A brief history about analytic tools in medical imaging: splines, wavelets, singularities and partial differential equations

We present in this paper a series of operators coming from various domains of mathematical analysis (approximation theory, differential geometry, optimization and partial differential equations (PDE's)) and able to give adequate responses to low level image processing tasks like contrasting, segmenting and contouring objects of interest in bio-medical images. These operators are essentially based on powerful analytic tools, like splines, wavelets, singularities and PDE's, which will be described in a brief historical view.