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Cons of Gaussian Mixture Models?

Finally, both GMM and K-means work at the voxel level, so none of them can solve the issues of spatial incoherences seen previously in the brain example.

Different criteria can be used in clustering approaches, some include: Minimize cluster distances Maximize cluster distances Cluster by density Cluster by data type

Maximize cluster distances Cluster by density

What is clustering?

- Finding the best way to separate data so intra-group variability is minimal while intra group variability is maximal (Intra-group variability: this is the variability of sample points of the same group) (Inter-group variability: this is the variability of sample points belonging to different groups)

What is a disadvantage of the fuzzy C-means algorithm?

One of the disadvantages of fuzzy c-means is its lack of flexibility to model each group differently Finally, both GMM and K-means work at the voxel level, so none of them can solve the issues of spatial incoherences seen previously in the brain example.

Name a clustering technique that relay on distance metrics and the basic piece of information needed.

Classification of Voxels The information we extract from medical images is voxel intensity

What does supervised segmentation methods assume?

Unsupervised segmentation methods assume that data samples belonging to the same class share similar sample values.

What is the difference between k-means and gaussian mixture models (GMM)?

how k-mean has difficulties to cluster points on the lower parts of the “mouse ears”. This is due to the fact that k-means assumes groups having the same variance, whereas GMM can capture the cluster in a much better way

Pros of Gaussian Mixture Models?

One important difference, highlighted at the beginning of the descriptions for GMM, is its flexibility to model each group independently.

Unsupervised segmentation refers to: Fully unattended automated segmentation Semi attended segmentation without need of manual annotation Automated Segmentation w/o need manually annotated training data Segmentation based on EM algorithm

- Automated Segmentation w/o need manually annotated training data

What is the concept of classification of voxels?

Conceptually we group voxels trying to maximize the “distance” between the groups using voxel intensities this can modeled trough the Image Histogram

On what does the fuzzy C-means algorithm rely?

The algorithm relies on the definition of centroids (c_j) and membership degrees (\mu_ij), modeling the degree of membership of sample x_i to class j.

What is the idea of the Gaussian Mixture Models (GMM)?

- The main idea behind GMM is to model the underlying distribution (i.e., in our running example, the image histogram) as a combination of linearly weighted single Gaussian distributions, with each Gaussian distribution modeled through its own mean and covariance matrix Overlap of distributions is allowed as for the fuzzy c-means

Why is fuzzy C- means (each voxel can have different degrees of membership to a group) interesting for medical image analysis?

Recall from the previous lecture that in medical image analysis, we are dealing with a discreet representation of the reality (i.e. biological tissues), and inaccuracies and limitations in and of the measurements can lead to poor voxel descriptions of tissues (e.g. Partial Volume Effect). Here is where group overlapping can be used to model such (undesired) phenomenon.

What is the fuzzy C- means algorithm?

The Fuzzy* C-means is a generalization of the K-means algorithm. It aims at finding group centers, called centroids, which maximize inter-group distance and minimize intra-group distances. each voxel can have different degrees of membership to each group, enabling in this way the overlap of groups, such a given voxel can be in the transition between two or more different tissue types

What does the 3.0T and T2 mean?

3T à 3 Tesla à magnetic field A 3-tesla magnetic field is twice as powerful as the fields used in conventional high-field MRI scanners, and as much as 15 times stronger than low-field or open MRI scanners. This results in a clearer and more complete image T1-weighted images are produced by using short TE and TR times. The contrast and brightness of the image are predominately determined by T1 properties of tissue. Conversely, T2-weighted images are produced by using longer TE and TR times. In these images, the contrast and brightness are predominately determined by the T2 properties of tissue.

The idea behind fuzzy c-means is to … Iterate between cluster center and membership value updates Maximize voxel like hood based on intensity information Cluster noisy (fuzzy) intensity information using average estimations

Iterate between cluster center and membership value updates

What is the intra-group variability?

Intra-group variability: this is the variability of sample points of the same group

GMM uses the EM algorithm in order to … To speed up the segmentation GMM does not use EM To estimate model parameters and voxel labels To estimate one set of parameters and voxel labels Closed form to estimate voxel lables

To estimate model parameters and voxel labels

What is the inter-group variability?

Inter-group variability: this is the variability of sample points belonging to different groups

What shows an image histogram?

Representation of the frequency of P(i) intensity values i in the image Plot of Numbers of voxels to the voxel intensity

Which two steps build the fuzzy C-means algorithm?

The optimization of the energy term J is iterative and involves two steps. Calculation of membership degrees, and update of centroids.

What are the different criteria and metrics to quantify intra-group variability & inter-group variability

Cluster center (centroid) à distance to centroids à E.g., K-means Distribution models. E.g., Gaussian Mixture Models (GGM) Density models. Cluster = dense area à E.g., mean-shift

How can we use this voxel intensity to quantify distances among sample points?

- The image histogram gives a way to represent how the image intensity is distributed and can give us a notion of groups.

Overlap in defining cluster is used to … Model uncertainty stemming from imaging (e.g., PVE, poor SNR) Not really used as clusters are typically well separated Cope with intensity inhomogeneities

Model uncertainty stemming from imaging (e.g., PVE, poor SNR)

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MIA_Unsupervised_Segmentation