Engineering graphics for thermal assessment: 3D thermal data visualisation based on infrared thermography, GIS and 3D point cloud processing software

symmetry S S Article Engineering Graphics for Thermal Assessment: 3D Thermal Data Visualisation Based on Infrared Thermography, GIS and 3D Point Cloud Processing Software Daniel Antón1,2 and José-Lázaro Amaro-Mellado 3,4,*   Citation: Antón, D.; Amaro-Mellado, J.-L. Engineering Graphics for Thermal Assessment: 3D Thermal Data Visualisation Based on Infrared Thermography, GIS and 3D Point Cloud Processing Software. Symmetry 2021,13, 335. https://doi.org/ 10.3390/sym13020335 Academic Editors: Sergei D. Odintsov and JoséRojas Sola Received: 2 January 2021 Accepted: 16 February 2021 Published: 18 February 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Research Group ‘TEP970: Innovación Tecnológica, Sistemas de Modelado 3D y Diagnosis Energética en Patrimonio y Edificación’, Departamento de Expresión Gráfica e Ingeniería en la Edificación, Escuela Técnica Superior de Ingeniería de Edificación, Universidad de Sevilla, 4A Reina Mercedes Avenue, 41012 Seville, Spain; [email protected] 2The Creative and Virtual Technologies Research Laboratory, School of Architecture, Design and the Built Environment, Nottingham Trent University, 50 Shakespeare Street, Nottingham NG1 4FQ, UK 3Departamento de Ingeniería Gráfica, Universidad de Sevilla, 41092 Seville, Spain 4Instituto Geográfico Nacional—Servicio Regional en Andalucía, 41013 Seville, Spain *Correspondence: jamar[email protected] Abstract: Engineering graphics are present in the design stage, but also constitute a way to communicate, analyse, and synthesise. In the Architecture-Engineering-Construction sector, graphical data become essential in analysing buildings and constructions throughout their lifecycles, such as in the thermal behaviour assessment of building envelopes. Scientific research has addressed the thermal image mapping onto three-dimensional (3D) models for visualisation and analysis. However, the 3D point cloud data creation of buildings’ thermal behaviour directly from rectified infrared thermography (IRT) thermograms is yet to be investigated. Therefore, this paper develops an open-source software graphical method to produce 3D thermal data from IRT images for temperature visualisation and subsequent analysis. This low-cost approach uses both a geographic information system for the thermographic image rectification and the point clouds production, and 3D point cloud processing software. The methodology has been proven useful to obtain, without perspective distortions, 3D thermograms even from non-radiometric raster images. The results also revealed that non-rectangular thermograms enable over 95% of the 3D thermal data generated from IRT against rectangular shapes (over 85%). Finally, the 3D thermal data produced allow further thermal behaviour assessment, including calculating the object’s heat loss and thermal transmittance for diverse applications such as energy audits, restoration, monitoring, or product quality control. Keywords: 3D thermal data; 3D thermograms; point cloud data; visualisation; temperature; heat loss; infrared thermography; GIS; 3D point cloud processing software; engineering graphics 1. Introduction As a graphical expression, engineering graphics are useful for conceptual and project representation in the design stage, but also constitute a way to communicate, analyse and synthesise [ 1 , 2 ]. In the Architecture-Engineering-Construction (AEC) sector, the use of graphical data becomes essential when dealing with the analysis of the built environment, buildings and constructions throughout their lifecycles [ 3 ]. This type of data can involve the use of two-dimensional (2D) and three-dimensional (3D) graphics, in the form of raster and vector representations, as well as data and models based on 3D coordinates, respectively. Within this framework, several digital technologies allow the integration of additional information to the graphical data, such as Geographic Information Systems (hereinafter, GIS) and Building Information Modelling (henceforth, BIM) [ 4 ]. This can be useful for the analysis of both geometric and geographical issues, as well as buildings and construction processes. In this sense, there are relevant scientific works to be highlighted dealing with the Symmetry 2021,13, 335. https://doi.org/10.3390/sym13020335 https://www.mdpi.com/journal/symmetry Symmetry 2021,13, 335 2 of 18 tools that support this research: Lerma et al. [ 5 ] implemented an architectonic GIS to analyse multi-source data, including thermal images, and rectified imagery; Previtali et al. [ 6 ] used a GIS-assisted method to improve the thermal anomalies recognition, mainly for thermal gradient assessment; Yuanrong et al. [ 7 ] designed a GIS to bring both Unmanned Aerial Vehicles and Terrestrial Laser Scanning data together for façade construction supervision; Chen et al. [ 8 ] used a GIS-based platform to integrate the façade data from different sources, such as infrared thermography (hereinafter, IRT), laser scanner, or high definition digital cameras; and Wang et al. [ 9 ], in the frame of digital cities, studied the semantic information on parametrised 3D buildings’ façades by hierarchical topological graphs. In the scientific literature analysed, the information associated with the geometry of the studied objects has been considered an attribute. Therefore, these attributes have not been represented as an integral part of 3D geometric data where one of the coordinates is not geometric. Concerning the rectification of images, it is worth highlighting the work by Yue et al. [ 10 ], who automatically rectified the building images helped by a local symmetry feature graph. Thus, the authors matched both the original and the corrected image in order to conduct their fusion. Finally, Soycan and Soycan [ 11 ] revised the models to achieve rectified photographs for further façades analysis. Regarding the use of 2D graphical data for building analysis, IRT is a versatile, nondestructive technology that enables the recording and visualisation of the thermal radiation emitted by the bodies. This can be used to determine energy loss in building envelopes, issues in building services, construction defects, among many others [ 12 ]. Likewise, active IRT has been proven useful to detect hidden openings or structural elements [ 13 ]. The thermal image produced by IRT, called thermogram, is 2D. Still, certain proprietary software for this sort of equipment such as InfReC Analyzer [ 14 ] or Fluke SmartView [ 15 ] can complement these images with 3D graphs [ 16 , 17 ]. Nevertheless, the 3D data that can be produced do not represent the thermal images’ real magnitude, given the IRT survey data’s perspective distortion. Furthermore, these applications can generally be acquired together with the equipment or in a complementary manner, which entails additional investment. Scientific research has also addressed thermal image mapping onto 3D models for visualisation and analysis. Alba et al. [ 18 ] proposed a method to texture 3D building models using infrared images. Vidas et al. [ 19 ] presented a hand-held mobile system that combined a range sensor with an IRT camera to produce 3D models mapped with infrared and RedGreen-Blue colour (hereinafter, RGB) images. Wang et al. [ 20 ] developed a hybrid system integrating Light Detection And Ranging (LiDAR) technology and an infrared camera to produce thermal models of building envelopes. Borrmann et al. [ 21 ] combined 3D laser scanning, IRT, and a photo camera to map 3D building façade models. Rangel et al. [ 22 ] presented an automatic approach to creating 3D thermal models by fusing IRT images and spatial data from a depth camera. Ham and Golparvar-Fard [ 23 ] proposed a 3D thermal mesh modelling method to display the as-is condition assessment of buildings. Thus, the method permitted the visualisation of R-value distributions and potential condensation issues. Moghadam and Vidas [ 24 ] designed a hand-held 3D thermography device called ”HeatWave” that combined IRT, a range sensor and a photo camera to create 3D models with augmented temperature and visible information of the objects. Moghadam [ 25 ] also presented a hand-held 3D device for medical thermography to simultaneously show both 3D thermal and colour information to facilitate diagnosis. Matsumoto et al. [ 26 ] developed a hand-held system based on IRT and an RGB-D (RGB depth sensor) camera for 3D model and temperature change visualisation from arbitrary viewpoints via augmented reality. Nakagawa et al. [ 27 ] established a system combining IRT and an RGB-D camera for scene 3D reconstruction; later, the authors applied the Viewpoint Generative Learning method to the RGB 3D model to display the difference between the temperature of random scene viewpoints and known camera poses. Natephra et al. [ 28 ] integrated thermographic images along with air temperature and relative humidity values into BIM to create 4D models of the performance of existing building envelopes. Finally, Landmann et al. [ 29 ] presented a high-speed system based on a structured-light sensor and an infrared camera to measure Symmetry 2021,13, 335 3 of 18 3D geometry and the fast-moving objects’ temperature. The reviewed scientific literature continues to address the problem of representing the thermal behaviour of objects by associating thermal attributes (images and RGB values) to purely geometric 3D data, with spatial coordinates. In view of the above, the creation of 3D point cloud data of buildings’ thermal behaviour for visualisation and analysis directly from rectified IRT thermograms is yet to be investigated. Given this knowledge gap, the aim of this paper is to provide an open-source software graphical method to produce three-dimensional thermal data from the infrared thermovision technique. It should be noted that, with the emergence and development of open data and open-source software, this can be addressed free of charge or at low cost. Consequently, the low-cost approach developed in this research (excluding the cost of IRT equipment), applies both thermographic image rectification in GIS and 3D point cloud data management. It has been proven useful to achieve, without perspective distortions, the 3D visualisation of the temperature of the objects surveyed. Thus, the methodology enables additional analysis of their thermal behaviour, which could not have been carried out if the thermal information (attribute) had not been converted into a third geometrical variable (coordinate) in the 3D thermal data set produced. The proposed method is tested in two case studies: (1) a quasi-symmetrical building façade sector, and (2) a non-symmetrical façade sector. This research also studied the impact of choosing between rectangular and non-rectangular 3D thermograms after the image rectification in GIS in terms of thermal data loss. The rest of the paper is structured as follows: (Section 2) the methodology is described and subdivided into stages corresponding to each technology used in this research; ( Section 3 ) the results of the two cases studied are presented; and (Section 4) the results of this research and its limitations are discussed; likewise, conclusions and future work are provided. 2. Methodology As mentioned above, this research is based on the combination of IRT and GIS, plus the treatment and management of 3D point cloud data for analysis. Thus, each technology constitutes a stage in the suggested methodology: 2.1. Thermal Imaging The first stage of the proposed method is to record the façade building components’ temperature via IRT. In this research, this was carried out in two surveys in Andalusia, Spain (Figure 1): Survey A, in the south of the city of Seville (inland Mediterranean climate), and Survey B, in Alhaurin de la Torre, near Malaga (coastal Mediterranean climate). The IRT surveys focused on the thermal bridge caused by the buildings’ reinforced concrete structure due to the lack of thermal insulation between the pillar and slabs and (1) the rendered brick façade (Survey A, a quasi-symmetrical sector), and (2) the vibrated concrete rough block façade (Survey B, a non-symmetrical sector). The recording of the surface temperature in the IRT surveys is affected by changes in the directional emissivity due to different viewing angles (between the direction of the camera and the object’s emission direction) higher than 40 ◦ [ 30 – 34 ]. Moreover, the camera operators themselves constitute a source of emissions that must be taken into account by avoiding the perpendicularity between the camera direction and the object. These aspects were considered in the surveys of this research so that both procedural errors and environmental radiant sources, respectively, were minimised in the recording of the façades’ surface temperatures. Besides, the weather conditions were recorded 24 h before the surveys using a portable weather station with sensors inside and outside the buildings. The hygrothermal indicators, input in both the camera settings and the thermographic software along with the material’s emissivity to produce the thermograms (graphical output of the IRT surveys), are gathered in Table 1. Symmetry 2021,13, 335 4 of 18 Symmetry 2021, 13, 335 4 of 20 Figure 1. Location of IRT Surveys A and B. The IRT surveys focused on the thermal bridge caused by the buildings’ reinforced concrete structure due to the lack of thermal insulation between the pillar and slabs and (1) the rendered brick façade (Survey A, a quasi-symmetrical sector), and (2) the vibrated concrete rough block façade (Survey B, a non-symmetrical sector). The recording of the surface temperature in the IRT surveys is affected by changes in the directional emissivity due to different viewing angles (between the direction of the camera and the object’s emission direction) higher than 40° [30–34]. Moreover, the camera operators themselves constitute a source of emissions that must be taken into account by avoiding the perpendicularity between the camera direction and the object. These aspects were considered in the surveys of this research so that both procedural errors and environmental radiant sources, respectively, were minimised in the recording of the façades’ surface temperatures. Besides, the weather conditions were recorded 24 h before the surveys using a portable weather station with sensors inside and outside the buildings. The hygrothermal indicators, input in both the camera settings and the thermographic software along with the material’s emissivity to produce the thermograms (graphical output of the IRT surveys), are gathered in Table 1. Table 1. Hygrothermal conditions in surveys A and B. Scheme Date and Time Exterior Temperature (°C) Interior Temperature (°C) Atmospheric Pressure (mbar) Exterior HR (%) Interior HR (%) A 28/01/2016 6:11 a.m. 9.0 18.7 1053 91 72 B 02/09/2016 8:22 a.m. 22.6 28.6 1020 87 67 HR represents the relative humidity. Wind speed was 0 m/s. Surveys A and B took place in winter and summer, respectively, and early in the morning to avoid direct sunlight as a radiation source; there was no rain or wind during the surveys. Additional considerations to minimise possible temperature reading errors and, therefore, errors when producing the 3D data, were avoiding targets with a Figure 1. Location of IRT Surveys A and B. Table 1. Hygrothermal conditions in surveys A and B. Scheme Date and Time Exterior Temperature (◦C) Interior Temperature (◦C) Atmospheric Pressure (mbar) Exterior HR (%) Interior HR(%) A28/01/2016 6:11 a.m. 9.0 18.7 1053 91 72 B02/09/2016 8:22 a.m. 22.6 28.6 1020 87 67 HRrepresents the relative humidity. Wind speed was 0 m/s. Surveys A and B took place in winter and summer, respectively, and early in the morning to avoid direct sunlight as a radiation source; there was no rain or wind during the surveys. Additional considerations to minimise possible temperature reading errors and, therefore, errors when producing the 3D data, were avoiding targets with a temperature outside the thermal camera’s calibration range, such as the sky or extremely reflective surfaces [ 35 ]. The thermographic camera used was a FLIR E60bx, with an 18 mm FOL lens and resolution of 320 × 240 pixels. The camera was placed 6 m away from the façades in both surveys. Once the data were recorded, this research used free thermographic software to produce the thermograms in the two cases. Flir Tools version 6.4.18039.1003 [ 36 ] allowed to input the infrared images, the hygrothermal indicators (Table 1), and the material’s emissivity coefficient [ 37 ] in the façades (0.85 and 0.92, respectively). In order to encompass all the possible temperature values in the thermograms, the range was set from 6.0 ◦ C to 15 ◦ C for Survey A, and from 22.0 ◦ C to 27 ◦ C for Survey B, given the ambient and surface temperatures in the scenes. The iron palette (colour configuration for thermograms) was firstly selected to show heat distribution and subtle details [ 38 ]. Still, the monochrome (grey) palette was chosen to ease image management in the GIS (Figures 2and 3). It is worth noting that the temperature ranges specified above were not included in Figures 2and 3as colour scales because these thermograms were exported for further processing. Finally, for the purpose of this research, it was necessary to extract the maximum and minimum temperature values from the thermograms (hottest and coldest points, Symmetry 2021,13, 335 5 of 18 respectively). Thus, the extent of the third dimension (of the 3D thermal data) could be next obtained from the temperature range using GIS. Symmetry 2021, 13, 335 5 of 20 temperature outside the thermal camera’s calibration range, such as the sky or extremely reflective surfaces [35]. The thermographic camera used was a FLIR E60bx, with an 18 mm FOL lens and resolution of 320 × 240 pixels. The camera was placed 6 m away from the façades in both surveys. Once the data were recorded, this research used free thermographic software to produce the thermograms in the two cases. Flir Tools version 6.4.18039.1003 [36] allowed to input the infrared images, the hygrothermal indicators (Table 1), and the material’s emissivity coefficient [37] in the façades (0.85 and 0.92, respectively). In order to encompass all the possible temperature values in the thermograms, the range was set from 6.0 °C to 15 °C for Survey A, and from 22.0 °C to 27 °C for Survey B, given the ambient and surface temperatures in the scenes. The iron palette (colour configuration for thermograms) was firstly selected to show heat distribution and subtle details [38]. Still, the monochrome (grey) palette was chosen to ease image management in the GIS (Figures 2 and 3). (a) (b) Figure 2. Thermograms of Survey A for GIS processing: (a) Iron palette; (b) Grey (monochrome) palette. (a) (b) Figure 3. Thermograms of Survey B for GIS processing: (a) Iron palette; (b) Grey (monochrome) palette. It is worth noting that the temperature ranges specified above were not included in Figures 2 and 3 as colour scales because these thermograms were exported for further processing. Finally, for the purpose of this research, it was necessary to extract the maximum and minimum temperature values from the thermograms (hottest and coldest Figure 2. Thermograms of Survey A for GIS processing: (a)Iron palette; (b)Grey (monochrome) palette. Symmetry 2021, 13, 335 5 of 20 temperature outside the thermal camera’s calibration range, such as the sky or extremely reflective surfaces [35]. The thermographic camera used was a FLIR E60bx, with an 18 mm FOL lens and resolution of 320 × 240 pixels. The camera was placed 6 m away from the façades in both surveys. Once the data were recorded, this research used free thermographic software to produce the thermograms in the two cases. Flir Tools version 6.4.18039.1003 [36] allowed to input the infrared images, the hygrothermal indicators (Table 1), and the material’s emissivity coefficient [37] in the façades (0.85 and 0.92, respectively). In order to encompass all the possible temperature values in the thermograms, the range was set from 6.0 °C to 15 °C for Survey A, and from 22.0 °C to 27 °C for Survey B, given the ambient and surface temperatures in the scenes. The iron palette (colour configuration for thermograms) was firstly selected to show heat distribution and subtle details [38]. Still, the monochrome (grey) palette was chosen to ease image management in the GIS (Figures 2 and 3). (a) (b) Figure 2. Thermograms of Survey A for GIS processing: (a) Iron palette; (b) Grey (monochrome) palette. (a) (b) Figure 3. Thermograms of Survey B for GIS processing: (a) Iron palette; (b) Grey (monochrome) palette. It is worth noting that the temperature ranges specified above were not included in Figures 2 and 3 as colour scales because these thermograms were exported for further processing. Finally, for the purpose of this research, it was necessary to extract the maximum and minimum temperature values from the thermograms (hottest and coldest Figure 3. Thermograms of Survey B for GIS processing: (a)Iron palette; (b)Grey (monochrome) palette. 2.2. GIS-Based Image Management GIS are tools that facilitate the handling of geographic information rigorously in each process phase, such as data entry, storage, management, integration, edition, or visualisation. Their most common use is in work on the horizontal plane, as shown in the recent literature, such as [ 39 – 43 ]. By contrast, there are fewer cases for working with elevation [5,8], even if this only involves a change in coordinate axes. In this work, a GIS has been used to carry out the thermogram’s geometric rectification and assign temperatures to the rectified image. QGIS v3.8.2 software [ 44 ] was used in this research. In both surveys, it has been assumed that the area of interest is contained in a plane. Thus, the relief (depth) of the façade is not deemed. For this reason, instead of an orthorectification, only a 2D homography, or projective transformation is required. Here, eight parameters are considered to conduct perspective removal. This planar homography aims at transforming one plane into another, and can be expressed as [11]:   x y 1  =H  X Y 1  =  h11 h12 h13 h21 h22 h23 h31 h32 h33    X Y 1  (1) Symmetry 2021,13, 335 6 of 18 Although the matrix presents nine parameters, the transformation poses eight degrees of freedom because the values are usually normalised, considering h33 = 1 (Figure 4). The eight parameters can be easily calculated from four pairs of points, both identified in the two spaces. Symmetry 2021, 13, 335 6 of 20 points, respectively). Thus, the extent of the third dimension (of the 3D thermal data) could be next obtained from the temperature range using GIS. 2.2. GIS-Based Image Management GIS are tools that facilitate the handling of geographic information rigorously in each process phase, such as data entry, storage, management, integration, edition, or visualisation. Their most common use is in work on the horizontal plane, as shown in the recent literature, such as [39–43]. By contrast, there are fewer cases for working with elevation [5,8], even if this only involves a change in coordinate axes. In this work, a GIS has been used to carry out the thermogram’s geometric rectification and assign temperatures to the rectified image. QGIS v3.8.2 software [44] was used in this research. In both surveys, it has been assumed that the area of interest is contained in a plane. Thus, the relief (depth) of the façade is not deemed. For this reason, instead of an orthorectification, only a 2D homography, or projective transformation is required. Here, eight parameters are considered to conduct perspective removal. This planar homography aims at transforming one plane into another, and can be expressed as [11]: 󰇩𝑥 𝑦 1󰇪=𝐻𝑋 𝑌 1=ℎ ℎ ℎ ℎ ℎ ℎ ℎ ℎ ℎ 𝑋 𝑌 1 (1) Although the matrix presents nine parameters, the transformation poses eight degrees of freedom because the values are usually normalised, considering h33 = 1 (Figure 4). The eight parameters can be easily calculated from four pairs of points, both identified in the two spaces. Figure 4. Homographic transformation to remove the perspective distortion. First, the geometrical measurement framework has to be defined. In this case, since this research presents a low-cost method, it has been preferred not to use classic topographical methods but a plumb, a spirit level, and a measuring tape. • For Survey A, the façade itself served as a reference: - Y-axis: the (left) vertical limit of the façade; - X-axis: a mortar joint; a spirit level was used to check its horizontality. • For Survey B: - Y-axis: a vertical joint, after checking with a plumb that its extension coincides with another of the lower joints; - X-axis: a horizontal mortar joint, whose horizontality has been verified using a spirit level. Contrary to conventional topography, the distance measurements have been established a posteriori. To this end, it has been checked that the four points that will Figure 4. Homographic transformation to remove the perspective distortion. First, the geometrical measurement framework has to be defined. In this case, since this research presents a low-cost method, it has been preferred not to use classic topographical methods but a plumb, a spirit level, and a measuring tape. •For Survey A, the façade itself served as a reference: - Y-axis: the (left) vertical limit of the façade; - X-axis: a mortar joint; a spirit level was used to check its horizontality. •For Survey B: - Y-axis: a vertical joint, after checking with a plumb that its extension coincides with another of the lower joints; - X-axis: a horizontal mortar joint, whose horizontality has been verified using a spirit level. Contrary to conventional topography, the distance measurements have been established a posteriori. To this end, it has been checked that the four points that will define the geometric frame are identifiable in the thermogram, using the diagonal as a verification. The measurements (and the axes) taken are displayed in Figure 5on each thermogram. Symmetry 2021, 13, 335 7 of 20 define the geometric frame are identifiable in the thermogram, using the diagonal as a verification. The measurements (and the axes) taken are displayed in Figure 5 on each thermogram. (a) (b) Figure 5. Measurements taken for perspective correction: (a) Survey A; (b) Survey B. Along with the geometrical 2D-homography, a radiometric conversion must be undertaken. Thereby, a digital number (DN) value must be assigned to each pixel of the resulting image. Besides, a bicubic interpolation has been chosen to conduct the resampling process. After obtaining an image with the rectified geometry and the corresponding DN, the next step is for each pixel’s DN to correspond to the thermogram’s temperature. In both surveys, each thermogram was encoded on 8 bits, i.e., 256 values, as radiometric resolution. For the DN value to correlate with the temperature, a linear normalisation formula must be applied: 𝐷𝑁 =𝑎×𝐷𝑁+𝑏 (2) where a is the slope, that is related to the rectified image’s thermal sensitivity, and b is the intercept, the minimum temperature value. From the temperature values of each case, the calculated parameters are shown in Table 2. Thus, it can be concluded that the thermal resolution for the rectified image for Survey B is approximately three times better than that for Survey A: Table 2. Extreme temperatures and conversion parameters for each survey. Scheme Tmin (°C) Tmax (°C) DNmin DNmax a b A 6.9 14.0 0 255 0.02784 6.9 B 23.0 25.4 0 255 0.00941 23.0 For each pixel in the new image, the DN coincides with the temperature recorded. The image border has a dark background, which corresponds to the absence of data. This fact is inherent in any “photograph”. Due to the inclination, there will be points on the resampled image that lack information. The tilt is determined by the commitment to obtain an image covering as much spatial coverage as possible without a significant loss of geometric resolution (pixel size on the facade). This matter is especially relevant since the thermographic camera used only has 320 × 240 pixels. Theoretically, a rectangular region of interest (hereinafter, ROI), in which all the pixels would have their temperature recorded, is more appropriate in terms of graphic language. However, this is not always suited, as information not included in the rectangle Figure 5. Measurements taken for perspective correction: (a) Survey A; (b) Survey B. Along with the geometrical 2D-homography, a radiometric conversion must be undertaken. Thereby, a digital number (DN) value must be assigned to each pixel of the resulting image. Besides, a bicubic interpolation has been chosen to conduct the resampling process. After obtaining an image with the rectified geometry and the corresponding DN, the next step is for each pixel’s DN to correspond to the thermogram’s temperature. In both Symmetry 2021,13, 335 7 of 18 surveys, each thermogram was encoded on 8 bits, i.e., 256 values, as radiometric resolution. For the DN value to correlate with the temperature, a linear normalisation formula must be applied: DNtemp =a×DN +b(2) where ais the slope, that is related to the rectified image’s thermal sensitivity, and bis the intercept, the minimum temperature value. From the temperature values of each case, the calculated parameters are shown in Table 2. Thus, it can be concluded that the thermal resolution for the rectified image for Survey B is approximately three times better than that for Survey A: Table 2. Extreme temperatures and conversion parameters for each survey. Scheme Tmin (◦C) Tmax (◦C) DNmin DNmax a b A 6.9 14.0 0 255 0.02784 6.9 B 23.0 25.4 0 255 0.00941 23.0 For each pixel in the new image, the DN coincides with the temperature recorded. The image border has a dark background, which corresponds to the absence of data. This fact is inherent in any “photograph”. Due to the inclination, there will be points on the resampled image that lack information. The tilt is determined by the commitment to obtain an image covering as much spatial coverage as possible without a significant loss of geometric resolution (pixel size on the facade). This matter is especially relevant since the thermographic camera used only has 320 ×240 pixels. Theoretically, a rectangular region of interest (hereinafter, ROI), in which all the pixels would have their temperature recorded, is more appropriate in terms of graphic language. However, this is not always suited, as information not included in the rectangle can be lost. This happens in survey B, where the slab thermal bridge above the rectangle has further temperature data. Operating in a GIS environment allows fitting as much work area as possible by defining an area of interest that is not rectangular. This area has been used as a mask when exporting the data for the following processes. 2.3. 3D Point Cloud Data Treatment For the purpose of this work, the three-dimensional data produced in the GIS platform need certain transformations to constitute the final 3D thermal data. This was carried out in CloudCompare v2.91 for 64-bit Microsoft Windows [ 45 ], although there are other open-source applications such as MeshLab [46] that can be used. Firstly, the data were imported into the programme as the XYZ file created in the previous stage in GIS. Next, a height ramp [ 47 ] or a height map of the 3D point set was generated to enhance the visualisation and readability of the 3D thermal data produced. This was performed using a monochrome linear gradient, 8-bit encoding (black for the lowest temperature, white for the highest), and a direction (Z-axis). The red, green and blue values of the RGB colours applied were therefore automatically associated with the coordinates of each point in the 3D point cloud. It should be also noted that the temperature range of the thermograms determines the distribution of the points in the 3D thermal data. In other words, given that the third coordinate (Z) is represented in the three-dimensional thermal data as its temperature values ( ◦ C), it may be that these values are actually higher than the XY coordinates (dimensions of the object studied). As a result, interpretating the 3D point cloud’s proportions may not be easy. Therefore, to reduce the ”temperature-value/X-Y-dimensions” ratio, a scale factor of 0.10 was applied to the Z-axis (temperatures). Thus, a more representative 3D point set of the thermal behaviour of the façade was obtained. Symmetry 2021,13, 335 8 of 18 Further management of the 3D thermal data makes it possible to gather useful information such as those façade sectors at a similar temperature. This can be carried out by creating point cloud contours by elevation (Z coordinate) thresholds. Considering that the Z-axis represents the temperature, these contours or 2D isolines—points with the same height or Z coordinate as in topographic maps—represent the thermogram isotherms—image regions within the same temperature range. The ”Rasterize” plugin [ 48 ] in CloudCompare helps create these isotherms by setting the gap (step) between the lines in the ”Contour plot” sub-tool, according to the temperature range of the façades. In this case, Survey B was considered to show the isotherms creation, conducted every 0.25 ◦ C from 23.25 ◦ C to 25.00 ◦ C. The contours can be exported in different file formats such as the broadly-used DXF. The results of the isotherm creation process are presented in the following section. Finally, the ‘Rasterize’ plugin enables the creation of meshes from point clouds through the Delaunay 2.5D triangulation algorithm in the XY plane [ 49 ]. This is a suitable method to create 3D meshes from rather flat point clouds oriented to the Z-axis as in this research. 3. Results In line with the methodology, this section is divided into the different technologies and processes considered in this research, particularly GIS and 3D point cloud data. The reason for not including the IRT results is that the thermograms from Surveys A and B are the method’s data source. Besides, they are already presented in Section 2.1 as an inherent part of the IRT surveys. 3.1. Image Management in GIS The perspective correction was performed as per Section 2.3 to produce a rectangular ROI for the thermogram in Survey A. Nevertheless, given the slab’s thermal bridge in Survey B, the ROI selected included the thermal data of that area in the 3D point cloud (Figure 6). Symmetry 2021, 13, 335 9 of 20 Survey B, the ROI selected included the thermal data of that area in the 3D point cloud (Figure 6). (a) (b) Figure 6. Rectified thermograms from Survey B: (a) Rectangular image; (b) Better-fitted image. In order to avoid duplication of figures, the rectified thermogram from Survey A will be presented in the following section as 3D thermal data. 3.2. 3D Thermal Data Following Section 2.3, an 8-bit monochrome linear gradient height ramp was applied to the point sets, and a factor of 0.10 was next used to scale the Z-axis (temperature) to obtain a more representative 3D thermal data set (better point distribution) (Figures 7 and 8). (a) (b) Figure 7. Isometric view of the 3D thermal data from Survey A: (a) original height-map 3D thermal data; (b) scaled height-map 3D thermal data. Figure 6. Rectified thermograms from Survey B: (a) Rectangular image; (b) Better-fitted image. In order to avoid duplication of figures, the rectified thermogram from Survey A will be presented in the following section as 3D thermal data. 3.2. 3D Thermal Data Following Section 2.3, an 8-bit monochrome linear gradient height ramp was applied to the point sets, and a factor of 0.10 was next used to scale the Z-axis (temperature) to obtain a more representative 3D thermal data set (better point distribution) (Figures 7and 8). Symmetry 2021,13, 335 9 of 18 Symmetry 2021, 13, 335 9 of 20 Survey B, the ROI selected included the thermal data of that area in the 3D point cloud (Figure 6). (a) (b) Figure 6. Rectified thermograms from Survey B: (a) Rectangular image; (b) Better-fitted image. In order to avoid duplication of figures, the rectified thermogram from Survey A will be presented in the following section as 3D thermal data. 3.2. 3D Thermal Data Following Section 2.3, an 8-bit monochrome linear gradient height ramp was applied to the point sets, and a factor of 0.10 was next used to scale the Z-axis (temperature) to obtain a more representative 3D thermal data set (better point distribution) (Figures 7 and 8). (a) (b) Figure 7. Isometric view of the 3D thermal data from Survey A: (a) original height-map 3D thermal data; (b) scaled height-map 3D thermal data. Figure 7. Isometric view of the 3D thermal data from Survey A: ( a ) original height-map 3D thermal data; (b) scaled height-map 3D thermal data. Symmetry 2021, 13, 335 10 of 20 (a) (b) Figure 8. Isometric view of the 3D thermal data from Survey B: (a) original height-map 3D thermal data; (b) scaled height-map 3D thermal data. Also, the top-view visualisation of the 3D height ramp produced shows the (rectified) original thermogram obtained using GIS as per Section 2.2. In turn, this helps to identify in 2D the most significant façade components or parts with the highest temperature and, consequently, those with the greatest energy loss (Figures 9 and 10). Figure 9. Top view of the 3D thermal data from Survey A. Figure 8. Isometric view of the 3D thermal data from Survey B: ( a ) original height-map 3D thermal data; (b) scaled height-map 3D thermal data. Also, the top-view visualisation of the 3D height ramp produced shows the (rectified) original thermogram obtained using GIS as per Section 2.2. In turn, this helps to identify in 2D the most significant façade components or parts with the highest temperature and, consequently, those with the greatest energy loss (Figures 9and 10). Symmetry 2021, 13, 335 10 of 20 (a) (b) Figure 8. Isometric view of the 3D thermal data from Survey B: (a) original height-map 3D thermal data; (b) scaled height-map 3D thermal data. Also, the top-view visualisation of the 3D height ramp produced shows the (rectified) original thermogram obtained using GIS as per Section 2.2. In turn, this helps to identify in 2D the most significant façade components or parts with the highest temperature and, consequently, those with the greatest energy loss (Figures 9 and 10). Figure 9. Top view of the 3D thermal data from Survey A. Figure 9. Top view of the 3D thermal data from Survey A. Symmetry 2021,13, 335 16 of 18 services, or product quality control in the industry. Therefore, the method proposed in this paper is initially more suitable to be applied to (approximately) flat surfaces. This is because a GIS is used in this research to restore the objects’ real dimensions. Thereby, the image distortion is corrected to obtain an orthogonal view that guarantees that the temperature is represented by the Z-axis in an adequate coordinate system. In contrast, in curved and other non-flat objects, the recording of the surface temperature in the IRT survey is affected by the aforementioned directional emissivity [ 30 – 34 ]. This entails that the temperature (Zcoordinate), initially, could not be a reliable value of the 3D thermal data of the object. However, according to Campione et al. [ 58 ], this can be corrected in concave and convex geometries, which increases the possible applications of the proposed method to non-flat objects. 4.4. Future Work Future work on this research involves working on the bodies’ out-of-plane parts and perpendicular faces to combine their 3D thermal data with the main bodies’ data without overlapping. Moreover, an ad hoc script can be developed to automate the analysis of the 3D thermal data produced: the creation of isotherms; the calculation of their area; the calculation of the minimum, maximum and average temperatures; and the corresponding thermal transmittance value. Regarding the future GIS-related work, another possible investigation is related to the design and placement of thermal targets on the façades for IRT recording. Along with the implementation of an algorithm in QGIS, this would automate the image rectification, the homography between the original thermogram and the plane of the façade. In view of the results in this research, the image rectification would be performed by considering non-rectangular thermograms to increase the amount of 3D thermal data. Author Contributions: Conceptualization, D.A. and J.-L.A.-M.; methodology, D.A. and J.-L.A.-M.; software, D.A. and J.-L.A.-M.; validation, D.A. and J.-L.A.-M.; formal analysis, D.A. and J.-L.A.-M.; investigation, D.A. and J.-L.A.-M.; resources, D.A. and J.-L.A.-M.; data curation, D.A. and J.-L.A.-M.; writing—original draft preparation, D.A. and J.-L.A.-M.; writing—review and editing, D.A. and J.-L.A.-M.; visualization, D.A. and J.-L.A.-M.; supervision, D.A. and J.-L.A.-M.; project administration, D.A. and J.-L.A.-M.; funding acquisition, D.A. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Universidad de Sevilla through VI Plan Propio de Investigación y Transferencia (VIPPIT), grant number CONV-822 and VIPPIT-2019-II.3. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study is contained within the article. Acknowledgments: The Authors wish to acknowledge the Departamento de Expresión Gráfica e Ingeniería en la Edificación of Universidad de Sevilla for access to the infrared camera and portable weather station. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. References 1. Sorby, S. Developing 3D spatial visualization skills. Eng. Des. Graph. J. 1999,63, 21–32. 2. Marunic, G.; Glazar, V. Spatial ability through engineering graphics education. Int. J. Technol. Des. Educ. 2013 ,23, 703–715. [CrossRef] 3. Ruiz-Jaramillo, J.; Mascort-Albea, E.; Jaramillo-Morilla, A. Proposed methodology for measurement, survey and assessment of vertical deformation of structures. Struct. Surv. 2016,34, 276–296. [CrossRef] 4. Volk, R.; Stengel, J.; Schultmann, F. 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