Digital Images & Image Quality

Transcription

1 Introduction to Medical Engineering (Medical Imaging) Suetens 1 Digital Images & Image Quality Ho Kyung Kim Pusan National University Radiation imaging DR & CT: x-ray Nuclear medicine: gamma-ray Ultrasound imaging: ultrasonic waves MRI: RF waves 2

2 Frequency Visible light Electromagnetic (EM) radiation with wavelengths between 400 and 700 nm Each wavelength corresponds to a different color Monochromatic vs. polychromatic colors Monoenergetic vs. polyenergetic energy Waves The speed of EM radiation is constant = (m Hz = m cycles/s = m s -1 ) e.g., What is the frequency () of blue light with a wavelength () of 400 nm? = = ( /) ( /) = s = Hz 3 Energy Particles Photons: the discrete (particle-like) packets (or quanta) of EM energy = h =! h= Plancksconstant = J s= ' kev s kev =.+ () or ev =.+ (,) 4

3 Spectrum As a function of x-ray wavelength 5 Spectrum As a function of x-ray photon energy 6

4 Digitization Sampling (space) + quantization (intensity) Intensity Space Pixel pitch 7 Sampling The conversion from a continuous function to a discrete function retaining only the values at the grid points larger pixel 8

5 Quantization The conversion from analog samples to discrete-value samples 8 bits 7 bits 6 bits 5 bits 4 bits 3 bits 2 bits 1 bit 9 Digital images 8 bits/pixel 4 bits/pixel Sampling and quantization (integer) Dynamic range: the set of possible gray levels Contouring: an artificial looking height How many gray values are needed to produce a continuous-looking image? 10

6 Consider an image expressed with -gray values with intensities.,.,. 1,. 2 e.g., For a 8-bit/pixel image,. = 0,. 2 = 255, and - = 256 Sometimes called the dynamic range= Human eye cannot distinguish subsequent intensities. 1 and. 17 if they differ less than 1% (i.e., ) Therefore, for continuous looking brightness, - = 463(9 bits) for dynamic range = = 694(10 bits) for dynamic range = 1000 Most digital medical images use 4069 gray values (12 bits per pixel) The problem with too many gray values is that small differences in brightness cannot be perceived on the display Gray value transformation (e.g., expanding a small gray value interval into a larger one) 11 Histogram A probability distribution on the set of possible gray levels h. 1 = - : = ;<=>?@ ABC=D EFGBH H>FI GFD;= 3 J K?KFD ;<=>?@ ABC=D Too bright Too dark 12

7 Image quality Resolution Ability to depict details Factors affecting image resolution: the characteristics of imaging systems (focal spot, detector blur) the scene characteristics & geometry (subject shape, position & motion) the viewing conditions Contrast A measure of differences in brightness (or intensity) in adjacent regions Noise Random fluctuations in image intensity Inevitable due to the statistical nature of imaging(emission, detection, conversion) Poisson statistics 13 Artifacts Artificial image features such as dust or scratches in photos May also be introduced by digital image processing (e.g., edge enhancement) Should be avoided or at least understood their origins because they hamper the diagnosis or yield incorrect measurements 14

8 Resolution Point-spread function (PSF), line-spread function (LSF) Full width at half maximum (FWHM) 15 Optical transfer function (OTF) Fourier transform of PSF or LSF Modulation-transfer function (MTF): the amplitude of OTF Spatial frequency: the distinguishable number of line pairs per millimeter (lp/mm) 16

9 Contrast 17 The amplitude of the Fourier transform of an image as a function of spatial frequency Factors affecting image contrast: The imaging process (source intensity & the absorption efficiency or sensitivity of the detector) The scene characteristics (physical properties, size & shape of the object, use of contrast agents) The viewing conditions (room illumination, display equipment) Because the OTF drops off for larger frequencies, the contrast of very small objects will be influenced by the resolution as well 18

10 19 Assuming that the spatial resolution is only determined by the pixel size of a detector, can you estimate the pixel size of the detector providing the following radiograph? 20

11 Noise Signal-to-noise ratio (SNR) A high SNR is no guarantee for a good perceptibility of image objects Contrast-to-noise ratio (CNR) To distinguish the neighboring objects (SNR in terminology of images) Wiener noise-power spectrum: Fourier transform of the autocorrelation of a flat-field image 21 22

12 Both contrast and noise are frequency dependent Image courtesy of Dr. M. J. Yaffe 23 Artifacts 24