Improvements on contours based segmentation for DNA microarray image processing

In this paper we present an improvement of the Segment Based Contours (SBC) method by implementing a higher order of finite difference schemes in the partial differential equation used in our mathematical model. Two methods are presented: one is a 4th order method and the other a 8th order method. The 4th order method could be applied to segment both the cDNA microarray images and the Affymetrix GeneChips, while the 8th order method could only be applied to processing the cDNA microarray images, due to the limitation of the current image resolution. Additionally, we provide both the mathematical derivations for the partial differential equations (their 4th or 8th order approximations) as well as the validation trough simulations of the microarray images by using real images as seeds for the Nykter's 2006 methodology. We conclude by showing that both the 4th order method as well as the 8th order one are superior to the SBC and the widely used GOGAC method implemented in the Affymetrix standard processing package for microarrays.