Lecture 5 - Image processing 1

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Problem formulation Image Reference Image jjii
Problem formulation Consider the image as a func9on in 3D (here 2D) I x, y ( )(scalar, real valued) We have a discrete representa9on of the func9on I i, j ( )(evaluated at voxel (i,j)) Image transforma9on means • coordinate transforma9on I R( i, j) ~ I ( x = f x(i, j), y = f y(i, j) )• not changing the “image func9on” itself
Page 2: Overview Block 2: Image processi
Page 5 and 6: 1. Mul7ple imaging modali7es Mot
Page 7 and 8: Overview Today: Intra-‐modalit
Page 9: Problem formulation Image I i, j(
Page 13 and 14: Image transformation !#"xy$&%= f i
Page 15 and 16: Rigid registration Angles and le
Page 17 and 18: Affine registration Most general
Page 19 and 20: Optimization problem Determining
Page 21 and 22: Calculating derivatives Calcula9ng
Page 23 and 24: Calculating derivatives !e ij!" k=
Page 25 and 26: Example: affine transforma9on !##
Page 27 and 28: Bilinear interpolation (i, j)I ( x
Page 29 and 30: Consider smoothed image: I SCalcu
Page 31 and 32: Image gradient Image y-‐compon
Page 33 and 34: Local minima Mean Squared Differ

Lecture 5 - Image processing 1

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