The introduction to medicine of techniques coming from areas like Computational Fluid Dynamics, Structural Analysis, and Inverse Problems, made the use of imaging data such us Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Single Photon Emission Tomography (SPECT), Positron Emission Tomography (PET) and Ultrasound (US) mandatory in order to apply this techniques to patient specific data. The process of identification of different tissues and organs, called segmentation, is a maior concern in this analysis. This process can be tedious and time consuming when done by hand, so its been an early concern in image processing to automatize it. Many contributions have been made to the area since the introduction of the Mumford and Shah functional. This functional is endowed to quantify the
associated to a specific segmentation.
Our aim in this paper is to present an image segmentation method based on the configurational derivative of the cost functional
endowed to the image data. The configurational derivative can be viewed as an extension of the well established concept of topological derivative when, instead of a hole, a small inclusion is introduced at a point in the domain. More specifically, for an appropriate functional
is the given image data, a segmentation algorithm is proposed with the following objective: find the segmented image
. Finally, some results are presented in order to show the computational performance of this methodology.