Elastic-band transform for visualization and detection

This paper presents a new multiscale transformation for statistical analysis of one-dimensional data such as time series under the concept of the scale-space approach. The proposed method uses regular observations (eye scanning) with a range of different intervals. The new approach, termed ‘elastic-band transform,’ can be considered as a collection of observations over various intervals (length of elastic-band) of viewing. It is motivated by how people look at an object, such as a sequence of data repeatedly to overview a global structure of the object and find some specific features of it. Some measures based on the transformed elastic-bands are discussed for describing characteristics of data, and multiscale visualizations induced by the measures are developed for a better understanding of data. Several numerical experiments are performed to demonstrate the usefulness of the proposed transform for visualization and detection.