PDE Based Algorithms for Smooth Watersheds

Algorithms for PDE-Constrained Optimization

In this paper we review a number of algorithmic approaches for solving optimization problems with PDE constraints. Most of these methods were originally developed for finite dimensional problems. When applied to optimization problems with PDE constraints, new aspects become important. For instance, (discretized) PDE-constrained problems are inherently large-scale. Some aspects, like mesh indepe...

Road Segmentation by Watersheds Algorithms

A road segmentation technique is proposed based on a mathematical morphology tool called watershed transform. Starting from a coarse marker of the road to be segmented, we modify the gradient image of the scene and compute the watershed transform of this image. The result provides a fair segmentation of the road. The marker itself is produced by using the watershed transform, and a simplified r...

Computation of Watersheds Based on Parallel Graph Algorithms

Parallel Algorithms for PDE-Constrained Optimization

PDE-constrained optimization refers to the optimization of systems governed by partial differential equations (PDEs). The simulation problem is to solve the PDEs for the state variables (e.g. displacement, velocity, temperature, electric field, magnetic field, species concentration), given appropriate data (e.g. geometry, coefficients, boundary conditions, initial conditions, source functions)....

Image Restoration Using A PDE-Based Approach

 Image restoration is an essential preprocessing step for many image analysis applications. In any image restoration techniques, keeping structure of the image unchanged is very important. Such structure in an image often corresponds to the region discontinuities and edges. The techniques based on partial differential equations, such as the heat equations, are receiving considerable attention i...