Metrological issues in the use of mobile mapping systems for planning emergency response

The paper intends to investigate some metrological aspects concerning data acquisition in determining the slope of escape routes in existing building, in order to provide this information as input for subsequent evacuation planning algorithms. The analysis is based on the point cloud acquired by a laser scanner and deepens different aspect that can impact on the slope uncertainty, linked to the choice of the algorithm for determining the slope itself, the values of the different parameters to set, and the different possible study strategies of the floor surface. The analysis will be conducted by using a commercial software, with the aim, in a future work, of investigating other kinds of algorithms and approaches, but also non-commercial data processing methods that may provide further useful information.


Introduction
In recent years, the three-dimensional reconstruction of cities or of individual buildings has gained value for a number of applications [1][2][3][4][5][6][7], including evaluating seismic damage and emergency response planning.A typical 3D model can be created using a variety of techniques, such as photogrammetry, laser scanning, tilt photography from unmanned aerial vehicles (UAVs), Synthetic Aperture Radar (SAR) approaches, and more [8,9].
In case of internal/external mapping of buildings, points clouds acquired by laser scanner and their processing is one of the most used application of 3D reconstruction, which can be useful for many purposes, like restoring, maintenance, and evacuation planning in existing buildings; furthermore, the use of laser scanner is particularly useful when the reconstruction calls for particular detail and the acquisition conditions are stringent, as they are in emergency scenarios, due to its resolution, accuracy, usability, relative affordability, speed of data collecting and processing, and ability to measure at a safe distance [10].
For this purpose, in the past manual processing of the points cloud has been employed, but there are significant issues which should be considered, in particular in the case of complex structures with huge proportions:  need for big data management techniques. low reproducibility of the results, due to human contribution while tracing profiles.
Even automatic approaches as well as point fitting, outlier removal, and artificial intelligence, presents challenges when the geometry of the area is very irregular, as in the case of buildings with artistic decorations, presenting niches and sharp variations in direction of the walls, statues, columns, bas-reliefs, etc… Among the point cloud-based building mapping applications, evacuation planning in emergency situations is one of the most important from the point of view of social impact.
The study of emergency evacuation from buildings analyses the movement of a crowd at the stresses represented by a real or apparent danger, taking into account psycho-physical state of the people, location, number and types and characteristics of the evacuation escape routes, speed and time of evacuation and, in the event of fire, spread of the fire itself and smoke.The elements that contribute to the study of the exodus are therefore many, and each of them can reasonably vary within certain limits.
This kind of study, on existing buildings, requires reconstructing the paths and examine the locations that can safely evacuate people.
Many factors showed a significant impact on the final solutions concerning evacuation plan.Among the others, the most important can be considered the uncertainties in mapping the floor and the slope of it along the allowed escape tracks.The former are due to the presence of barriers in the laser beam's path (included people, because the church is normally accessible to the public), which cause gaps and holes in the resulting cloud; the laser scanner positioning in relation to the target point, when the angle with respect to the façade is unfavourable; the presence of highly reflective objects like windows or glass doors.The latter influence remarkably the characteristics of people movement.
In fact, the slope is an important factor in the dynamic of the evacuation, because, in general, pedestrians acquire a different speed according to it.Numerous works focus on the study of the biomechanics of walking as a function of the slope of the floor [15,16].Given that it is one of the most important walking characteristics that is related to the prediction of evacuation time in case of emergencies, researchers have given evaluation of pedestrian speed a lot of attention [17][18][19][20][21].
While designing public areas and buildings like stadiums, subway stations, shopping centres, airport and walkways, it's imperative to take pedestrian speed into consideration.Yet, it is equally crucial to take into account this factor in emergency planning for already-existing public buildings that may be outdated and not optimized for evacuation.One of the prerequisites for crowd evacuation planning from structures, particularly in emergencies (e.g., fire), is speed assessment.
The construction of models and simulations of pedestrian crowd movement during routine and emergency evacuations include speed as a crucial element [22].It has been noted that the speed of a pedestrian in an emergency situation differs from that in other circumstances [19,23].In emergency situations, people frequently adopt a higher speed due to the need to leave as soon as possible: that moving at a higher pace, in specific conditions, can result in a "faster-is-faster" effect that shortens the evacuation time [24].But this higher speed sometimes can lead to a "faster-is-slower" effect, creating delays in the evacuation process [25,26].
Furthermore, it should be considered that the higher speed, further increased by a steep downward slope in the direction of the escape, can cause a worsening of the risk when the panic arises: in these situations, each person would obey the imperative to get away at all costs in the shortest time possible, trying with strength to reach the outside, with disastrous consequences.
In a previous application [11], the authors dealt with the aforementioned issues related to the reconstruction of the maps of a building, and assessed the uncertainty of determination of them, with reference to an Italian baroque church, characterized by a complex structure, where hundreds of people may be present at once.The evaluation of the measurement uncertainty is an essential step [12,13], especially when it comes to very critical applications regarding safety and public health aspects.
In this work the problem of determining the slope of the floor on the basis of point clouds is evaluated [14].
In the light of the above considerations, this paper intends to investigate the problem of determining the slope of escape routes, also in order to provide this information as input for subsequent evacuation planning algorithms.The aspects that will be examined relate to the impact on slope uncertainty of the choice of:  the algorithm for determining the slope itself. the values of the different parameters that can be set for each of the algorithms examined. the different possible study strategies of the floor surface.The analysis will be conducted, in this first step, with reference to a commercial software, with the aim, in a future work, of investigating any other (non-commercial) data processing methods that may provide further useful information.
The study refers to the same test case taken into consideration in the aforementioned work by the authors, i.e. a church very frequented by the public, of which, in particular, the terraces will be examined, which present a particular irregularity in the slope of the floor.Some indications of technical fire prevention standards will be considered to take into account tolerances and limits of the slope.In particular, in the Italian Ministerial Decree 3 August 2015, a horizontal evacuation route is considered as a portion of the evacuation path at a constant height or with a slope ≤ 5 %.Ramps with a slope in excess of 5 % are deemed to be vertical escape routes.In general, occupants with motor disabilities cannot autonomously use ramps with a slope in excess of 8 %.It should be also considered that ramps with a slope in excess of 12 % must only be used for evacuation in exceptional circumstances.
In Section 2, the hardware and software tools used will be described, and the methodology will be illustrated; in Section 3 the results obtained will be shown and, finally, concluding considerations and future developments will close the paper in the Conclusions Section.

Material and methods
As expressed in Section 1, the considered test case is a baroque cathedral located in Central Italy.It is characterized by having many tourists present at the same time.For this reason, an accurate emergency response is crucial.The cathedral is a large structure with an internal area of more than 15000 m2 where the central nave has remarkable dimensions.In this study, the rooftop of the church has been considered since it is partially open to the public, but the floor has slopes to drain the rain.
In this work, a Leica RTC 360 terrestrial laser scanner has been used to acquire and to generate a point cloud.All the cloud processing phases have been carried out using the Leica software suite.During the acquisition phase Leica Register360 has been used to join the clouds acquired from the different setups.To reduce the joining error, the instrument has a Visual Inertial System (VIS) that traces the instrument movements between to subsequent acquisitions.The acquisition campaign has been carried out during weekdays while there were people visiting the site.For this reason, the "Double Scan" function of the instrument has been selected to delate all the moving objects in the point cloud.In this case, the instrument performs two acquisitions for each setup and compare all the points in the cloud to identify the ones that moved from one acquisition to the other.
Due to the extension of the structure, multiple setups have been required to scan the rooftop.The whole area has been acquired using 454 different setups.The resulting point cloud is composed of 11223.9 million of points.For each setup the laser scanner has been placed on a tripod with a high of 1.7 m.
For all analysis, a Windows 11 PC with an Intel Core i7-12700H CPU and 16GB of RAM has been used.
The analysis of the point cloud has been carried out using Leica Cyclone 3DR software.Since manipulating very large point clouds can lead to problems and unstable behaviour of the software, the number of points has been reduced to 200 million prior the analysis.The software removes the point where the density is high without causing great changes in the surfaces.
A representative portion of the floor of the rooftop has been selected.This is characterised by having different slope angles.
In order to analyse the slope of the point cloud, the slope analysis tool provided by Cyclone 3DR has been used.This function associates a slope value for each point according to the angle between the local normal of the surface and the horizontal.For the point cloud analysis, this function provides a Local Normal Smoothing slider to vary the radius of the zone where the local normal is calculated.Smaller diameters provide the slope values between one point of the cloud to the other whereas increasing the dimension offers a more globally slope measurement of the cloud.
From the rooftop cloud, a part of interest has been selected.This area is characterized by not having other elements on the floor.It also has different slopes in order to drain water.From this area, the central zone has been designated for the further analysis.Figure 1a shows the top view of the examined floor section.The selected part of the zone is highlighted in white.On the left there is a balustrade and on the right there is a railing.Figure 1b shows the section of the point cloud, the slope increases moving from the railing to the balustrade in order to drain rainwater.As a first step, a preliminary examination of the considered area has been carried out using the slope analysis tool.At this stage, the aim of the analysis is to find a suitable division of the zone of interest.In this case, a division in 10 subareas seemed the most appropriate.
In order to study the slope trend, this section has been subdivided into 10 non overlapping bands of the same dimensions.This bands have been created moving along the X direction, generating vertical strips, and along the Y direction, producing horizontal bands.Each band has been numbered from top to bottom moving along the Y direction and from left to right along the X direction.
Figure 2 displays the generated bands for each direction. the heatmap and the histogram of the slope values of the whole selected portion of terrace;  the heatmap and the histogram of the slope value for each band, along the X and Y direction;  the mean and the standard deviation of the slope in the different bands along the X and Y direction.

Results
The first analysis of the selected surface consists in the creation of a heatmap of the slopes calculated on areas of settable width (Local Normal Smoothing parameter), as described in Section 2. Figure 3 shows the heatmaps obtained by setting a minimum ("Min smoothing", Figure 3.a) and maximum ("Max smoothing", Figure 3.b) calculation area: it should be noted that the choice of the lowest spatial resolution allows to clearly identify two areas with a prevailing and distinct slope.Then, in accordance with the methodology described in Section 2, the analysis of the selected area is deepened by dividing it into bands along the X and the Y direction (see definition of bands along X and Y directions in Figure 2).The results are shown in Figure 4 in terms of frequency distributions of the slopes in the different bands examined, both in X and Y direction.
Furthermore, for each band, both in X and Y direction, the mean value and the standard deviation of the slopes are represented in Figure 5.
With reference to Figure 4 it can be noticed that: In the case of the Y direction:  the distribution of slopes is very similar in all bands;  the distributions obtained using the "maximum smoothing" option, i.e. worst spatial resolution (Figure 4.b), appear to be clearly bimodal;  the distributions obtained using the "minimum smoothing" option, i.e. better spatial resolution (Figure 4.a), present the bimodality characteristic much less evident; In the case of the X direction:  the distribution of slopes is different in the various bands (Figures 4.c and 4.d);  the distributions obtained with both the "minimum smoothing" and the "maximum smoothing" for each band are unimodal, but the latter are characterized by a lower variability (Figure 4.c and 4.d).
These observations can be explained by referring to Figure 3.b, in which it can be seen that the portion of the terrace considered presents two macro areas with two different level of slope: an area with a slope greater than 5% (the outermost one, which slopes towards the balustrade on the left), and the remaining part with a slope lower to 5%, which can, therefore, be approximated to a horizontal plane according to the Italian standard.
In the case of Figures 4.a and 4.b, the bands are all transverse to these slope variations (see Figures 2 and 3), and this explains why the distributions presents two prevailing slope values and are the same for all the bands.The bimodality is less evident in the case of "minimum smoothing", since the better spatial resolution produces a greater variability of the calculated slope values, and this makes the two peaks wider and, therefore, less separate.
In the case of Figures 4.c and 4.d, the bands are all longitudinal to these slope variations (see Figures 2 and 3), and this explains why each band is characterized by a more uniform slope and a unimodal distribution.Even in these last two cases, the higher spatial resolution ("Min Smoothing") produces greater variability and breadth of the distributions.As far as the bands along the Y direction are concerned, the difference (Δs) between the average values for each band and the overall average has been also represented in figure 5.c: this graph is significant in the fact that moving in the Y direction, there are no variations in slope, as moving on a horizontal line.It should be noted, however, that in this direction the feet would rest on different heights if one moves close to the balustrade on the left, where the slope in the X direction is higher, and this creates a certain discomfort when walking.
Finally Figures 5.b and 5.e show that, both for the bands along the X direction and for those along the Y direction, the best spatial resolution ("Minimum Smoothing") produces, as already observed, higher dispersions than in the case of "Maximum Smoothing".
It is also interesting to note that along the X direction the dispersion in each band is significantly lower than in the Y direction in the case of " Maximum Smoothing".The same cannot be said when using the " Minimum Smoothing" option, which produces similar standard deviations along the X and Y direction.This confirms that lower spatial resolution reduces variability and allows macroscopic differences in slope to be better highlighted.

Conclusions
The aims of the work are to evaluate the effect of the change of some parameters of Leica Cyclone 3DR software for the analysis of the slopes of a floor and to outline an operative strategy for the slope assessment.
Firstly, a region of the rooftop of a church has been selected.Then, the slope analysis of the floor has been carried out considering the whole region and subsequently subdividing this zone in different bands along the X and Y direction respectively.
The results show that moving along the Y direction where the bands are horizontal, each of them contains all the angles.Whereas considering the vertical bands and moving along the X direction the angles in each band tend to be more uniform.
The analysis has been carried out considering the maximum and the minimum values for the local normal smoothing parameter.For the bands along the Y direction, the mean values of the slopes are constant using the minimum or the maximum value for the normal smoothing.While the standard deviation is greater when the normal smoothing is set to the minimum.For the bands in the X direction, the mean values of the slope in each band is the same whether the normal smoothing is at the greater value or at the lower.
In both cases, the different slope values in each stripe have been highlighted.As for the Y direction, using a greater area to evaluate the normal leads to a reduction of standard deviation.This is due to the reduction in the spatial resolution that decreases the influence of slope differences between closer points.Having a smoother value for the normal also gives a more global view of the slope distribution in the heatmap of the point cloud.
This work focuses only on the analysis of the points in the cloud.In the next step the post-processing features of the software will be evaluated.

Figure 1 .
Figure 1.(a) Top view of the selected rooftop floor.In white is highlighted the central part used for the analysis; (b) Section of the point cloud of the central zone.

Figure 2 .
Figure 2. (a) Horizontal bands numbering moving along Y direction; (b) Vertical bands numbering moving along X direction.

Figure 3 .
Figure 3. Heatmap of the selected area for the analysis obtained by setting the option: (a) Min Smoothing; (b) Max Smoothing.

Figure 4 .
Figure 4. Relative frequency distribution for the slope for each band (from 1 to 10) along Y direction, in correspondence to: (a) minimum smoothing and (b) maximum smoothing; along X direction, in correspondence to: (c) minimum smoothing and (d) maximum smoothing."Tot" refers to the distribution of the slopes in the whole area considered.

Figure 5 .
Figure 5. Mean (a), standard deviation (b) and Δs (c) of the slope in each band from 1 to 10, along Y direction.Mean (d) and standard deviation (e) of the slope in each band from 1 to 10, along Xdirection These considerations allow us to define a method of approach to the problem of determining slopes, which can be schematized as in the diagram of Figure6: in essence, this scheme suggests choosing a lower spatial resolution when areas with different slopes need to be highlighted, and a better resolution if local variability and surface asperities are of interest.

Figure 6 .
Figure 6.Diagram of slope analysis strategy