Analyzing Spatial Dependence in Functional Data and Shapes of 2D Curves

Oregon Convention Center 

In this work, we model the shapes of spatially dependent functional data or boundaries of two-dimensional (2D) objects, i.e., spatially dependent shapes of parameterized curves. Functional data is often composed of two confounded sources of variation: amplitude and phase. Amplitude captures shape differences among functions while phase captures timing differences in these shape features. Similarly, boundaries of 2D objects represented as parameterized curves exhibit variation in terms of their shape, translation, scale, orientation and parameterization. We study the spatial dependence among functions or curves by first decomposing given data into the different sources of variation. The proposed framework leverages a modified definition of the trace-variogram, which is commonly used to capture spatial dependence in functional data. We propose different types of trace-variograms that capture different components of variation in functional or shape data, and use them to define a functional/shape mark-weighted K function by considering their locations in the spatial domain as random. This statistical summary then allows us to study the spatial dependence in each source of variation separately. Efficacy of the proposed framework is demonstrated through extensive simulation studies and real data applications.

shape

clustering

trace-variogram

kriging 

Section on Statistics in Imaging