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.