# A New Method for the Assessment of Spatial Accuracy and Completeness of OpenStreetMap Building Footprints

^{*}

## Abstract

**:**

^{2}and comprising respectively about 1 million buildings in OSM and 2.8 million buildings in the authoritative dataset. The results of the comparison show that the positional accuracy of the OSM buildings is at least compatible with the quality of the reference dataset at the scale of 1:5000 since the average deviation, with respect to the authoritative map, is below the expected tolerance of 3 m. The analysis of completeness, given in terms of the number of buildings appearing in the authoritative dataset and not present in OSM, shows an average percentage in the whole region equal to 57%. However, worth noting that the opposite, namely the number of buildings in OSM and not in the reference dataset, is not zero, but corresponds to 9%. The OSM building map can therefore be considered to be a valid base map for direct use (territorial frameworks, map navigation, urban analysis, etc.) and for derived use (background for the production of thematic maps) in all those cases where an accuracy corresponding to 1:5000 is required. Moreover it could be used for integrating the authoritative map at this scale (or smaller) where it is not complete and a rigorous quality certification in terms of metric precision is not required.

## 1. Introduction

## 2. Related Work

## 3. Methodology: Spatial Accuracy

_{1}on a map m

_{1}is homologous to a point P

_{2}on a map m

_{2}if the two geographic shapes related to the two points correspond in geometry and semantics.

- -
- The general affine transformation, consisting of a roto-translation with anisotropic variation of scale and skew (six parameters), can be used when there is no information on the reference system of the map to be evaluated and/or the acquisition methods (e.g., digitization of scanned paper maps) may have been homogeneously distorted the map altering the corners (e.g., altering the scale only along the acquisition axis of the scanner);
- -
- The conform transformation, consisting of a roto-translation with isotropic variation of scale (four parameters), can be used when you want to be sure that the transformation does not change the shape of the geometries (preserving the corners of the original map);
- -
- The translation, consisting of a degeneration of the affine transformation in which only the two shifts along the Cartesian axes are estimated (two parameters), can be used when the two maps are not in the same reference system but these are known: it is therefore possible to apply a datum transformation, usually implemented by the most common GIS. In these cases, the translation can compensate for any slight misalignments due to the fact that in some cases these transformation formulas are not rigorous but derived from approximate estimates.

_{1}(i),P

_{2}(k)) is the distance from the point P

_{1}(i) on map m

_{1}to point P

_{2}(k) on map m

_{2}, for each P

_{1}(i) (i = 1, …, N) on m

_{1}we search for the point P

_{2}(k) on m

_{2}which satisfies the condition of minimum distance from P

_{1}(i). If P

_{1}(i) and P

_{2}(k) are “geometrically compatible” (as described in detail below), P

_{1}(i) and P

_{2}(k) are set as homologous points.

_{0}, which can be compared, with a fixed significance level α, with the critical value Fα of a Fisher distribution of (2, n − m) degrees of freedom. The first degree of freedom (the value 2) expresses the fact that we are considering a bi-dimensional problem. In the second degree of freedom, the number of observations used in the least square estimate—i.e., the n coordinates of the n/2 homologous points, and the m transformation parameters (6, 4, or 2, according to the chosen transformation) appear.

_{0}: {P

_{1}is homologous of P

_{2}} can be formulated as follow: if H

_{0}is true then F

_{0}must be smaller than Fα with probability (1 − α), otherwise H

_{0}is false.

_{1}(i) on m

_{1}and the N points P

_{2}(k) (k = 1, …, N) on m

_{2}which satisfy the hypothesis H

_{0}, we selected the pair with smallest F

_{0}.

_{TOL}(see Figure 3).

- manual selection of five homologous points on the two maps m
_{1}and m_{2}; - application of an affine transformation estimated using coordinates of the previous five points;
- repeat
- for each point P
_{1}on the map m_{1}:- search the point P
_{2}on the map m_{2}which satisfies the following conditions:- minimum distance from P
_{1}to P_{2} - the direction angles of all the incoming segments from the point P
_{1}are similar, within a certain tolerance α_{TOL}, to all the incoming segments from the point P_{2} - the inner corner of the edges P
_{1}measured along the perimeter of the polygon in a clockwise orientation is similar, within a certain tolerance α_{TOL}, to the inner corner of the edges P_{2} - if P
_{2}exists, set P_{2}as the homologous point of P_{1}

- application of an affine transformation estimated using the new automatically detected homologous points

- until the count of homologous points converges

- for each point P
_{1}on the map m_{1}:- search the point P
_{2}on the map m_{2}which satisfies the following conditions:- minimum distance from P
_{1}to P_{2} - the direction angles of all the incoming segments from the point P
_{1}are similar, within a certain tolerance α_{TOL}, to all the incoming segments from the point P_{2} - the inner corner of the edges P
_{1}measured along the perimeter of the polygon in a clockwise orientation is similar, within a certain tolerance α_{TOL}, to the inner corner of the edges P_{2}

- if P
_{2}exists, set P_{2}as the homologous point of P_{1}

## 4. Methodology: Completeness

_{data}, was defined. This can be calculated by comparing the number of detected points with the total number of vertices of all the buildings on the two maps (therefore we have two values, corresponding respectively to the former and latter map). Moreover, for dealing with the different levels of detail, to avoid considering missing buildings, a corrective calculation was introduced which does not consider the vertices of the buildings present in the first map that are not represented in the second one when counting the potential homologous pairs (i.e., the total number of vertices of the buildings).

_{data}. These points are called “isolated points”.

_{tol}, already defined to compute the angular compatibility of the vertices, can be used to set the threshold under which not to consider an edge significant and therefore disregard it in the search algorithm.

## 5. The Lombardy Region Case Study

#### 5.1. The Regional Topographical Database (DBT)

^{2}, a population of about 10 million and a population density of 420 people per km

^{2}. This area was chosen because of its high level of urbanization and because of the availability of a good authoritative map to be used for checking the quality of the OpenStreetMap data. The official vector base map of the Lombardy region is named Regional Topographical Database (DBT). The DBT is the digital reference base for all planning tools made both by local authorities and the region, as defined in article 3 of the Regional Law 12/2005 for the Government of the Territory. It is a geographic database comprising various digital territorial information layers that represent and describe the topographic objects of the territory. Its main contents are: buildings, roads, railways, bridges, viaducts, tunnels, natural and artificial watercourses, lakes, dams, hydraulic works, electricity networks, waterfalls, altimetric information (contour lines and elevation points), quarries and landfills, plant covers, etc. Each object consists of a cartographic feature and an alphanumeric table, to which any other descriptive information is added according to the thematic layer: use and state of conservation of the building (residential, industrial, commercial, etc.), type of road surface (asphalted, starred, composite pavement, etc.), type of vegetation (divided into forests, pastures, agricultural crops, urban green, areas without vegetation), etc.

#### 5.2. Zonal Positional Accuracies

^{2}. Considering the total area of the case study, the minimum cell number of a regular grid that contains the whole region is equal to 49 (7 × 7). The irregular shape of the region leaves 11 cells without data. Hence the following results will refer to a sub-dataset of 38 cells instead of 49.

_{OSM}) and in the DBT map (P

_{DBT}). By calculating these two values, it emerged that P

_{OSM}was always significantly greater than P

_{DBT}and it can be explained taking into consideration the redundant points. In the OSM map, the buildings are less detailed than in the DBT map and therefore there are more vertices in the DBT map that do not have a corresponding point in the OSM map. These points cannot be used by the algorithm and the result of the ratio between the number of homologous points detected and the total number of the points in the map inevitably decreases.

_{OSM}, referred to the less detailed map, can be considered a reliability/quality index of the statistics reported in the figure as it represents the correct percentage of used data compared to potentially usable data.

#### 5.3. Positional Accuracies on the Province Capitals

#### 5.4. Completeness

#### 5.5. Performance of the Assessment of Spatial Accuracy and Completeness

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**(

**a**) The regular grid used to analyze the Lombardy region delimited by red line; (

**b**) one example of the OSM map (

**up**) and the DBT map (

**bottom**) of the same place.

**Figure 5.**Homologous points detected without transformation in the search process. (

**a**) Number and percentage of detected points with respect to the total number of OSM points; (

**b**) mean (M) and standard deviation (S) in meters of the distance of the homologous points.

**Figure 6.**Homologous points detected using the general affine transformation in the search process. (

**a**) Number and percentage of detected points with respect to the total number of OSM points; (

**b**) Mean (M) and standard deviation (S) in meters of the distance of the homologous points.

**Figure 7.**(

**a**) OSM buildings identical to the DBT buildings; (

**b**) percentage of identical buildings in each cell with respect to the total number of OSM buildings.

**Figure 8.**(

**a**) Provincial capitals of the Lombardy region; (

**b**) homologous points statistics for each capitals.

**Figure 10.**(

**a**) Percentages of OSM buildings without a corresponding DBT building; (

**b**) percentages of DBT buildings without a corresponding OSM building.

Transformation | Number of Points | M (m) | S (m) | Percentile (m) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

20% | 40% | 60% | 80% | 85% | 90% | 95% | 100% | ||||

None | 3,790,003 | 1.460 | 1.346 | 0.020 | 0.863 | 1.555 | 2.500 | 2.867 | 3.377 | 4.197 | 6.000 |

Translation | 3,797,752 | 1.475 | 1.369 | 0.020 | 0.868 | 1.564 | 2.518 | 2.891 | 3.409 | 4.250 | 7.312 |

Conform | 3,799,273 | 1.478 | 1.374 | 0.020 | 0.870 | 1.565 | 2.522 | 2.895 | 3.416 | 4.260 | 7.729 |

General Affine | 3,800,380 | 1.480 | 1.378 | 0.020 | 0.870 | 1.567 | 2.525 | 2.899 | 3.421 | 4.269 | 9.533 |

Homologous Points Check | Completeness Maps Check | ||||||
---|---|---|---|---|---|---|---|

Number of buildings | Homologous points | Wrong points | Missing points | Number of building | Only in OSM | Only in DBT | Wrong classification |

1140 | 5347 | 172 (3%) | 269 (5%) | 1140 | 570 | 570 | 0 (0%) |

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**MDPI and ACS Style**

Brovelli, M.A.; Zamboni, G.
A New Method for the Assessment of Spatial Accuracy and Completeness of OpenStreetMap Building Footprints. *ISPRS Int. J. Geo-Inf.* **2018**, *7*, 289.
https://doi.org/10.3390/ijgi7080289

**AMA Style**

Brovelli MA, Zamboni G.
A New Method for the Assessment of Spatial Accuracy and Completeness of OpenStreetMap Building Footprints. *ISPRS International Journal of Geo-Information*. 2018; 7(8):289.
https://doi.org/10.3390/ijgi7080289

**Chicago/Turabian Style**

Brovelli, Maria Antonia, and Giorgio Zamboni.
2018. "A New Method for the Assessment of Spatial Accuracy and Completeness of OpenStreetMap Building Footprints" *ISPRS International Journal of Geo-Information* 7, no. 8: 289.
https://doi.org/10.3390/ijgi7080289