This chapter deals with an efficient and accurate approach in image segmentation: active contours. The general idea behind this technique is to apply partial differential equations (PDEs) to deform a curve or a surface toward the boundaries of the objects of interest in the image. The deformation is driven by the forces that use information about the objects of interest in the data. In particular, this chapter describes the ideas that have emerged from the geodesic active contours framework, focusing on some of the main models and referring to the literature for other applications. This is an example of using PDEs for image processing and analysis. In this case, such PDEs are derived as gradient-descent processes from geometric integral measures. This research field considers images as continuous geometric structures and enables the use of continuous mathematics such as PDEs and differential geometry. The chapter also discusses the computer image processing algorithms that are actually the numeric implementations of the resulting equations. © 2005 Elsevier Inc. All rights reserved.