On the Noise and Scale Behaviour of Relational Descriptions

The paper presents a concept for analysing the quality of relational descriptions of digital images. The investigations are based on the relational description automatically derived by a new coherent procedure for feature extraction providing a feature adjacency graph containing points, edges and segments and their relations. A new notion of scale (integration scale) is introduced, relating to a non linear function of the image, providing new stable descriptions. Based on the feature extraction we analysed the quality of the relational descriptions in dependency on the signal-to-noise ratio and on the control parameters of the feature extraction process, i. e. the signiicance level, the smoothing scale and the integration scale. First results on the quality of the features, focussing on their existence, distinct attributes and relations are given. The scope of this research is to predict the quality, especially probabilities of components of the relational description from a few measures depending on noise, scale and local properties of the image content. This is motivated by the applications we are dealing with, namely extracting man-made 2D or 3D structures by grouping procedures or image matching as both tasks are optimization problems where the probability of the unknown 2D or 3D model has to be maximized. 1 Motivation Images may be represented at diierent levels of abstraction , relational descriptions being the most general ones. Therefore deriving relational image descriptions is a fundamental step in automatic scene interpretation. They not only contain features or primitives and their corresponding attributes, but also their mutual topological, geometrical and possibly semantic relations and their attributes. There are many applications relying on relational descriptions such as image matching (cf. Christmas et al. 1994), object or sensor orientation (cf. Vosselman 1992) or object reconstruction and recognition. Figure 1: Relational description within image analysis tasks. For two classical tasks the information ow is shown in Fig. 1. Given two images IA and IB, feature extraction (FEX) leads to the relational descriptions DA and DB. These may be immediately used for relational matching, e. g. in order to derive a 3D-description DO of the scene. Perceptual grouping (GR) may be applied to the initial relational description (cf. Herault and Horaud 1992, Treutler 1992) in order to obtain a relational description which leads to better results in the matching stage. This may be due to the aggregation of features to higher level features or to the increase of consistency within the …