Regular Pattern Detection and Analysis Using Shapelets
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The presence of regular patterns in natural and technological phenomena is pervasive, often being present in both time and space. To increase our understanding of many phenomena where patterns are present, measurable quantities or metrics are typically defined and used for quantitative analysis. In many fields of study, methods for robustly computing these metrics do not exist, impeding further progress in these areas. Self-assembled materials is one area where significant advances in microscopy techniques have enabled the generation of detailed imaging of self-assembled domains. Unfortunately, image analysis methods to quantify self-assembly patterns in this imaging data either do not exist or are severely limited in their applicability. With the ability to acquire this data but not quantify it, scientists and engineers face significant challenges in determining relationships between structure and properties of these materials. In this work, a generalized method for the quantitative analysis of pattern images is developed which addresses many of the existing challenges, specifically for the field of self-assembled materials. The presented method is based upon a family of localized functions called shapelets and is fundamentally different from existing approaches. The method is composed of sets of shapelets reformulated to be "steerable" filters and a guided machine learning algorithm. We demonstrate using realistic surface self-assembly data that this approach is able to quantitatively distinguish between uniform (defect-free) and non-uniform (strained, defects) regions within the imaged self-assembled domains. In addition to being a fundamental departure from existing pattern analysis methods, we show that the presented method provides a generalized (pattern agnostic) analysis method with significantly enhanced resolution (pixel-level) compared to existing techniques (pattern feature-level).