Lecture 5 - Image processing 1

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1. Mul7ple imaging modali7es Motivation different images (CT, MR, PET, …) show different features 2. <strong>Image</strong>s from different 7me points examples: planning CT + cone beam CT in treatment posi9on diagnos9c image + follow-‐up images 3. Atlas registra7on for atlas based segmenta9on
Overview Today: Intra-‐modality registra7on e.g. CT to CT (Hounsfield number is quan9ta9ve) Formulate as op7miza7on problem Problem formula9on <strong>Image</strong> transforma9on Gradient calcula9on Next lecture: Mul7-‐modality registra7on Mutual informa9on
Page 2: Overview Block 2: Image processi
Page 5: 1. Mul7ple imaging modali7es Mot
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 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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