Lecture 5 - Image processing 1

More documents

Recommendations

Info

Most generic algorithm: gradient descent ! t+1 " ! t #! $ !COptimization algorithm $&&! "C =&&&&%#C#" 1!#C#" n'))))))(Note: calcula9ng the gradient is also the basis for more advanced algorithms e.g. Quasi-‐Newton methods
Calculating derivatives Calcula9ng deriva9ves (chain rule) !C!" k=!C# !e ij!e ij!" ki, jinfluence func9on “how much does the error in voxel (i,j) change if the transforma9on parameters change” “how much does the objec9ve func9on change if the error in voxel (i,j) changes” ( ) " I R ( i, j)( )= 2e ij= 2 I x(i, j;!), y(i, j;!
Page 2: Overview Block 2: Image processi
Page 5 and 6: 1. Mul7ple imaging modali7es Mot
Page 7 and 8: Overview Today: Intra-‐modalit
Page 9 and 10: Problem formulation Image I i, j(
Page 11 and 12: Problem formulation Consider the
Page 13 and 14: Image transformation !#"xy$&%= f i
Page 15 and 16: Rigid registration Angles and le
Page 17 and 18: Affine registration Most general
Page 19: Optimization problem Determining
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?