A method for interactive recognition of three-dimensional adjacency patterns in point sets, based on relative neighbourhood graphs : an archaeological application
This thesis proposes an exploratory method of spatial analysis oriented to the recognition of adjacency patterns in point sets. The underpinning elements of such method are the relative neighbourhood concept, the retrieval of proximity graphs, the measurement of graph-theoretic relational properties, both at global and local levels; and the visualisation of spatial patterns in three dimensions. This is called Relative Neighbourhood Method of Spatial Analysis, or RN-Method, for short. The method was specifically designed to analyse a special type of archaeological deposit, which we denominate as 'spatial symbolic contexts.' Spatial symbolic contexts are artefact arrangements, ordered in such a way that the literal significance of each item acquires a parallel meaning thanks to its spatial associations with other elements of the set. These appear frequently as a subject of study in archaeology. Unfortunately, before the start of this project, there were not appropriate methods to investigate them. We undertook the challenge of improving such a state of affairs by focusing on the requirements of an interesting study case, namely the Mexica offerings. The Mexica offerings are archaeological deposits which contain a great diversity of ritual objects. The specific arrangement of the items responded to Aztec religious beliefs, whose decipherement is of great relevance for the understanding of such culture. The RN-Method provides formal means to explore the topology of such arrangements as a previous step to interpreting the overall meaning of the caches. These include a graph representation of the offerings in which artefacts correspond to vertices and edges model their spatial adjacency. The specific types of graph used in this thesis are the so-called Relative Neighbourhood Graph, Gabriel Graph, Beta-skeleton, and Limited Neighbourhood Graph. All of them are based on an interesting morphological notion known as relative neighbourhood. This retrieves spatial relations based on the relative position of points, as opposed to their absolute location. In this sense, the concept is different from traditional 'metric' notions such as nearest neighbour. Two major steps of the RN-Method are the visualisation and quantification of global structure, from which it is possible to identify overall similarities or differences in the offerings layout, as well as to make comparisons accross multiple deposits. The method also adopts some measures to assess the relative importance of vertices. Applying such measures to the Mexica offerings, we are able to identify objects located in positions of lower and higher control, as well as objects in integrated and segregated places. In addition, the method includes the application of a visual clustering technique, oriented to the identification of regular combinations of artefacts that may have constituted a 'symbolic theme'. Finally, we illustrate with three offerings the type of interpretation procedure that can be applied to decipher the meaning of these spatial symbolic contexts.