Image Enhancement and Preprocessing

Matching the range:

Sensitive to outliers —> e% of CDF

Solves global intensity shifts

SOlves not the contrast differences

Matching mean and std:

less sensitive to outliers

Intesity shifts but ni contrast difference

Non-linear transformation

Histogram normalization with landmarks

Piecewise mapping

Problem:

• random noise

• imaging artifacts due to imprerfections in aquisition

• fast aquisition

• implants

Additive noise: J(x) = I(x) + e(x)

Multiplicative noise: J(x) = I(x)e(x)

Rician noise in MRI:

Given noisy image J remove noise to get I

Sum: discrete case, integral continuous case

Easy to implement, efficient, linear

Blur edges, not context aware, sensitive to outliers

Linear filters always blur edges while removing noise

For each location, rank all neighboring intensities and reassign the median as result

Sliding window approach as with conv

Other rank filters: min, max, non-linear, not commutative

Robust to outliers, no response to spikes, preserves edges, easy to implement, no new intensities

Patchy results, image content can change (structures etc.)

Takes a mean of all pixels in the image weighted by how similar these pixels are to the target pixel —> use redundancy in image

w(x,y) assess similarity between image information at x and y

Use W(x) instead of all pixels: averaging in a small search window

High noise suppression and preserves edges

may create artifacts, and low efficiency

Denoising as energy minimization problem

lambda: weight coefficient

D(I,J): Data consistency

R(I): Regularization

Acquisition artifact: field inhomogeneity, electrical characteristics of tissue, poor uniformity of coils, gradients and eddy currents, MRI has it

minimal effect on viual interpretation, but high effect on algorithms

Non-linear effect on intenities that vary spatially

Mathematical: j=bi + n —> multiplicative factor

Methods: hardware side, manuallly plaxed landmarks, joint segmentation, N3

c= a+b => fc = fa * fb when a and b are independent random variables

Bias Problem: j(x) = b(x) + i(x)

J(j) = I * B

Step 1: Field estimate - estimate b given i

Step 2: I(i) estimation: J = I * B

• Approximate I by sharpening J

I is only an approximation because filter is only an estimation and we ignored noise

If B too wide inverse filtering may fail —> iterate naby times with a small Gaussian

Problem: Images with different pixel/image size/FOV —> compare heterogeneous images

Reasons: differences in acquisition, FOV; pixel site

! When comparing meas, registration, ML applications

Formula to match pixel sizes: ratio = original pixel size/new pixel size

Important: Use pixel size of each image fro matching

Pad or crop to make the image size the same

Information is stored in DICOM files