Lecture 5: Image Registration Flashcards
What is image registration and why is it useful?
Image registration is the process of transforming different sets of data into one coordinate system. Data may be multiple photographs, data from different sensors, times, depths, or viewpoints.
Spatially align two or more images to obtain a common geometric reference in 2D, 3D or 4D.
Explain the difference between mono- and multimodal registration.
- Monomodal registration: All images acquired with the same imaging technique
- Multimodal Registrations: Different imaging techniques
Which criteria can be used to classify different registration algorithms?
- Dimensionality
- Modalities (Mono-/Multimodal)
- Subject/Object
- Transformation
- Extrinsic (external markers) or intrinsic (intensity based or anatomical landmarks) registration.
- Number of images (pairwise / groupwise)
Which transformations do you know and what are the respective
restrictions / degrees of freedom?
- Rigid: Include 3 Transformation and 3 rotation.
6 DOF - Global scale transformation: Include transformation, rotations and single scale parameter.
7 DOF - Affine Transformation: Include translation, rotations, scales, and/or skewing scale parameter
- 9 DOF
- 12 DOF includes both scale and skew parameters in the matrix
Explain the general iterative scheme for image registration! Which steps have to be performed in one iteration?
Find transformation T that maximizes the similarity measure S between If and T(Im).
- Apply current transformation T to the moving image Im
- Compute similarity between images If and T(Im) using the full image content
- Optimize transformation parameters to maximize the similarity criterion (minimize the alignment error)
- Repeat steps 1-3 until convergence
Why are SSD and SAD measures not suited for multimodal registration?
Due to the different intensities of the multimodal image
How could a multimodal approach be modified to be able to use SSD or SAD?
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Explain the idea of using information theoretic similarity measures!
Compare histograms of two images. Where px(i) is the probability of a voxel in image X having the intensity value i
How is entropy defined and what is the general idea of entropy?
Entropy is a measure for the “degree of surprise”, the “degree of disorder”.
Computing the expectation of the information content H(x) yields the average amount of
information needed to specify the state of a random variable, the so called entropy.
Entropy is maximal (not necessarily 1) for uniform distributions and decreases, the more non-uniform (sharply peaked) the distribution gets.
Explain the concept of joint entropy and mutual information! Should those criteria be maximized or minimized for multimodal
registration?
Joint entropy: Minimized if images are aligned
Mutual information: Maximized upon alignment
Which algorithm can be used if point correspondences are available and how does it work?
Closed form for known correspondence.
- Determine the rotation and translation that minimize SSD between corresponding points xi and yi
- Compute the center of mass of each point set
- Center the point sets at the origin before computing the transform, by substracting the respective center of mass from every point
- Compute covariance matrix of the transformed points
- Use Singular Decomposition (SVD) to represent the covariance matrix as rotations and stretching matrices
- Removes the stretching to obtain the final rotation matrix
- To prevent mirroring as the optimal solution, the following adaptation can be used.
How could correspondences be established?
- Correspondence known:
Umeyama method (least squared) - Correspondence unknown:
a. Iterative optimizie the transformation until an optimal alignment is established (Iterative Closest Points)
b. In the presence of noise, use Random Sample Consensus (RANSAC) to discard false correspondence
Explain the iterative closest point algorithm
Correspondence unknown.
- Apply current transformation teta_t to the moving point set and establish correspondences (using the spatial nearest neighbor)
- Estimate new transformation parameter teta_t+1 (Using the SVD method)
- Repeat steps 1 and 2 until convergence
What is the general idea of elastic registration? Which conceptually different methods do you know and how do they (roughly) work?
Elastic registration provides localized stretching of images to correct local non-linear deformations
What is the general idea of spatial transformer networks?
To incoporate spatial transformation to a CNN.
Spatial transformer is differentiable module that applies a spatial transformation to a feature map and can be incorporate to the usual network architecture.
Spatial transformer networks are a generalization of differentiable attention to any spatial
transformation.
Spatial transformer networks allow a neural network to learn how to perform spatial
transformations on the input image in order to enhance the geometric invariance of the
model.
