  Washington Fajardo  Senseable City Lab,
Department of Urban Studies and Planning, Massachusetts Institute of
Technology  Carlo Ratti  Senseable City Lab, Department of Urban Studies and
Planning, Massachusetts Institute of Technology

###### Abstract

Keywords: morphology, urban planning, informal settlements, LiDAR, laser
scanning

##  Introduction

Of the roughly four billion people who live in cities
worldwide,111https://data.worldbank.org/indicator/SP.URB.TOTL nearly one
billion live in informal settlements as of
2020.222https://www.worldbank.org/en/topic/urbandevelopment/overview. Informal
settlements are aggregations of homes and businesses constructed by their
residents, in an initially unplanned form of urbanization. Their complex
morphology is the outcome of spontaneous and competitive building without
official land tenure, which results in dense and multilayered structures built
up around labyrinthine street networks. These environments tend to be
insalubrious and unsafe compared to the formally developed parts of the city:
their exclusion from urban infrastructure and official management exposes them
to a variety of public health and security challenges, and their typical
location on undesirable land can result in several forms of environmental
precarity. As the growing urban population continues to outpace the
construction of new affordable housing by official channels, these settlements
are expanding around the
world.333https://unstats.un.org/sdgs/report/2019/goal-11/

Morphology is a productive angle to study informal settlements because it
allows for a systematic understanding of their development patterns,
character, and how they cope with change (Conzen and Conzen, 2004; Moudon,
1989; Siksna, 1997). For informal settlements in particular, measuring
morphology is an entry point to broader inquiry about the tendencies of
unfettered urban development and the challenges that attend it, including lack
of accessibility and cadastral mapping, crowding, environmental health, and
safety. Moreover, characterizing the morphology of informal settlements can
inform effective urban design interventions and policies to alleviate the
negative impacts of living in informal settlements.

The irregular and complex morphology typical of informal settlements can act
as a barrier to traditional forms of mapping and morphological analysis.
Remote sensing data is available and useful for differentiating informal
settlements from other land cover (Prabhu, Parvathavarthini and Raja, 2020;
Schmitt et al., 2018), but its resolution is insufficient for detailed study
within individual settlements. Aerial data collection with photography or
radar, though more granular than remote sensing data (Gevaert et al., 2017;
Sliuzas et al., 2017), tends to suffer from occlusions and fails to capture
the vast heterogeneity in materials, building types, and design that are
typical of informal settlements. Finally, ethnographic or observational data
gathered inside the settlements benefits from the richness and nuance of
community engagement but is too labor intensive to yield more than a partial
or piece-wise analysis in most cases (Cavalcanti, 2017; Mukeku, 2018). These
challenges have left informal settlements understudied in proportion to their
relevance to urban planning research.

This paper addresses these shortcomings by introducing a scalable method of
quantitative morphological analysis for informal settlements using data
obtained from three-dimensional LiDAR (Light Detection and Ranging) laser
scanning. LiDAR scans provide data on the environment in the form of unordered
point clouds. The core of our methodology is a procedure to extract geometric
properties of streets and facades from unordered point clouds to analyze their
morphology. The first part of the paper focuses on measuring the morphology
of“street scenes,” a spatial unit consisting of a street segment and all its
facades. We propose five spatial metrics, which we show how to compute using
the LiDAR data: _street width; street elevation; facade heterogeneity_ , a
measure of inconsistency in facade height; _facade density_ , a measure of
crowding among buildings; and _street canyon_ , a metric that captures the
width and depth of the facade relative to the street. We use these metrics to
furnish a _global_ analysis comparing different street scenes to one another.
In the second part of the paper, we extend our analysis to a higher resolution
by constructing _local_ measurements of the same metrics, at half-meter
increments along the primary axis of each street scene, allowing us to trace
the morphological variation within each street scene. Finally, we map our
local results directly into plans of the favela, showing the nuances of
morphological variation in context. These complementary resolutions provide
detailed insights on the morphology of informal settlements, which could
inform policy interventions designed to improve infrastructure or reduce
environmental risk. Furthermore, the perspective of our terrestrial LiDAR data
privileges the view from the street, enabling our analysis to capture the
built environment from an embedded vantage point.

We implement our methodology using LiDAR data collected at the street level in
Rocinha, the largest favela (informal settlement) in Rio de Janeiro, Brazil.
The point cloud data we use consists of two sample LiDAR scans collected in
the year 2020 from separate areas of Rocinha, which capture a range of spatial
conditions. The first scan corresponds to a formalized public plaza, which we
refer to as the “Courtyard Scan” and the second scan corresponds to an
informal residential area that we refer to as the “Hillside Scan.” We use the
morphological variety across these two scans to demonstrate the efficacy of
our morphological metrics for analyzing the spectrum of development forms
present in the favela.

Our analysis demonstrates how terrestrial LiDAR can be used to create scalable
quantitative measures of morphology to study the spatial organization of
informal settlements. In particular, we show that our measurements constructed
using LiDAR data reveal meaningful differences and commonalities both in terms
of the global morphology of the favela and in terms of the local variations
within street scenes. As an expansive and consolidated favela, Rocinha makes a
favorable object of study because it is sufficiently well mapped to offer
ground truth for our analysis.444The community of Rocinha first emerged in
1927 and by 1933 comprised a group of 67 shacks. Today it is recognized as an
administrative region of Rio de Janeiro (as of 1993) and may house as many as
150,000 people (Fabricius, 2008). To validate that our measurements are indeed
capturing meaningful morphological characteristics, we evaluate them according
to the ground truth established by Google Earth and local maps created by the
Public Works Company of the State of Rio de Janeiro (Empresa de Obras Publicas
do Estado do Rio de Janeiro).

This paper complements current methods of quantitative morphological analysis
for informal settlements using remote sensing data. Remote sensing-based
studies have refined methods of identifying informal settlements and modeling
their growth. Wurm et al. (2019) demonstrate the utility of satellite imagery
for slum identification, showing that favelas in Rio de Janeiro delineated
using visual assessment of satellite images matched the official boundaries
listed in the Brazilian Census with an accuracy of almost 94%. Complementary
work uses machine learning models trained on satellite imagery to predict the
presence and expansion of slums (Duque, Patino and Betancourt, 2017; Wurm et
al., 2019; Stark et al., 2020). Morphologically, these studies focus on
identifying the overall shape and size of informal settlement footprints by
differentiating their texture from those of other types of land cover as it
appears in 2D satellite image data. Our study extends this literature by
differentiating between the distinct urban patterns within informal
settlements, quantitatively analyzing the internal variations in urban texture
across the favela beyond its overall morphological differences from other
forms of development.

A second related category of research focuses on the definition and
classification of informal settlement topologies using street network maps.
This literature aims to analyze the morphology of informal settlements either
in contrast to that of the formal city or as a globally consistent urban
typology of its own (Sobreira, 2007). Analytical methods that produce wide-
ranging taxonomies of urban plans (Louf and Barthelemy, 2014; Boeing, 2021;
Taubenböck, Kraff and Wurm, 2018) are replicated in studies that focus on
classifying the street networks of informal settlements (Zappulla, Suau and
Fikfak, 2014; Loureiro, de Medeiros and Guerreiro, 2017) or comparing them to
other topological conditions such as those of the medieval Portuguese towns
that could be considered their ancestors (Loureiro, de Medeiros and Guerreiro,
2019). Work on this topic addresses morphological trends and characteristics
within informal settlements, considering more detail and internal variation
than remote sensing-based studies do, while still reducing the built
environment to its plan. In slums and informal settlements in general, but
especially in favelas, vertical expansion is a key architectural dynamic:
families build new floors on top of existing structures as relatives move in,
or occasionally sell roof space to another tenant to build upon as if it were
empty land. Topological studies that only address street networks deemphasize
this key dynamic of informal settlement construction. Our analysis addresses
factors related to topology, such as street width, while approaching the built
environment with attention to 3D factors that topological analysis typically
does not consider, such facade height and street canyon.

This study also contributes to a third category of research that focuses on
studying informal construction at the building scale. This literature has
focused mostly on approaches derived from concepts like pattern language
(Alexander et al., 1977) and shape grammar (Knight and Stiny, 2015), which
have been applied to analyze patterns of construction in informal settlements
(Kamalipour and Dovey, 2020; Dovey et al., 2020), occasionally for the
purposes of growth modeling or parametric design (Dovey, 2013; Bardhan et al.,
2018; Chokyu and Dias, 2018; Verniz and Duarte, 2020). While these lines of
inquiry address 3D morphology in great detail as it relates to the
establishment and structural evolution of individual buildings, they are
difficult to scale to entire settlements. Our study similarly focuses on 3D
morphology and extends this approach by considering building-scale attributes
and contextualizing them within their larger volumetric and topographical
environment through the combination of the local and global analysis.

Finally, our work also contributes to a limited selection of LiDAR-based
analyses that have been conducted in favelas at small scales. These approaches
rely on manual data processing, making them unsuitable for analyzing large
areas. Research in this area has primarily focused on delineating roof
boundaries for Digital Elevation Model (DEM) development and counting the
number of units in buildings for cadastral surveying (Temba et al., 2015;
Ribeiro et al., 2019). This paper presents a method to analyze the morphology
of informal settlements at scale, which allows us to move beyond case study
evidence when sufficient LiDAR data is available.

The paper is organized as follows. Section 2 discusses the LiDAR data. Section
3 describes how the morphological measurements taken in each LiDAR sample are
calculated. Section 4 details the global and the local morphometric analysis,
summarizes the results in morphological maps of the favela, and validates the
measurements they are based on. Section 5 discusses the significance of these
results in relation to the real urban conditions of Rocinha. Finally, in
section 6 we discuss the conclusions that can be drawn from our analysis,
their contribution to the goal of understanding informal settlements
worldwide, and the opportunities they open for future study.

##  Data Description

To analyze the morphology of street scenes we use data obtained from LiDAR: a
3D scanning technology that captures laser range measurements by measuring the
level to which a laser pulse emitted from the tripod-mounted scanner reflects
its beam. The resulting data are a set of individual distances stored as
points with 3D coordinates registered spatially using the GPS position of the
sensor, also known as a point cloud.555Each point also stores information
including its normal (the vector perpendicular to it), an intensity value that
measures the strength of the reflected laser beam, and an RGB color derived
from a separate process of photogrammetry. Our data was gathered by a company
that offers laser scanning services in Brazil.666For more details on the
company, see https://www.brtech3d.com.br/ [ scanned at a rate of 750,000
points per second, from a total of 22 survey points]

Unlike many point clouds used for urban research, which rely on aerial LiDAR
scanning for tasks like building delineation (Temba et al., 2015), the LiDAR
data used in this study was taken by a team of technicians working
terrestrially to capture the streets of Rocinha. The main advantage of using
terrestrial over aerial LiDAR data in this context is coverage. Given the
steep and narrow roads in the favela, it is challenging to collect clear and
comprehensive data using mobile LiDAR scanning via transportation modes such
as cars or buses. For instance, our scanned areas include a park and a narrow
exterior staircase, two areas that only foot traffic could penetrate. Access
to pedestrian-only areas of the favela is fundamental to our ultimate
objective of comprehensively understanding its built environment: currently,
only 23% of Rocinha’s total road distance is included in Google Street View,
because only that fraction of the settlement could be smoothly captured from a
car. Terrestrial LiDAR scanning allows us to measure the morphology of areas
beyond the small and disproportionately formalized portion of Rocinha
previously available for study. An important consequence of the terrestrial
scanning approach on our data is that the point cloud includes relatively
clear information for the ground and building facades, but it does not capture
roof data for buildings reliably. For this reason, we focus our analysis on
streets and facades rather than building footprints.

The scanning sample for this project was collected in two separate parts of
Rocinha: a Courtyard and a Hillside that cover about 480 square meters of
ground in total. Figure 1 shows the locations of both scans. The Courtyard
Scan is located below a main road, and the Hillside Scan is near it, further
up the hillside. Both scans are on the upper and outer fringes of Rocinha,
representing the range of conditions possible within Rocinha’s informal
development. The urban environment of the Courtyard is more formalized than is
typical of Rocinha, but it is useful as an analytical starting point and a
comparison to the Hillside scan. It represents a public plaza called Praca da
Vila Cruzada, formalized and renovated to be the site of a tourist center and
handicraft fair due to its panoramic views of the favela. In contrast to the
Courtyard Scan, the Hillside Scan captures the compact, layered morphology
typical of Rocinha’s piecewise development: it follows a staircase that
strings together a conglomeration of small buildings as it runs up a steep
incline and intersects with a flat cross-street. This scan incorporates a
range of built conditions common to Rocinha, including the steep public
street, small facades, and covered areas. In this scan, the boundaries between
public and private space are unclear. While the Courtyard is a distinctly
public space, the Hillside Scan includes street scenes that represent
residential buildings that open onto the enclosed staircase connecting them
together.

Figure 1: Map showing the scan locations.

Prior to processing, the point cloud included a total of 116,772,368 points
(Courtyard: 45,342,425 points, Hillside: 71,429,943 points), scanned from 22
different survey locations (Courtyard: 5 survey points, Hillside: 17 survey
points). For the purposes of this study, we downsample the data to 50 mm
resolution, reducing the point cloud to 2,071,769 points in total (Courtyard:
607,219 points, 99.15% reduction; Hillside: 1,464,550 points, 96.8%
reduction). This lower resolution allows us to retain all the information
relevant to the scale of the street while limiting the size of our data to the
minimum required for the analysis.

To summarize the morphological properties of the favela, we divide it into a
series of spatial units that we call “street scenes.” Each street scene
includes a street segment and the building facades that directly face it. To
extract street scenes from LiDAR point cloud data, we follow two main steps:
(1) extracting the street segments and building facades (horizontal and
vertical planes, respectively) from the point cloud, and (2) grouping street
segments and their adjacent building facades together. In the subsections that
follow, we explain these steps in more detail.

###  Extracting Planes from the Point Cloud

To extract horizontal and vertical planes from the LiDAR point cloud we use a
two-part process of shape detection and plane regression. Both steps use
versions of the Random Sample Consensus (RANSAC) algorithm, which is well
suited to fitting models when there is a high proportion of outliers in the
data (Fischler and Bolles, 1981). In our case, these outliers come from trees,
humans, and urban furniture that need to be filtered out of the point cloud
before its built environment can be analyzed. Figure 2 shows a graphical
representation of the two RANSAC steps, with shape detection (step 1) on the
left, and plane regression (step 2) on the right.

Figure 2: Graphic explanation of the plane extraction from point cloud shown
as a section view of vertical plane. Left panel shows the RANSAC shape
detection step. The right panel shows the RANSAC plane regression step.

We first use the RANSAC shape detection method introduced by Schnabel, Wahl
and Klein (2007) to extract shape models from unorganized point
clouds.777Schnabel, Wahl and Klein (2007) adaptation of the RANSAC algorithm
for shape detection uses a recursive process to find the best plane model. We
set the distance $\epsilon$ to 0.005, and we allow the maximum deviation angle
$\alpha$ to range between 12.5 and 35, to allow more variance on the size of
the output planes. We set the minimum support points $\tau$ to 750 to include
small planes from buildings but exclude other objects, such as urban
furniture. See appendix for a detailed explanation of the parameters used. The
algorithm takes a point cloud as input (as well as a set of specific
parameters—see Table A1 in the appendix) and outputs fragments of the point
cloud that roughly fit the shape of a plane within a specified margin (Figure
2, left panel). Using this algorithm, we obtained 111 point cloud fragments in
total: 52 fragments for the Courtyard Scan and 59 fragments for the Hillside
Scan. These fragments vary widely in size, comprising anywhere from 807 to
136,599 points.

The second part of our plane extraction process uses RANSAC regression to
establish a geometric plane model for each point cloud fragment detected in
the first step. The objective of this step is to find the plane model that
best fits each point cloud fragment (Figure 2, right panel), which is
important because the coefficients of that plane model enable us to project
the 3D point cloud fragment into 2D. Once we have projected the 3D points from
a point cloud fragment into 2D using its regression plane, we can find the
convex hull—a bounding shape—for the plane, which allows us to measure the
geometric properties of the facade or street segment it represents.

###  Constructing Street Scenes from Planes

To aggregate the extracted planes into street scenes, we group each horizontal
plane (street) with the nearest vertical planes (facades) above it, using a
nearest-neighbors approach.888We only consider facades located at the same or
higher elevation as the street in order to avoid analyzing roofs, which are
also horizontal planes but whose nearest facades would be below them. This
step relies on categorizing each plane as either horizontal or vertical using
their normal direction.999If the dot product of the regression plane’s normal
vector with the z vector is greater than 0.95, the plane is horizontal. If it
is less than 0.05, the plane is horizontal. Our street scenes are intended to
be semi-continuous and overlapping: the same facade may appear in multiple
street scenes when separate public areas exist on either side of the same
wall. Also, they vary substantially in size, since a horizontal plane of any
scale may be considered a street as long as it forms the ground plane
corresponding to the nearest facades. In total, we identified 94 planes in the
point cloud and organized them into 10 street scenes: 2 from the Courtyard
Scan and 8 from the Hillside Scan.101010Planes having a point density of less
than 150 points per meter are considered noise and are not considered in the
analysis. We extract 111 planes in total, classify 17 of them as noise, and
proceed with the remaining 94. Each street scene includes between 4 and 11
planes.

##  Morphology Metric Calculation

This section describes our method for constructing morphological metrics for
each street scene in our sample, at both global and local levels. The two
scales of analysis are shown in Figure 3, which outlines the level of point
cloud aggregation for each one. We compute a set of five metrics at each
scale. These include street width and street elevation, which aim to describe
the size and configuration of street scenes; and facade heterogeneity, facade
density, and street canyon, which aim to describe the facade distribution and
its relationship to the street. Our focus on these particular metrics draws on
precedents in informal settlement studies that seek to identify and
characterize unplanned areas using sets of quantitative measurements about the
built environment (Kohli et al., 2012; Kuffer, Barros and Sliuzas, 2014). We
also draw from a subset of LiDAR literature that uses point clouds to extract
key metrics related to urban morphology (Bonczak and Kontokosta, 2019; Tooke,
Coops and Webster, 2014).

Figure 3: Figure shows a selected street scene depicting the components of the
global and the local analysis. For global analysis, our calculations are based
on the convex hulls of the planes in the street scene (left panel). For our
local analysis, we divide each street scene into half-meter-wide bands (right
panel). The two diagrams on the bottom of the figure represent the different
resolutions achieved by this dual approach.

###  Global Metric Calculation

To calculate the global metrics, we take measurements for each street scene
using the convex hulls of the planes that compose it (see Figure 3, left
panel). In the following paragraphs we describe in detail how each metric is
calculated.

_Street Width_ is an important and applicable morphological metric, governing
which and how many forms of transit can access a given location. We calculate
it using a series of steps. To calculate overall street width for a street
scene, we identify pairs of facades in the street scene that are effectively
parallel (within 15 degrees) to one another. Then, we select the subset of
these pairs that represent facades on opposite sides of the street from one
another. To get the street width, we measure the perpendicular distance
between these parallel facades that straddle the street.111111 We cannot
simply take the dimension of the street’s convex hull in the X direction
(“xdist”) because the inclusive nature of the convex hull inflates this value
dramatically, especially when a street segment is curved. If there are
multiple pairs of facades that satisfy these calculations, we use the average
of the distances between them. This metric relates to infrastructure and can
be connected to connective bottlenecks in the favela that cause safety issues
when essential and emergency services cannot access certain areas(Brelsford et
al., 2018).

_Street Elevation_ is intended to capture the overall topography of the point
cloud and locate each street scene within it. It is calculated as the Z value
of the centroid (middle point) of the horizontal plane identified as the
street.121212Based on the plane segmentation algorithm we use, this point
exists in both the original point cloud fragment for the street and its
estimated regression plane. This metric has implications for safety and
accessibility. Favelas tend to occupy steep, unstable land unsuitable for
formal development, making them vulnerable to landslides and structural
compromises associated with their unforgiving topography (Sandholz, Lange and
Nehren, 2018). The constant elevation changes in these settlements pose a
major obstacle to the roughly 100,000 elderly people living in Rio’s favelas
as of the 2010 census, who have trouble navigating uneven sidewalks and
staircases, and who will be a larger segment of Rio’s population than children
under 15 by 2030 (Guitarães and Taylor, 2016). Identifying sharp elevation
changes between street scenes is a step towards efficiently improving
connectivity and safety in the favela.

_Facade Heterogeneity_ in a street scene is a representation of the uniformity
or disorder among building heights in the street. It is calculated using the
standard deviation of vertical plane heights in each street scene. This metric
is useful in various contexts. It can be applied to structural stability
analysis, where risk can be correlated to building height (Shan, Petrone and
Kunnath, 2019); and it can also be connected to population density (Jedwab,
Loungani and Yezer, 2021) and microclimate in an area Kakon et al. (2010).
Moreover, this metric can also be related to the degree of informality in an
area of the built environment: low facade variance indicates the standardized
construction of large formal interventions like public housing projects, while
high facade variance is associated with buildings in various stages of
informal vertical expansion (Martins and Farias, 2019).

_Facade Density_ is calculated as the number of facades in a street scene
divided by the surface area of the street they surround. Facade density is a
proxy for crowding in the favela and is an important indicator in this
analysis because it distinguishes between street scenes with a small number of
large buildings from street scenes with many small ones.

Finally, we calculate _Street Canyon_ , which is the ratio of the maximum
facade height in the scene to the width of the street. This spatial
relationship has implications for the fresh air and sunlight that can reach
certain areas, reflecting the level to which a given street scene is enclosed.
This metric signals other issues at work in the built environment of a favela,
since airflow and ventilation are highly related to urban morphology and have
significant effects on pollution exposure (Jana, Sarkar and Bardhan, 2020).
This issue is exacerbated in informal settlements, which tend to have higher
levels of heat exposure than formalized urban areas (Scott et al., 2017; Wang
et al., 2019).

###  Local Metric Calculation

We now turn to discuss the adaptation of each calculation to collect the same
measurements for the half-meter-wide bands of points that constitute our local
analysis. This process requires slight modifications to some of the metric
calculations. To calculate the local metrics at a higher resolution, we
subdivide the point cloud into smaller segments. In particular, we subdivide
the point cloud segments into half-meter-wide bands along the centerline
(width) of each street scene, such that each band spans the street and
includes segments of the facades on either side (see Figure 3, right panel).
Finally, we perform the same two-step process of plane extraction (RANSAC
shape detection and plane regression) for each band in order to delineate
planes that represent the half-meter-wide street and facade segments within
each band. We then calculate the morphological metrics for each band.

Street width and street elevation are calculated exactly the same way for
these bands as they are for entire street scenes. Instead of facade
heterogeneity and facade density, which cannot be calculated at a scale
smaller than a single facade, we construct a measure of facade height within
each band by finding the height of the tallest facade segment on each side of
the street and recording their average. If there are no facades on one side of
the street, we simply record the facade height of the other side. We then use
this facade height value to calculate our street canyon metric, the same way
as for the global analysis. This results in a set of four metrics (street
width, street elevation, facade height, and street canyon) that can be
measured at half-meter intervals along every street scene to indicate
morphological changes within it.

##  Morphometric Analysis

In this section, we use the metrics computed at the global scale to compare
different street scenes of the favela to one another, and the ones computed at
the local scale to unpack the variation of morphometric metrics within a
single street scene (at half-meter resolution).

###  Global Analysis

Figure 4 shows the 3D shape of each street scene and its values for the five
morphological metrics (morphological profile) below it. The street scenes are
numbered continuously, such that street scenes labeled with adjacent numbers
are located next to each other in the favela. To ease the interpretation of
the morphological metrics, we normalize each one relative to its maximum
value. The figure shows the wide range of street types that can be found in
the favela. For instance, more compact street scenes (street scenes 4, 6, and
9) tend to have the lowest street canyon values. In contrast, elongated street
scenes characterized by tall facades and a narrow street (street scenes 3, 7,
and 8) exhibit among the highest street canyon values. It is also apparent in
this figure how different morphological dimensions vary together across street
scenes: for instance, street scenes 1 and 2 have the highest values for street
width, and facade homogeneity—so they might be considered thoroughfare street
scenes. This pattern contrasts with the profiles of street scenes 8 and 9,
which show some of the lowest values for those metrics and could be described
as secluded, or low-traffic street scenes. A direct consideration of the
similarities and differences among street scenes according to this global
analysis can be achieved by visualizing each street scene as a point in 5
dimensions, where each dimension is a morphological metric (see Figure A1 in
the appendix).

Figure 4: Figure shows the global analysis results for each street scene.

Beyond the typological similarities captured by the 5 morphology metrics,
street scenes can also be analyzed in terms of their spatial similarities. As
we will show, there are also strong similarities across neighboring street
scenes that distinguish proximate streets from those located farther away.
Street scenes 1 and 2 are located in the Courtyard Scan, so they share
qualities of scale and spaciousness associated with the large, formalized
public plaza they represent. Meanwhile, street scenes 3 through 10 are located
in order of descending elevation in the Hillside Scan, and they exhibit the
compact and variable nature of their more informal environment. The fact that
our morphology metrics capture these differences is reassuring as it enables
us to trace morphological trends in the favela that are spatially continuous
as well as those that are not.

###  Local Analysis

Our global analysis shows how morphological metrics vary across the entire
scanning area, indicating trends and relationships across all of the street
scenes. In our local analysis, we go one step further to show how each
morphological metric varies within individual street scenes.

Figure 5 shows the variation in each of the 5 morphological metrics within
each street scene. Each bar graph indicates the values for a given metric at
half-meter intervals along the primary axis of the street scene. Each row of
plots shows the metrics for a given street scene, and each column (and color)
of plots represents a different metric, in the following order: street width
(red), street elevation (purple), facade height (pink), street canyon (blue).
Within each plot, the X axis represents the actual distance in meters from one
end of the street to the other, such that the bars along it correspond to the
half-meter-wide bins of points into which we divide the street.131313Some
plots do not show values for every bin. Several factors can produce these
gaps: the Y value for a given bin may be equal to the minimum for the street
scene, or there may not be facades present for the bin (calculating street
width requires two facades on opposite sides of the street, and calculating
facade height requires at least one facade adjacent to the street; street
canyon requires both a street width and a facade height for a given bin). The
Y axis of the plot represents the morphological metric value, which we
calculate for each half-meter-wide bin.

The figure sheds light on the morphological fluctuations within street scenes:
for instance, the plots for street scenes 1 and 3 indicate sloped terrain as
elevation steadily declines along the street. Similarly, a comparison of the
facade height between street scenes 3 and 6 depicts nuanced changes in the
distribution of tall and short buildings along the street. In street scene 3,
the pink bars with similar high facade height values represent one building or
pair of buildings across the street from one another, and the subsequent
segments of smaller bars indicate shorter buildings in the same sense.

The local results also reveal key insights about the spatial configuration of
street scenes across the Courtyard and Hillside Scans. Within the Courtyard
Scan, for example, the plots show that the street width is very consistent
across street scenes 1 and 2. However, despite having similar street width,
the street canyon plots show that their street configuration looks very
different. In particular, the street canyon values of street scene 2 are much
lower than those of street scene 1, suggesting that its a much wider and more
open street environment.

The local results for the Hillside Scan indicate its morphological distinction
from the Courtyard Scan. The local results for the Hillside street scenes stay
very constant within the street scenes. For example, there is little
fluctuation in the street width of street scene 10, or the facade height in
street scenes 7 and 9. This might be attributed to the fact that street scenes
in this scan tend to be very short (scene 9 is only 3.5 meters long), which
leaves very little space for the morphological metrics to vary significantly.

In summary, the global analysis enables an overall comparison that captures
the less-variable profiles of smaller street scenes, while the local analysis
allows for an interpretation of the nuanced morphological changes typical of
larger and more varied street scenes that may be masked by the global
analysis.

Figure 5: Figure shows the local analysis results for each street scene.

###  Mapping Morphology

Our local analysis traces morphological variations in the built environment at
a high spatial resolution, making it easily translatable from the sphere of
abstract analysis to that of concrete urban mapping. To accomplish this
transition, we produce maps of each scanning area and superimpose our local
analysis measurements as strings of pixels, as shown in Figure 6. Each pixel
represents one band of points in a street scene. Each pixel is located at the
centerline of the street within its band and colored according to the
morphological metric value measured for that band, such that darker colors
represent higher values. The values used for each metric are normalized to
their maximum within each scan. We present a separate map for each
morphological metric in each scanning location.

Figure 6: Maps show the local analysis results for each scan, situated within
the favela.

Using these detailed morphological maps, allows us to trace the variation of
each metric not only within the extent of a single street scene (as in our
local analysis), but also across the larger context of the surrounding built
environment. Like our global analysis, these maps are productive for overall
comparison of street scenes or areas to one another, but they specify this
comparison by separating its components by metric and locating the
measurements geographically in space. Thus, this rendering of our results
enables simultaneous local and global exploration of morphology in the
scanning area.

This final step of mapping our most detailed results onto the favela’s plan
makes the insights from our analysis clear and actionable. As a set of
samples, these maps can show morphological variation across space such as
topography, the pinching and widening of streets, and clusters of tall
buildings. Extended to the scale of the entire favela, such maps would reveal
hotspots of crowding, steep inclines, and dangerous overlaps of the two,
enabling city officials and urban planners to pinpoint locations in need of
intervention. These maps demonstrate the utility of LiDAR as a means of
concisely and legibly articulating informal settlement morphology to the
institutions that can act upon it.

###  Measurement Validation

To validate our morphology measurements we compare our global results with
official maps from the Public Works Company of the State of Rio de Janeiro at
the locations of the scans, as well as satellite and 3D mesh data from Google
Earth. The Public Works maps were collected as part of a participatory
planning initiative with the community in 2004 (Toledo, 2004).141414These maps
are only available for the year 2004. Although they have not been updated
recently, they offer the most comprehensive official data source available to
ground-truth our data. We use these plans to confirm our measurements of
street width. To ground-truth our elevation measurements, we compared them to
a 3D model of Rocinha produced by the Public Works Company of the State of Rio
de Janeiro. Recall that the elevation values in the point cloud are
established relative to the first point in each scan rather than absolute
meters above sea level, therefore we validate elevation in terms of the
elevation difference between street scenes rather than as absolute elevation
values. Finally, to validate our measurements of facade height and density, we
compare them to building counts from satellite images and building heights
obtained from Google Earth Pro. Table A2 in the appendix shows a comparison of
our calculations relative to the official sources. Reassuringly, there were
not meaningful differences between the two.

##  Discussion

In this section, we contextualize the findings of our morphological analysis
within the present-day urban configuration of the scanning area and the
historical development of Rocinha.

Our results align closely with historical evidence tracing the development of
the favela. For example, our global analysis indicates that street scenes 1
and 2, which are both in the Courtyard Scan, are much more similar to each
other than they are to other street scenes in our sample. The high street
width values close to the global maximum can be explained by the formal
intervention that widened the courtyard as a social gathering space, and high
facade heterogeneity due to the presence of both tall buildings and low
retaining walls. Their low facade densities can be explained by the large
buildings organized along the spacious courtyard, and their low street canyon
values can occur because the scale of the street forces the ratio of facade
height to street surface area down. Thus, our morphology metrics capture
meaningful properties of the built environment that are consistent with the
urban reality of the Courtyard Scan.

Similarly, our results for street scenes in the Hillside Scan capture the
spatial dynamics we expect of an informal residential area: compactness,
density, and verticality. The facade heterogeneity, facade density, and street
canyon values in street scenes 6-10 are markers of a built environment
characterized by a variable conglomeration of facades that crowd and tower
over narrow streets. These morphological profiles are consistent with the
traditions of informal construction in favelas, where unregulated property
lines enable buildings to encroach on street space, and the expansion strategy
of building additional floors on top of flat-roofed homes results in variable
facade heights.

Extending our morphological analysis to the local level enables us to unpack
variations and differences that are not immediately apparent in our global
analysis. These high-resolution measurements are indicative of sharp changes
in the favela environment that occur across short distances: even within a
single street scene, the built environment may look very different from one
end of the street to the other. This dynamic underscores the importance of
high-resolution morphological analysis in informal settlements, and it
emphasizes the utility of LiDAR data, whose pointwise and aggregate dimensions
enable the interpretation of the favela at multiple levels.

##  Conclusion

This paper uses terrestrial LiDAR data to analyze the morphology of informal
settlements. We take Rocinha, the largest _favela_ in Rio de Janeiro, Brazil
as a case study to illustrate this application. As a consolidated and well-
mapped favela, Rocinha enables us to ground-truth our measurements and thereby
validate this approach for replication elsewhere. Our methodology reveals
meaningful morphological differences and commonalities both in terms of the
global morphology of streets and their local variations. To measure the
morphology of the informal settlement we propose a series of five metrics.
related to the geometric characteristics of the street and its facades: street
width; street elevation; facade heterogeneity; facade density; and street
canyon and validate them using official maps and historical evidence of the
favela’s development. Our approach has two primary advantages. First, from a
methodological point of view, the 3D measurements we extracted from LiDAR are
flexible in terms of their resolution: the point cloud data can be aggregated
and measured at various scales, enabling both global and local analysis.
Another advantage of this approach is that it allows us to quantify
morphological properties of informal settlements at large, given its automatic
and data-efficient nature. Both of these strengths prime our approach for
implementation as a survey and management tool for local agencies to determine
and execute strategic improvements in the favela. Moreover, morphological
analysis of informal settlements provides a basis for the study of important
environmental and social issues that impact informal settlements, such as
airflow, landslide risk and structural safety, property rights, and
accessibility.

Our global and local results demonstrate the benefit of conducting
morphological analysis at two different scales and emphasize the utility of
the street scene approach. The global results consist of morphological
summaries of each street scene, making them best suited to comparing small
street scene such as those in the Hillside Scan. Meanwhile, the complexity of
larger street scenes simplified in the global analysis is fully expressed in
our local analysis, which indicates morphological variation within street
scenes. This dual approach to morphological analysis culminates in maps
showing the local results for each morphological metric situated in a plan of
the favela, which represent our highest resolution measurements in context.
All together, these complimentary scales of analysis offer useful comparative
insights about morphology for the range of urban conditions in the favela.

This paper provides several fruitful areas for future research that can
complement and improve our methodology. First, the LiDAR data we use for the
descriptive analysis is only available for two relatively small areas of
Rocinha. This means that the insights we can draw about the morphology of the
informal settlement are limited to these areas. A full scan of the favela
could allow future work to incorporate other complementary morphology metrics,
such as connectivity, compactness, and other properties of the settlement that
can be best measured at larger scales. Second, our plane extraction model can
be improved to better match streets defined by their intersections. Our
current approach focuses on extracting large horizontal and vertical planes,
and cannot accurately identify very small connected planes such as staircases.
This results in a series of small street scenes located at different
elevations rather than a continuous street scene connecting them. Access to
more LiDAR data and the development of complementary plane extraction
procedures could enhance morphological studies looking to characterize the
complexity of informal settlements.

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## Appendix

RANSAC Shape detection procedure: We use the RANSAC shape detection method,
introduced by Schnabel et al (2007) to extract shape models from unorganized
point clouds. The algorithm to extract planes works as follows:

Given a point cloud $\mathcal{P}=\\{p_{1},\dots,p_{N}\\}$ with associated
normals $\\{n_{1},\dots,n_{N}\\}$, the output of the algorithm are planes
$\\{\Psi_{1},\dots,\Psi_{n}\\}$ with its corresponding set of disjoint points
$\\{\mathcal{P}_{\Psi_{1}},\dots,\mathcal{P}_{\Psi_{n}}\\}$. To construct the
planes, the algorithm first extracts a set of points $\mathcal{P}_{\Psi}$ that
belong to a plane $\Psi$ from a all the points remaining in the point cloud
$\mathcal{R}$ ($\mathcal{R}\subset\mathcal{P}$). To do this, it calculates the
parameters of a candidate plane $\Psi_{m}$ from $3$ randomly selected points
$\\{p_{1},p_{2},p_{3}\\}$ (every combination of 3 points in $\mathcal{R}$
constitute a minimal set that can define a candidate plane), and then finds
the corresponding set of points $\mathcal{P}_{\Psi_{m}}$ that lie within a
given distance $\epsilon$ to this candidate plane ($\epsilon$ is a ratio of
the point cloud bounding box width, we use a value of 0.0045—the typical value
of this parameter for a single building is 0.002, but since informal
settlements are built piecewise, allow a ratio of 0.0045 to allow more
variance on the output planes). We run this random selection process for $T$
iterations (the iterations $T$ are required to find a shape with minimum
support points $\tau$ in subset $\mathcal{R}$ with an overlooking probability
$p_{t}$. We set $p_{\tau}$ to 0.1, which means we have a $90\%$ probability of
detecting the best model. Recall that our goal is to extract the relevant
points, not to find the best model for each plane, so we limit the number of
iterations. The best candidate plane constitute the largest connected
component on the shape and is chosen using the number of inlier points, the
points in $\mathcal{P}_{\Psi_{m}}$ that do not deviate from the plane normal
for more than the maximum deviation angle $\alpha$ (we use a normal deviation
angle $\alpha$ of 12.5 - 35.0 ($\epsilon$ / 0.012) to adjust for the fact that
buildings vary widely in scale in our context —a typical value $\alpha$ = 20
is used model focused on a single building). The best plane candidate
$\Psi_{m_{b}}$ is only accepted when the number of points
$|\mathcal{P}_{\Psi_{m_{b}}}|$ is no less than the threshold $\tau$(we set
$\tau$ to 750 in order to include small planes from buildings, but exclude
urban furniture). Once a best plane model is found, the corresponding set of
points $\mathcal{P}_{\Psi_{m_{b}}}$ are removed from the point cloud
$\mathcal{P}$ and the algorithm is repeated until the only remaining points
are noise that do not constitute a plane with minimum support points. In
addition, the algorithm also requires a sampling resolution $r$, which defines
how the algorithm samples points from the point cloud, we set $r$ to be 0.05m,
corresponding to the distance between neighboring points in the data. We
choose this number to balance the risk of classifying more noise planes but
blending groups of small planes together as one large plane (larger values)
and classifying fewer noise planes but having large streets or facades divided
into small planes (smaller values). A summary of the parameters we used is
shown in Table A.

Table A1:

Parameters used in the RANSAC Procedure Parameters Definition Reasoning
Hillside Scan Courtyard Scan Minimum Support Points $\tau$ Minimum number of
points required for a point cloud fragment to be considered a plane candidate
We use a value that allows us to include building facades but exclude urban
furniture 750 750 Maximum distance to primitive $\epsilon$ Maximum distance of
sample points to plane to be included in the corresponding set of points of
the plane, given as a ratio of bounding box width The value has a linear
relationship with maximum bounding box width, so that more variance is allowed
for larger areas 0.15 0.3 Sampling resolution $r$ (m) Distance between
neighbour sampling points, equivalent to the point cloud resolution the value
we use corresponds to the scan resolution 0.05 0.05 Maximum normal deviation
$\alpha$ (degrees) Maximum deviation of the normal of initial randomly
selected points from the normal of the plane defined by them Calculated based
on a linear relationship with maximum distance to primitive 12.5 25.0
Overlooking Probability $p_{t}$ The probability that no other better primitive
candidates are overlooked (the chosen candidate is the best) during sampling.
We selected a probability value that balances between the overall iterations
and best plane model 0.1 0.1 Notes: The Table shows the parameters used for
the RANSAC calibration. Column 1 shows the parameter used. Column 2 and 3
describes the parameter and provide a brief intuition of its use. Columns 4
and 5 show the parameter values used for the hillside and the courtyard scan,
respectively.

Figure A1: Figure shows global analysis as comparative plots in 5 dimensions
(X, Y axes, and R, G, B colors), where each dimension is a morphological
metric. Table A2:

Ground Truth Metric Values Street Scene Number Street Width Elevation Maximum
Building Height Building Count Source Rocinha Masterplan (Public Works Company
of the State of Rio de Janeiro) Rocinha 3D plan (Public Works Company of the
State of Rio de Janeiro) Google Maps Satellite Google Earth Pro 3D Mesh 1 6.21
m 177 m 18.23 m 12 2 5.78 m 172 m 8.71 m 3 3 3.29 m 193 m 10.28 m 6 4 2.67 m
198 m 2.62 m 2 5 3.41 m 187 m 3.61 m 2 6 0.81 m 189 m 9.42 m 2 7 1.94 m 190 m
6.03 m 2 8 1.73 m 181 m 6.35 m 2 9 2.29 m 182 m 5.21 m 2 10 2.10 m 177 m 3.86
m 3 Notes: The Table shows the ground truth information used to validate the
street scene measurements. Each column refers to a different ground truth
metric. Row 1 shows the source used to gather the values for each metrics, and
rows 2-11 show the values identified for each street scene. This information
confirms the validity of the street scene analysis, which does not differ
significantly from the ground truth.