Elastic-band Transform and Heavy-snow Transform: New Multiscale Method

Abstract

This thesis presents two multiscale transforms. First proposed transform uses regular observations (eye scanning) with a range of different intervals. The results, termed `elastic-band transformation' can be considered as a collection of observations over various intervals (length of elastic-band) of viewing. Elastic-bands transformation is newly defined. Then, some measures based on elastic-bands are discussed for describing characteristics of data, and multiscale visualizations induced by the measures are developed for understanding and detecting important structures of data. Furthermore, statistical applications such as detection and signal extraction are studied. Secondly proposed transform, termed 'heavy-snow transform', is motivated by observing snow accumulation. Heavy-snow transform provides multiscale visualization which can capture the shape of land (or data structure) with different resolution. Some measures based on heavy-snow transform are newly defined to describe dissimilarity between data and the importance of data. Furthermore, statistical applications such as detection and smoothing are studied.