Lecture 1 Flashcards
Analog to digital
Sampling
Digital to analog
Interpolation
Discrete
Objects are represented in terms of discrete pixels
Continuous
Each color at any image point is reproduced as a single tone
Levels per pixel
Different number of bits 2^bits
Bitdepth
how many values each pixel element can take. The scale in which you convert incoming signal in digital image
RGB bits
24
Noise sources
Photon noise
Thermal noise
Readout noise
Quantization noise
Probability and variance noise
P[X=k]=mean^k*e^-mean/k!
mean=E[X]=VAR[X]
Gaussian noise
Signal independent and additive: sigma0=sigmaB
SNR=mean0-meanB/sigmaB
Poisson noise
signal dependent and modulatory. Standard deviation changes
sigma0=!sigmaB
SNR=mean0-meanB/sigma0
Resolution
Determined by PSF. Formula on slide. Describes what a single point in the object looks like in the image and blurring of it.
Cut off frequency
Lowest distance that can be resolved. fc=1/rc=2NA/lambda
Abbe Criterion
PSF full width at half maximum
da=o.5*lambda/NA
Rayleigh criterion
PSF peak to first zero
dR=0.61*lambda/NA
Zoom
Nearest neighbor: look at value neighbor and take its value
Linear: neighbors average
Cubic: Nice line through the points
Shannon Sampling theorem
to reconstruct a one-dimensional signal from a set of samples, the sampling rate must be equal to or greater than twice the highest frequency in the signal. fn = 1/2Δt
Nyquist interval
rs=rc/2=lambda/4NA
Interpolation
I(x)=(Isg)(x)=sum(Is(i)g(x-i))
Theoretical interpolation
g(x)=sinc(x)=sin(pix)/pix
Practical interpolation
Can be found by inputting an impulse: Is(i)=sigmai is either 1 (i=0) or 0 (else) I(x)=g(x)
Image file formats
- JPEG: image compression is lossy
- GIF: Image compression is lossless but conversion to GIF may give losses
- TIFF: Supports all diminsions and bits, uncompressed, flexible format
