This thesis presents a GPU implementation of the Livewire algorithm. The algorithm is divided in three phases: Sobel or Laplacian filter convolution, image modeling as a grid graph and solving the non-negative weighted edges single-source shortest path problem. In order to calculate the shortest path, an adapted version of the delta-stepping algorithm was developed for GPUs, using CUDA. A critical result analysis shows that intense speedups are seen in image filtering algorithms. On the other hand, the wide use of dependent device memory look-ups has constrained delta-stepping algorithm from achieving higher performance than CPU implementation although a better performance is expected for wider graphs. Besides showing the viability of the Livewire algorithm implementation, this thesis makes available an open-source image segmentation GPU based application, which can be used as example for future GPU algorithm implementations at http://code.google.com/p/gpuwire/.