# Semantic Component Association within Object Classes Based on Convex Polyhedrons
### The Problem and the Contributions  
The problem addressed in this paper is more precisely stated as follows. Let us consider a database of 3D models of objects belonging to the same class, represented by triangular meshes. There is a number of such datasets that are publicly available. An algorithm selects a small subset of representative objects from this dataset. On each representative object, a human expert annotates the target component specific for a certain task. According to these annotations, the algorithm identifies the semantically corresponding component of each of the remaining models in the database, referred to in this paper as query objects. The proposed approach enables easy and fast expansion of the existing model database with new query objects. In an ideal case, the annotation of a component on a single representative object should be sufficient for identification of all corresponding components in a given object class. However, certain object classes can comprehend objects whose components differ significantly in their shape, size, and position. Therefore, often more than one annotated representative object is required. The focus of our research is computational efficiency, required for practical applications in robotics. Our goal is to develop a method that identifies the target component on a newly perceived object and add this object to the existing database in a few seconds.  
The approach presented in this paper is based on the detection of convex and concave surfaces, referred to in this paper as segments. Components are either represented by one or multiple segments. A selected component of the representative object is associated with the corresponding segments of the other instances of the same object class by constructing a component association graph (CAG). Graph nodes represent all segments of all models from the model database. The nodes are interconnected by edges. The weight of each edge represents a measure of the likelihood that these two segments belong to object components that have the same purpose. This measure is comprised of segment size, shape, position, and neighborhood similarity. The proposed similarity measures are based on the convex template instance (CTI) descriptor, proposed in [3], which describes object segments by approximating their shape with convex polyhedrons. A neighborhood similarity is defined by a novel descriptor, named the topological relation descriptor (TRED), which describes the topological relations between two segments in the model, which is also based on the CTI descriptor. Three methods for associating the selected component of the representative models with the segments of the other instances of the same object class using the CAG are proposed in this paper. The direct segment association method associates each segment according to its nearest neighbor in the CAG. The object-constrained association method associates the segments of the query object with each representative objects using a greedy search and computes the matching score between the query object and all representative object. The associations established between the query object and the representative object with the highest matching score are taken as the final result. The MST-based association method associates the query object segments with the representative object segments based on a minimum spanning tree (MST). As the result of any of these three methods, the selected component of the representative model defined for a certain task is associated with the corresponding segments of all models from the model database.  
Accordingly, the following contributions of this paper are proposed.  
1. A novel computationally efficient approach for establishing associations between components of an object of a given class, based on the component association graph.
2. A novel topologicalrelation descriptor (TRED), which describes the geometrical arrangement of components in a 3D object model.