Notes of Medical images

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INTRODUCTION Images can be seen as matrices of parallel measures that highlight biological structures; they can be maps (spatial representation of a physical quantity referred to the body surface), projections (in which each point represents the integral of a physical quantity on the projection line that pass through the internal volume) or tomographies (images from reconstruction of virtual sections of the body representing different physical quantities) Generation and processing of medical images: Different energy forms can interact with body tissues in order to generate images: ionizing radiation (X-Rays: RX and CT), γ-rays (single photon emission: scintigraphy and SPECT, positron emission: PET), radio waves in magnetic field (MRI), mechanical energy (ultrasounds: echography) Images are 2D functions defined on a discrete domain made by couples of x and y coordinates, called sampling grid; spatial resolution h is the minimum dimension of the structures which are recognizable in the image system; maximum spatial frequency that can be represented is f = 1/2h The real representation of the point in the 2D domain is not an ideal impulse but it assumes a bell shape, the Point Spread Function (PSF); the parameter characterizing the PSF is the FWHM (full width at half maximum); for an arbitrary form of the PSF, two point sources can be resolved when their separation is less than their FWHM; if the system is linear and space-invariant (LSI), the real image is the spatial convolution between the original (ideal) image and the PSF The 2D Fourier Transform of the PSF is the Modulation Transfer Function (MTF); the MTF of a bell- shaped PSF is a low-pass frequency response, as it blurs the smallest objects in the image, introducing a limitation to the spatial resolution The main…