Implementation of a Splitting Finite Difference Scheme to Segment Images with the Solution to the Poisson and Schrödinger Equations


Adam Bowden

Document Type


Degree Name

Master of Science (MS)



Date of Award

Summer 2014


Image segmentation is central to the theory and practice of image analysis and is one of the fundamental concepts in the applications of computer vision and recognition. Of the methods available in this field, some of the most often applied are the active contour models. Broadly, these models fall into three categories based on parametric curves, level sets, or partial differential equations. In this study, research is conducted into new and current active contour methods using partial differential equations and the minimization of energy functionals. Furthermore, new methods implemented and coded in MatLab are demonstrated. First, relevant theory is discussed. Then an original numerical method is shown which evolves a contour to object boundaries by solving the Euler-Lagrange partial differential equation. Next, the solution to Poisson's and Schr?dinger's equations over image data is presented along with their application in defining external energy in active contour methods. Finally, experimental results are given to validate the theory and implementation by applying the coded methods to a set of synthetic and skin lesion images.


Nikolay M. Sirakov

Subject Categories

Mathematics | Physical Sciences and Mathematics