Lecture 5 - Image processing 1

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Calculating image gradients <strong>Image</strong> is given at discrete posi7ons (i,j) But, registra9on requires evalua9on at (x,y) I x(i, j;!), y(i, j;!( )Gradient at (x,y) #%%%%$!I ( x(i, j;"), y(i, j;") )!x!I ( x(i, j;"), y(i, j;") )!y&(((('
Bilinear interpolation (i, j)I ( x, y) = I ( i +! x! , j +! y!)(x, y)= ! xI ( i +1, j +! y!) + ( 1"! x )I ( i, j +! y!)! yI ( i +1, j +1) + ( 1!! y )I ( i +1, j)! x! (1!! x)"(i +1, j +1)!
Page 2: Overview Block 2: Image processi
Page 5 and 6: 1. Mul7ple imaging modali7es Mot
Page 7 and 8: Overview Today: Intra-‐modalit
Page 9 and 10: Problem formulation Image I i, j(
Page 11 and 12: Problem formulation Consider the
Page 13 and 14: Image transformation !#"xy$&%= 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: Example: affine transforma9on !##
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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