Automatic Geometric and Semantic

Reconstruction of Buildings from Images

by Extraction of 3D-Corners and their 3D-Aggregation

Felicitas Lang ,Institute for Photogrammetry, Bonn University

Building Model

Object Model

Buildings reveal a high variability in structure which suggests to represent them as an aggregation of several simple building parts. This enables to cope with the problems caused by occlusions, low contrast, noise and disturbances.

We therefore propose a multi-level part-of hierarchy. It reflects different levels of the envisaged semantic abstraction. The primitives of each aggregation level are specialized by an is-a hierarchy into subclasses.

Each primitive is described by its semantics, its geometry and possibly its physical properties. Its class membership and its relations to other primitives formally describes its semantics. The geometry is described by pose and form parameters.

We at the moment employ four semantic levels for modeling complex buildings, which seems to be sufficient for a large class of buildings.

Fig 1: The different semantic levels of the part-of hierarchy are shown in vertical direction, the different levels of abstraction of the is-a hierarchy in horizontal direction, which is only shown for the 3D-model. The 2D-image model describes the expected appearance of the building in the different levels of the part-of hierarchy, which is indicated by not showing the hidden lines

The first level feature level contains features, namely attributed points, lines and regions. Attributes for lines and regions, for instance, are the orientation classifications horizontal(h), oblique(o) and vertical(v). Regions have an additional attribute describing its role: valid values among others are wall, roof and floor. In general the set of parameters is divided into positional parameters on one hand, describing position and orientation, and form parameters on the other hand like width, height and length.
The second level feature aggregate level contains feature aggregates which are induced by points, lines and regions, and contain all their direct neighbors. Each aggregate is defined by a feature graph, given by a set of features and adjacency relations. A Corner, for instance, contains one point and all its adjacent lines and regions.

Fig 2: shows the corner representation. A corner is composed from object parts of the level features, namely points, lines and regions. On the left side the graph representation is shown.
The third level building part level contains building parts. Currently, they are defined as corner graphs given by a set of corners and adjacency relations. They are parameterized volumetric objects. Each building part has at least one so called plug face which is used for connecting building primitives to each other. We discriminate terminals having exactly one plug face and connectors with two or more plug faces. The level building parts is skipped within the presented work but is comprised within the hierarchy for generality of the approach. For integration of this level we refer to the publications Extracting Buildings from Aerial Images Using Hierarchical Aggregation in 2D and 3D or Integration of 2D and 3D Reasoning for Building Reconstruction using a Generic Hierarchical Model.
The fourth level building level contains complete buildings. Buildings are defined as graphs with building parts as nodes, the arcs representing pairs of building parts connected by corresponding plug elements. Thus, the most simple building consists of two connected terminals. The access to buildings can also be performed skipping the third level and using corners and their connection as shown within this work.

Image Model

The image model describes the appearence of the different components on the corresponding aggregation level. We aim at a coherent representation in object and image space to enable linking image and object components.

Therefore the object model is transferred to the image model for the levels, which are relevant for image analysis. The specialization hierarchy can not be transferred to coherent components in image space as it mainly depends on geometric properties of the components.

On the level of features image components are 2d-points, 2d-lines and 2d regions. The characteristic appearence of these features and their mutual neighbourhood relationship depends on the underlying model, which is used during feature extraction (cf. dissertation C. Fuchs).
For the reconstruction process the level of feature aggregates is of particular importance, because the appearence of corners is fundamental for the transition from image space to object space. The destinction into subclasses can't be performed in image space until the geometric instance of the object model is fixed. We therefore basically use topological and structural characteristics for the classification of feature aggregates, which lead to the destinction into vertices, wings and cells, whereas vertices have the properties of corners.

Fig. 4: shows feature aggregates of type corner, wing and cell, which posses the topologic and structural properties of corners, wings and faces.
The figure shows different vertex appearences depending on the observability of the corner.

Fig. 5: The first row shows the observed features. The second row shows features in the neighbourhood ef the extracted point. a) shows an ideal corner of order 3. b)-d) show different observed corners, which differ from the ideal corner due to disturbances. Features may be missing, partly missing, splitted and merged. Spurious features may exist.

FL - 30.4.99