MIA_Registration

What are the steps of ICP?

1. Compute closest points {yi} on Y 2. Register points {xi} to points {yi} 3. Apply resulting transformation to points {xi} 4. Repeat until convergence

Describe the function of the ICP algorithm

ICP algorithm: Pick a set of predefined features in one data set. Choose the closest feature to each in the other data set. Solve the problem, bringing the data sets closer. Repeat the pairing selection until the distance is minimized. Converted to a local minimum Datasets must be “reasonably” close à requires a good initial guess (initialization) Local minima

Image registration is about: Comparing two images Finding a transformation that makes each image unique Finding a transformation that optimize a similarity metric Finding a transformation that minimizing a coast function

-       Finding a transformation that optimize a similarity metric

Image registration happens at the level of… Voxel units Real units (e.g., mm) It doesn’t matter

-       Real units (e.g., mm)

An example of multimodality is.. CT/MR Multiple CT images MR/MR CT/CT of two different patients

-       CT/ MR

A similarity transformation has… 3 parameters 6 parameters 9 parameters 12 parameters

-       9 parameters

What’s the difference between projective and affine transformation? Projective preserves parallelism, length, and angle Projective does not preserves parallelism, length, and angle The are actually the same

Projective does not preserves parallelism, length, and angle

What is a versor and how is it used to describe a rigid transform?

A versor is the turning factor of a quaternion. The change of one vector into another is considered in quaternions and made up of two operations; 1st, the rotation of the first vector so that it shall be parallel to the second. A versor expresses the amount and kind of the rotation. It is denoted geometrically by a line at right angles to the plane in which the rotation takes place, the length of this line being proportioned to the amount of rotation. 2d, the change of length so that the first vector shall be equal to the second. A tensor expresses the second operation. The product of the versor and tensor expresses the total operation, and is called a quaternion.

What's the difference between projective and affine transformations?

The sole difference between these two transformations is in the last line of the transformation matrix. The projective transformation does not preserve parallelism, length, and angle. But it still preserves collinearity and incidence. Since the affine transformation is a special case of the projective transformation (the first two elements of the last line should be zeros), it has the same properties. However unlike projective transformation, it preserves parallelism. Projective transformation can be represented as transformation of an arbitrary quadrangle (i.e. system of four points) into another one. Affine transformation is a transformation of a triangle. Since the last row of a matrix is zeroed, three points are enough.

What are good similarity metric features?

Extremum for correctly aligned images Smooth, best convex Fast computation Differentiable

What are some basic similarity metrics?

SSD/SAD (Sum of Squared Differences & Sum of Absolute Differences Cross Correlation Mutual Information Derivatives

What is the difference between SSD (Sum of Squared Differences) and SAD (Sum of Absolut Differences?

SSD is better against outliers à because of the square there is a much higher penalty for the wider away points SAD à Less sensitive on large intensity differences than SSD E.g., CT scan of bones à SSD to align bone material à bones intensity are very large à if there mistake on registration then there is a very big difference between the high intensity bone and the background If we want to register two images in which one has metal artefacts à SSD is very critical because it would penalize the metal artefact extrem

What is the limitation of SSD?

If there are two more or less identical images but with different illumination, we can have a very unstable SSD matric à pixel intensities are different à high penalty These differences can happen on MRI images because of a coil effect Solution: First normalization of the image and then registration

What is Normalized Cross Correlation?

Normalized Cross Correlation: Expresses the linear relationship between voxel intensities in the two volumes NCC works when there is a linear relationship between the two distributions of intensities à multimodality it will struggle à better solution mutual modality NCC is very fast to calculate and tend to be more robust than SSD E.g, if you have CT and a micro-CT of the same patient (modality with same principle à density) then NCC tents to be a good solution

What is a modern approach for multi-modality registration?

-       Apply sophisticated similarity measures

On what is Mutual Information (MI) based?

Does not assume any type of relationship of intensities. Focuses on structure. Main idea: maximize amount of explained information between images (seen as prob. distributions)

How we have a high entropy?

If we have a uniform distribution à max entropy

When we have a low entropy?

If we have a non-uniform distribution

For what is a joint histogram used?

joint histogram is a useful tool for visualizing the relationship between the intensities of corresponding voxels in two or more images.

How is a joint histogram calculated?

-       Two image as intensity map Overlap the images Plot the intensity values of the first image to the intensity values of the second image Compere where both are spotted