Published electronically January 24, 2020DOI: 10.1137/19S019073
Authors: Aidan Bowman (Socrates Preparatory School, Casselberry, FL) and Jonathan H. Yu (Homeschooled) Sponsor: Dr. Neal Gallagher and Kristina Vuong (Socrates Preparatory School Casselberry, FL)
Abstract: Multiple methods are brought together here. Change of base transformation for fractions, continued products, mixed radix representations, the binary Spigot Algorithm, and repeating decimals are all used to compute a million binary digits of π, and to investigate interesting properties of repeating decimals in arbitrary bases. An Excel spreadsheet utilizes the Spigot algorithm to compute binary digits of π. A Java program listing is also included that can be used to compute a million binary digits of π.
Published electronically January 24, 2020DOI: 10.1137/19S017621
Authors: Jacob Householder (Whittier College)Sponsor: Fredrick Park (Whittier College)
Abstract: Image segmentation is the task of finding salient regions of importance in an image. In this work, we take a curve evolution approach to this problem where we deform an initial curve in the inward normal direction with the objective of finding the boundaries of objects in an image. To achieve this, we propose a variational image segmentation model that incorporates a clique based shape signature with a geodesic active contours energy. The model scheme consists of evolving a parametric representation of an active contour to minimize the penalty that the model induces. This penalty is minimized when the curve is on the boundaries of objects in the image, areas with sudden change in pixel intensity i.e. light to dark. We demonstrate successful capture of illusory contours, segmentation of objects in a cluttered background, and segmentation of occluded objects.