Tracing Branched Curvilinear Structures with a Novel Adaptive Local PCA Algorithm

A vast variety of branched structures differing in size, shape, and function are found in Nature and engineering. Needed are robust and sufficiently general methods for extracting geometric information about structure-function arrangements and relationships from images of branched structures. This paper describes a novel mathematical algorithm called Adaptive Local Principal Component Analysis (ALPCA) for tracing branched curvilinear structures. Utility of this algorithm is demonstrated by its application to quantitative analysis of shape in various plant organs undergoing development. Specifically, time series of digital images representing seedling stems (hypocotyls) responding to light or root systems undergoing branching were automatically analyzed by ALPCA. Automated quantification of such structures changing size and shape will enable algorithmic classification of phenotypes (consequences of altered gene functions) and therefore add a new technological element to the field of plant functional genomics. The general design of ALPCA enables the tracing of gray-scale digital images of other categories of branched structures.