Recurrence networks - A novel paradigm for nonlinear time series analysis

This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network which links different points in time if the evolution of the considered states is very similar. A critical comparison of these recurrence networks with similar existing techniques is presented, revealing strong conceptual benefits of the new approach which can be considered as a unifying framework for transforming time series into complex networks that also includes other methods as special cases. It is demonstrated that there are fundamental relationships between the topological properties of recurrence networks and the statistical properties of the phase space density of the underlying dynamical system. Hence, the network description yields new quantitative characteristics of the dynamical complexity of a time series, which substantially complement existing measures of recurrence quantification analysis

From surfaces to objects : Recognizing objects using surface information and object models.

This thesis describes research on recognizing partially obscured objects using surface information like Marr's 2D sketch ([MAR82]) and surface-based geometrical object models. The goal of the recognition process is to produce a fully instantiated object hypotheses, with either image evidence for each feature or explanations for their absence, in terms of self or external occlusion. The central point of the thesis is that using surface information should be an important part of the image understanding process. This is because surfaces are the features that directly link perception to the objects perceived (for normal "camera-like" sensing) and because surfaces make explicit information needed to understand and cope with some visual problems (e.g. obscured features). Further, because surfaces are both the data and model primitive, detailed recognition can be made both simpler and more complete. Recognition input is a surface image, which represents surface orientation and absolute depth. Segmentation criteria are proposed for forming surface patches with constant curvature character, based on surface shape discontinuities which become labeled segmentation- boundaries. Partially obscured object surfaces are reconstructed using stronger surface based constraints. Surfaces are grouped to form surface clusters, which are 3D identity-independent solids that often correspond to model primitives. These are used here as a context within which to select models and find all object features. True three-dimensional properties of image boundaries, surfaces and surface clusters are directly estimated using the surface data. Models are invoked using a network formulation, where individual nodes represent potential identities for image structures. The links between nodes are defined by generic and structural relationships. They define indirect evidence relationships for an identity. Direct evidence for the identities comes from the data properties. A plausibility computation is defined according to the constraints inherent in the evidence types. When a node acquires sufficient plausibility, the model is invoked for the corresponding image structure.Objects are primarily represented using a surface-based geometrical model. Assemblies are formed from subassemblies and surface primitives, which are defined using surface shape and boundaries. Variable affixments between assemblies allow flexibly connected objects. The initial object reference frame is estimated from model-data surface relationships, using correspondences suggested by invocation. With the reference frame, back-facing, tangential, partially self-obscured, totally self-obscured and fully visible image features are deduced. From these, the oriented model is used for finding evidence for missing visible model features. IT no evidence is found, the program attempts to find evidence to justify the features obscured by an unrelated object. Structured objects are constructed using a hierarchical synthesis process. Fully completed hypotheses are verified using both existence and identity constraints based on surface evidence. Each of these processes is defined by its computational constraints and are demonstrated on two test images. These test scenes are interesting because they contain partially and fully obscured object features, a variety of surface and solid types and flexibly connected objects. All modeled objects were fully identified and analyzed to the level represented in their models and were also acceptably spatially located. Portions of this work have been reported elsewhere ([FIS83], [FIS85a], [FIS85b], [FIS86]) by the author