## 1 Introduction  
Nowadays, the use of service robots is more frequent in different environments for performing tasks such as: vacuuming floors, cleaning pools or moving the lawn. In order to provide more complex and useful services, robots need to identify different objects in the environment; but also, they must understand the uses, relationships and characteristics of objects in the environment. The extraction of an object's characteristics and its spatial relationships can help a robot to understand what makes an object useful. For example, the largest surfaces of a table and a bed differ in planarity and height; then, modeling object's characteristics can help the robot to identify their differences. A robot with a better understanding of the world is a more efficient service robot. A robot can reconstruct the environment geometry through the extraction of geometrical structures on indoor scenes. Wall, floor or ceiling extractions are already widely used for environment characterization; however, there are few studies on extracting the geometric characteristics of furniture. Generally, the extraction is performed on very large scenes, composed of multiple scans and pointsof view, while we extract the geometric characteristics of furniture from only a single point of view (Figure 1). Human environments are composed of many type of objects. Our study focuses on household furniture that can be moved by a typical human and that is designed to be moved during normal usage. Our study omits kitchen furniture, fixed bookcases, closets or other static or fixed objects; because they can be categorized in the map as fixed components, therefore, the robot will always know their position. The frequency each piece of furniture is repositioned will vary widely: a chair is likely to move more often than a bed. Furthermore, the magnitude of repositioning a piece of furniture will vary widely: the intentional repositioning of a chair will likely move farther than the incidental repositioning of a table. When an object is repositioned, if the robot does not extract the new position of the object and update its knowledge of the environment, then the robot's localization will be less accurate. The main idea is to model these pieces of furniture (offline) in order to detect them on execution time and add them to the map simultaneously, not as obstacles, but as objects with semantic information that the robot could use later. In this work, the object's horizontal or quasi-horizontal planes are key features (Figure 2). These planes are common in home environments: for sitting at a table, for lounging, or to support another object. The main difference between various planes is whether the horizontal plane is a regular or irregular flat surface. For example, the horizontal plane of a dining table or the horizontal plane of the top of a chest of drawers is different from the horizontal plane of a couch or the horizontal plane of a bed. Modeling these planes can help a robot to detect those objects and to understand the world. It can help a robot, for example, to know where it can put a glass of water. This work proposes that each piece of furniture is modeled with graphs. The nodes represent geometrical components, and the arcs represent the relationships between the nodes. Each graph of a piece of furniture has a main node representing a horizontal plane, generally the horizontal plane most commonly used by a human. Furthermore, this principle vertex is normally the horizontal plane a typical human can view from a regular perspective (Figure 2). In our framework, we take advantage of the fact that the horizontal plane most easily viewed by a typical human is usually the horizontal plane most used by a human. The robot has cameras positioned to provide the robot with a point of view similar to the point of view of a typical human. Figure 1: A service robot in a home-like environment. To recognize the furniture, the robot uses an RGB-D camera to acquire three-dimensional data from the environment.