Digital Imaging Digital image definition Image a twodimensional

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Digital Imaging

Digital Imaging

Digital image - definition Image = “a two-dimensional function, f(x, y), where x and

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

Image map 512 0 255 512

Image map 512 0 255 512

Image resolution is a measure of the degree to which the digital image represents

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

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

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

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

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

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

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

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

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

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

Signal to noise – shot noise 1000 photons / pixel 10 photons / pixel

Time and noise - tradeoffs • The number of photons collected by the camera

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 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 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

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

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

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.

Presentation of 16 -bit Image in OS Windows

Presentation of 16 -bit Image in OS Windows