Analysis of Microscopic Images: Boundary Detection Using a Modified Mumford-Shah Model
Arthur Kerst (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Neil Budko – Mentor
Emiel van Elderen – Graduation committee member
Jeroen Spandaw – Graduation committee member
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Abstract
Deformable energy-minimizing contours are used in image analysis, particularly to detect boundaries from objects. From the Mumford-Shah model we derive an equation to move such contours towards the boundary, which minimizes the functional. The external force is computed using the mean value of the inside and outside area of the contour. Various image filtering methods are proposed to enhance this model. We introduce an improved Mumford-Shah model to improve the computational time without losing accuracy. An artificial force is added at the beginning of the simulation to quickly yield an approximation of the contour. Finally, we consider a simplified version of the model, which we solve analytically. The solution is used to find suitable parameters for the model.