No abstract

Structured spatial point patterns appear in many applications within the natural sciences. The points often record the location of key features, called landmarks, on continuous object boundaries, such as anatomical features on a human face. In other situations, the points may simply be arbitrarily spaced marks along a smooth curve, such as on handwritten numbers. This paper proposes novel exploratory methods for the identification of structure within point datasets. In particular, points are linked together to form curves which estimate the original shape from which the points are the only recorded information. Nonparametric regression methods are applied to polar coordinate variables obtained from the point locations and periodic modelling allows closed curves to be fitted even when data are available on only part of the boundary. Further, the model allows discontinuities to be identified to describe rapid changes in the curves. These generalizations are particularly important when the points represent shapes which are occluded or are intersecting. A range of real-data examples is used to motivate the modelling and to illustrate the flexibility of the approach. The method successfully identifies the underlying structure and its output could also be used as the basis for further analysis.

Seismic studies are a key stage in the search for large scale underground features such as water reserves, gas pockets, or oil fields. Sound waves, generated on the earth’s surface, travel through the ground before being partially reflected at interfaces between regions with high contrast in acoustic properties such as between liquid and solid. After returning to the surface, the reflected signals are recorded by acoustic sensors. Importantly, reflections from different depths return at different times, and hence the data contain depth information as well as position. A strong reflecting interface, called a horizon, indicates a stratigraphic boundary between two different regions, and it is the location of these horizons which is of key importance. This paper proposes a simple approach for the automatic identification of horizons, which avoids computationally complex and time consuming 3D reconstruction. The new approach combines nonparametric smoothing and classification techniques which are applied directly to the seismic data, with novel graphical representations of the intermediate steps introduced. For each sensor position, potential horizon locations are identified along the corresponding time-series traces. These candidate locations are then examined across all traces and when consistent patterns occur the points are linked together to form coherent horizons.

Increasing amounts of image data are being routinely collected as part of the big-data revolution, with applications as diverse as automated security surveillance and dynamic medical imaging. To make best use of the data, the analyses must be automatic and rapid. Simple image properties can be used to highlight specific features in an initial screening or form input to elaborate classification techniques. A key stage in any image analysis is the identification of structure amongst the noise. It is important to realise that noise can be localized, independent and random, or it could contain small-scale structure which, in some ways, resembles the important features-this is called clutter. This paper uses the concept of the Hough transform to convert grey-level images into a more useful feature space representation. This space is searched for high density regions to identify dominant structure whilst taking into account micro-line clutter. Further, a directional distribution is introduced and a resulting dominant direct is proposed as a single structural summary. Many examples of simulated and real data images are used to illustrate the proposed techniques.