Singular Points of the Gradient Field of the Poisson-Image PDE Solution

Mengzhe Chen

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Date of Award

Spring 2018

Abstract

Poisson partial differential equation (PDE) has applications to industry and academia. One of the Poisson PDE's applications is in the field of active contour models. The researcher's goal for the present study was to use the solution of the Poisson PDE and generate a gradient vector field (PGVF) with several kinds of singular points. To reach the goal, the researcher and her advisor constructed and solved the Poison PDE with a right side, which includes the norm of the image gradient and the image. We call this equation Poisson-Image equation (PIE). The solutions to the PIE generate PGVF, which possesses singular points. Further, we discussed the correspondence between the critical points of the PIE solution u and the singular points of its PGVF. Then, we applied on u the function Ø = u + |�u|2 and proved the mapping between the critical points of u and Ø. The statements proved and correlations derived would be utilized for geometric features detection and object partitioning. The singular points generation method was coded in MATLAB based on the ELPAC software tool used by Bowden and Sirakov (2016). The new tool was validated on a number of synthetic and shape images from (Tari, 2011).

Advisor

Nikolay Metodiev Sirakov

Subject Categories

Mathematics | Physical Sciences and Mathematics

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