Fundamentals of digital image processing
Fundamentals of digital image processing
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Level set methods for curvature flow, image enhancement, and shape recovery in medical images
Visualization and mathematics
Digital Image Processing
Advanced algorithmic approaches to medical image segmentation: state-of-the-art application in cardiology, neurology, mammography and pathology
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
IEEE Transactions on Image Processing
A new method for inverse electromagnetic casting problems based on the topological derivative
Journal of Computational Physics
Computers in Biology and Medicine
Multi-object segmentation approach based on topological derivative and level set method
Integrated Computer-Aided Engineering
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The increasing complexity in several fields of science and technology has motivated the use of techniques originally conceived in other areas of applications. An illustrative example of this is given by the topological derivative which quantifies the sensitivity of a problem when the domain under consideration is perturbed by changing its topology. This concept, initially conceived to deal with topology optimization problems, has also been successfully applied to inverse problems and material properties characterization. Our aim in this paper is to present an other field of application for the topological derivative: image processing. An appropriate functional and a variational problem are associated to the cost endowed to an specific image processing application. Thus, the corresponding topological derivative can be used as an indicator function that leads, through a minimization process, to the processed image. We focus our attention on two image processing application. In the first, the topological derivative is used in image restoration, i.e. to restore an image that was somehow degraded (acquisition process, transmission, storage, etc.). Moreover, a novel fully discrete algorithm based on the topological derivative concept is presented. In the second application, we use the topological derivative to derive a ''continuous'' and a fully discrete novel image segmentation algorithms, i.e. for objects identification in an image. Finally and in order to show the performance of these algorithms, several numerical examples are also presented in this work.