Digital Imaging Digital image definition Image a twodimensional
- Slides: 38
Digital Imaging
Digital image - definition Image = “a two-dimensional function, f(x, y), where x and y are spatial coordinates, and the amplitude of f at any pair of coordinates (x, y) is called the intensity (gray level of the image) at that point. When x, y, and the amplitude values of f are all finite, discrete quantities, we call the image a digital image. ” (Gonzalez and Woods).
Image map
Image map 512 0 255 512
Image resolution is a measure of the degree to which the digital image represents the fine details of the analog image recorded by the microscope. : של התמונה הדיגיטלית נקבעת ע"י שני גורמים ( )רזולוציה • האיכות . המספר הכולל של הפיקסלים בתמונה - Spatial resolution • טווח ערכי הבהירות - Grayscale/Brightness range/Bit-depth. האפשרי לכל פיקסל •
Spatial resolution Changing the resolution of the image without changing bit-depth 512 x 512 256 x 256 128 x 128 64 x 64
Gray level - Bit depth Gray level resolution is a term used to describe the binning of the signal rather than the actual difference we managed to obtain when we quantized the signal. 8 -bit and 16 -bit images are the most common ones, but 10 - and 12 -bit images can also be found. 20=1 21=2 0, 1 Black and White Image 22=4 28=256 0, 1, 2, …. 255 256 Grey Levels Image 210=1024 214=16384 216=65536 הערכים כל . שחור מייצג גבוה הכי והערך לבן מייצג 0 המקרים בכל . אפור של שונות רמות מייצגים שבתווך
Bit depth Black and White (1 bit per pixel) 16 Greys (4 bits per pixel) 256 Greys (8 bits per pixel)
Low level Processing - Grey level display Eye has limited ability to distinguish grey levels/colours Above 32 grey levels images look smooth - 16 and below grey levels eye perceives objectionable banding = false contours. False contouring due to insufficient grey levels http: //www. lenswork. com/calibrate. htm#tones_t
Bit depth Changing the bit-depth of the image without changing spatial resolution 8 bit 4 bit 3 bit 2 bit 1 bit
Contrast a measure of changes in image signal intensity (ΔI) in relation to the average image intensity (I): C = ΔI/ I • the Rayleigh Criterion is not a fixed limit but rather, the spatial frequency at which the contrast has dropped to about 25 percent.
Signal to noise - definitions One of the most important limitations to image quality and image processing S: N ratio = Signal Variation in the signal Noise is NOT: background, auto-fluorescence or dark signal • Good image data has a high S: N ratio
Signal to noise – shot noise Fundamental limit = Poisson distributed statistics of photon detection also known as Shot Noise shot noise is associated with the particle nature of light. n Poisson distributed variation: S: N ratio = √n Statistics of photon counting dictate the minimum useful signal Average signal = 9, S: N ratio = 3 Average signal = 100, S: N ratio = 10 Average signal = 10, 000, S: N ratio = 100 A meaningful difference in intensity needs to be at least three times the noise level Additional sources of noise: digitisation, detector readout, thermal noise.
Signal to noise – shot noise A photon noise simulation, using a sample image as a source and a per-pixel Poisson process to model an otherwise perfect camera (quantum efficiency = 1, no read-noise, no thermal noise, etc). Going from left to right, the mean number of photons per pixel over the whole image is (top row) 0. 001, 0. 1 (middle row) 1. 0, 100. 0 (bottom row) 1, 000. 0, 10, 000. 0 and 100, 000. 0.
Signal to noise – shot noise 1000 photons / pixel 10 photons / pixel
Time and noise - tradeoffs • The number of photons collected by the camera generally determines the amount of noise in your image • Noise = square root (# of photons) • Doubling signal to noise ratio requires 4 -fold increase in exposure
Noise and resolution Theoretical perfect data Two spots separated by diffraction limit
Noise and resolution With shot noise 1000 ph/pixel at peak 10 ph/pixel at peak
Noise and resolution Expected error bars with shot noise 1000 ph/pixel at peak 10 ph/pixel at peak
Noise and resolution • High resolution and precise quantitation both require lots of light • This means bright samples or long exposures • This may cause problems with photobleaching and phototoxicity • Be aware of potential tradeoffs between precision, speed, and photobleaching
Signal to noise - take home messages • The definitions of noise components in image data are confusing. • Noise = variation in signal - you cannot simply subtract a “noise value”. Noise is NOT dark signal or background but they CONTRIBUTE to image noise. Dark signal = generated by camera Has an average value component and a noise (variation) component. Subtracting a dark offset value does not remove the noise component. Background = autofluorescence of sample Is a real fluorescence signal and has associated shot noise. Subtracting an autofluorescence image does not remove the noise.
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