# A Standard Indoor Spatial Data Model—OGC IndoorGML and Implementation Approaches

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## Abstract

**:**

## 1. Introduction

## 2. Related Work on Indoor Spatial Data Models and Standards

#### 2.1. Indoor Spatial Data Models

#### 2.2. Standards for Indoor Spatial Information

## 3. Requirements for Indoor Spatial Data Models

#### 3.1. Indoor Distance

#### 3.2. Complex Structures of Indoor Space

#### 3.3. Cell-Based Context Awareness

#### 3.4. Integrating Multiple Datasets

## 4. Basic Concepts of IndoorGML

#### 4.1. Cellular Space Model

**Definition 1**(Cellular space).

- 1.
- ${c}_{i}\cap {c}_{j}=\left\{\right\}$,
- 2.
- ⋃${c}_{i}\subseteq \mathbb{U}$ and
- 3.
- each cell c has its cell identifier $c.id$.

#### 4.2. Cell Geometry

- Option 1, no geometry: The first option is to exclude any geometric properties from IndoorGML data and to include only topological relationships between cells, which will be explained in the next subsection.
- Option 2, geometry in IndoorGML: The second option is to represent its geometry within IndoorGML data by geometric types defined in ISO 19107. For example, the three-dimensional geometry of a cell is defined as a solid of ISO 19107. Note that the geometry of the cell is an open primitive as defined in ISO 19107, which means that the boundary of the cell geometry does not belong to the cell. This definition is consistent with the non-overlapping condition of the cellular space defined in Section 4.1.
- Option 3, external reference: The third option is to include external references to the object in another dataset that contains geometric data. For example, a cell in IndoorGML data only points to an object in CityGML via the GML identifier that contains geometric properties.

#### 4.3. Topology between Cells

#### 4.4. Cell Semantics

#### 4.5. Multi-Layered Space Model

#### 4.6. Modular Structure of IndoorGML

#### 4.7. Implementation of IndoorGML Core Module

## 5. Cell Determination in IndoorGML

#### 5.1. Cell Determination and Subspacing

- different properties: if a space has different properties such as kitchen area and living room, it is desirable to partition it into two cells with virtual boundaries.
- big space as a cell: if a space is too big, like a long hall-wall or a big convention hall, it is recommended to split it into smaller subspaces.
- sensor coverages: it is also possible to divide a space in terms of sensor coverage, such as CCTV viewshed or WiFi and RFID coverages [29].
- cell without spatial extent: while cells have spatial extents in most cases, there are also cases where no spatial extent is necessarily required except a point. For example, each image spot in a panoramic image service shown in Figure 13 is represented as a cell without spatial extent except a point. Note that the panorama spot image layer is defined as a separate space layer of IndoorGML, and we define inter-layer connections with the cells in the topographic layer. We also assume that each navigation arrow connecting two image spots is considered as an edge in the connectivity graph for the panorama spot image layer, as in Figure 13.

#### 5.2. Thick-Wall Model vs. Thin-Wall Model

#### 5.3. Representing Hierarchical Structures

**Definition 2**(Hierarchical graph).

**Definition 3**(Single-layered graph).

- -
- ${N}_{i}=\{{n}_{i}^{k}\mid {n}_{i}^{k}\mathit{is}\mathit{the}k-\mathit{th}\mathit{node}\mathit{of}{G}_{i}\}$ and
- -
- ${E}_{i}=\{{e}_{i}^{k,l}=({n}_{i}^{k},{n}_{i}^{l})\mid {e}_{i}^{k,l}\mathit{is}\mathit{the}\mathit{edge}\mathit{connecting}\mathit{two}\mathit{nodes}{n}_{i}^{k},{n}_{i}^{l}\in {N}_{i}\}$.

**Definition 4**(Multi-layered graph).

- -
- ${N}_{M}=\bigcup {N}_{i}$,
- -
- ${E}_{M}=(\bigcup {E}_{i})\cup {E}_{I}$, and
- -
- ${E}_{I}=\{({n}_{i}^{k},{n}_{j}^{l})\mid {n}_{i}^{k},{n}_{j}^{l}\in {N}_{i},i\ne j\}$.

**Definition 5**(Hierarchical graph of IndoorGML).

- -
- ${N}_{H}=\bigcup {N}_{i}$,
- -
- ${E}_{M}=(\bigcup {E}_{i})\cup {E}_{I}$,
- -
- ${E}_{I}=\{({n}_{i}^{k},{n}_{i+1}^{l})\mid {n}_{i}^{k}\in {N}_{i},{n}_{i+1}^{l}\in {N}_{i+1},i=0,\dots ,h-1\}$,
- -
- If ${e}_{i,i+1}^{k,l}=({n}_{i}^{k},{n}_{i+1}^{l})\in {E}_{L},\mathit{then}R({n}_{i}^{k},{n}_{i+1}^{l})\in \{EQUAL,INSIDE,COVEREDBY\}$

## 6. Computing Indoor Distance Using IndoorGML

#### 6.1. Horizontal Distance

Algorithm 1. Indoor_Distance ($C,{G}_{D},{G}_{M},p,q$) |

Input: |

- topographic layer C: set of indoor cells with cell geometry, |

- door-to-door (D2D) layer graph ${G}_{D}=({V}_{D},{E}_{D})$, |

- multi-layered space model graph ${G}_{M}=({V}_{M},{E}_{M})$, and |

- starting and ending points $p,q$ |

Output: horizontal indoor distance $dis{t}_{H}$ |

Begin |

1. ${c}_{p}\leftarrow $ the cell containing point p; |

2. ${c}_{q}\leftarrow $ the cell containing point q; |

3. ${D}_{p}\leftarrow \{{d}_{pi}\mid {d}_{pi}\in {V}_{D},({c}_{p},{d}_{pi})\in L\}$ where L is the set of inter-layer connections; |

4. ${D}_{q}\leftarrow \{{d}_{qj}\mid {d}_{qj}\in {V}_{D},({c}_{q},{d}_{qj})\in L\}$; |

5. $DIS{T}_{p}\leftarrow \{dist(p,{d}_{pi})\mid {d}_{pi}\in {D}_{p}\}$; |

6. $DIS{T}_{q}\leftarrow \{dist({d}_{qj},q)\mid {d}_{qj}\in {D}_{q}\}$; |

7. ${P}_{i,j}\leftarrow \{{p}_{i,j}\mid {p}_{i,j}$ is the shortest path from ${d}_{pi}\in {D}_{p}$ to ${d}_{qj}\in {D}_{q}\}$ from D2D layer graph; |

8. $dis{t}_{H}=mi{n}_{i,j}\{dist(p,{d}_{pi})+length\left({p}_{i,j}\right)+dist\left({d}_{jq}\right)\}$ where ${d}_{pi}\in {D}_{p},{d}_{qj}\in {D}_{q}$, and ${p}_{i,j}\in {P}_{i,j}$; |

9. return $dis{t}_{H}$; |

End |

#### 6.2. Vertical Distance

#### 6.3. Multi-Modal Distance

## 7. Context-Awareness by IndoorGML

- Step 1: indoor map matching: ${F}_{IMM}\left(p\right)=c$
- Step 2: context reasoning from staying interval: ${F}_{ST}(c,I)=ct$
- Step 3: context reasoning from visit sequence: ${F}_{VS}\left({v}^{*}\right)=ct$

#### 7.1. Indoor Map Matching by IndoorGML

Algorithm 2. Indoor_Map_Matching_From_Point ($C,{G}_{A},{p}_{0},P\left(k\right),S$) |

Input: |

- topographic layer C: set of indoor cells with cell geometry, |

- accessibility graph ${G}_{A}=({V}_{A},{E}_{A})$, |

- current point ${p}_{0}$ and past trajectory $P\left(k\right)=\{{p}_{-k},{p}_{-(k-1)},\dots {p}_{-2},{p}_{-1}\}$, and |

- sensor readings S. |

Output: current cell c |

Begin |

1. ${c}_{candidate}\leftarrow $ Find $c(\in C)$ containing ${p}_{0}$; |

2. ${c}_{correct}\leftarrow $ Correct ${c}_{candidate}$ by analyzing the past trajectory $P\left(k\right)$ and accessibility graph ${G}_{A}$; |

3. $c\leftarrow $ Improve ${c}_{correct}$ by analyzing other sensor readings; |

4. return c; |

End |

#### 7.2. Context Reasoning from the Staying and Visit Sequence

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**UML class diagram of IndoorGML [4].

**Figure 4.**An example of Poincaré duality [27].

**Figure 5.**Derivation of the adjacency graph from topographic indoor space [4].

**Figure 6.**Cell classification from the indoor navigation viewpoint [4].

**Figure 7.**Example of the multi-layered space model [29].

**Figure 8.**Modular structure of IndoorGML [4].

**Figure 9.**XML schema for CellSpace of IndoorGML [4].

**Figure 10.**XML schema for CellSpaceBoundary of IndoorGML [4].

**Figure 11.**XML schema for State of IndoorGML [4].

**Figure 12.**XML schema for Transition of IndoorGML [4].

**Figure 14.**Thick wall [4].

**Figure 15.**Hierarchical structure and multi-layered space model of IndoorGML. (${d}_{i}$ and ${v}_{j}$ indicate the connections via the i-th door and the j-th virtual boundary, respectively).

**Figure 18.**Multi-modal transportation in an airport. $d{t}_{i}$ indicates a screen door at the train platform.

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Kang, H.-K.; Li, K.-J.
A Standard Indoor Spatial Data Model—OGC IndoorGML and Implementation Approaches. *ISPRS Int. J. Geo-Inf.* **2017**, *6*, 116.
https://doi.org/10.3390/ijgi6040116

**AMA Style**

Kang H-K, Li K-J.
A Standard Indoor Spatial Data Model—OGC IndoorGML and Implementation Approaches. *ISPRS International Journal of Geo-Information*. 2017; 6(4):116.
https://doi.org/10.3390/ijgi6040116

**Chicago/Turabian Style**

Kang, Hae-Kyong, and Ki-Joune Li.
2017. "A Standard Indoor Spatial Data Model—OGC IndoorGML and Implementation Approaches" *ISPRS International Journal of Geo-Information* 6, no. 4: 116.
https://doi.org/10.3390/ijgi6040116