Image registration

Question 1

What is image registration

Answer 1

• ‘image matching’
• images of same object taken at different times using different methods
• necessary to compare two objects
• determine unknown geometric transformation (rotated, translated, elastically deformed)

Question 2

Why use image registration

Answer 2

• analyse differences

- combine informations

Question 3

registration framework

Answer 3

• transformation (mapping)
• similarity measure
  optimization

Question 4

Registration in a closed loop:

Answer 4

1 init
2 estimate similarity 
3 check convergence
4 update transformation
5 warp template image -> 2

Question 5

transformation

Answer 5

goal: bring template image with transformation into alignment with reference image

Question 6

types of transformation

Answer 6

• highly dependend on expected spatial changes
• affine-linear
• non-linar

Question 7

Affine linear

Answer 7

• translation only
• rigid transformation (retains size and angular relations; involves translation and rotation)
• scaling (addition of isotropic scale to the rigid transformation)
• affine (preserves lines and parallel lines; angular relations no longer conserved; used when little information about image distortion is known)

Question 8

Non-linear (deformable) transformations

Answer 8

• no matrix representation, can be very complex
• compute image deformations from a fixed number of basis functions defined by the transformation parameters
• m=3 cubic splines (expressed in basis set of polynomials: B-spline)

Question 9

B-spline transformations

Answer 9

+ easy to implement and low complexity
+ computationally efficient
- no strict physical meaning
- knot positions not necessarly information-rich positions

Question 10

common applications of non-linear registration

Answer 10

• tissue motion
• deformation compensation
• longitudinal tissue changes

Question 11

Registration Basis

Answer 11

• extrinsic: (invasive vs. non-invasive)
• intrinsic: uses information available iwithin the images to estimate the transformation (landmark based, surface to surface)

Question 12

intensity based similarity measures

Answer 12

• calculation directly from voxel values
• SSD (sum of squared differences)
• NCC (normalized correlation measures)
• joint entropy
• NMI (normalized mutual information)

Question 13

Sum of squared differences

Answer 13

• subtract each tamplate image voxel from spacial corresponding ref image voxal
• used in academic settings
• unreliable for multi-model registration or registration of contrast varying images

Question 14

Normalized correlation coefficient

Answer 14

• estimates the difference of two statistical distributions in terms of their standard deviations around the mean
• computationally more expensive
• can be used for multimodal registration

Question 15

Information theoretic measures

Answer 15

• measures joint information content of reference and template images
• measured by entropy
• treat image intensities as random variables

Question 16

Joint histogram

Answer 16

• joint entropy, calculated in overlapping points of the image
• stuck in local optima
• maximize mutual information (high marginal entropie, low joint entropy)
• how well does one image explains the other?

Question 17

Optimization of registration

Answer 17

• iterative numerical optimization method
• maximize similarity, minimize error
• problem: getting stuck in local minimum

Question 18

Optimization - Gradient Descent

Answer 18

• analyze gradient of E
• parameter change proportional to negated gradient
• slow close to minimum
• finds local minimum

Question 19

Optimization - Conjugate Gradient Method

Answer 19

• parameter estimation considers estimates from previous steps
• faster convergence than gradient descent

Question 20

Newton Method

Answer 20

• requires finction that is twice differentiable

Question 21

Optimization without using derivative information

Answer 21

• powell method: perform line search to find optimal parameters
• Nelder-Mead Method: downhill simplex, heuristic search for nonlinear optimization

Question 22

Deformable Registration

Answer 22

• often non rigid registration (breathing motion)
• parametric approachers: describe transformation with weighted basis function
• optimization: parameter set and similarity measure for optimization

Question 23

Optical flow

Answer 23

• assumption: given small temporal difference, a moving voxel does not change intensity
• aperture problem: only motion perpendicular to visible structure can be measured

Question 24

Diffeomorphism

Answer 24

• diffeomorphic transformations: invertable, no foldings, preserve topology, essential vor computational anatomy

Question 25

Computational Anatomy

Answer 25

• human anatomy is modeled as a deformable template
• enable invertable mappings between exemplars which are generated vai medical imaging
• compare differences between subjects
• generate probability laws for anatomical variation