An Introduction To Automatic Tissue Classification Of Brain MRI. Colm Elliott Mar 2014

Transcription

1 An Introduction To Automatic Tissue Classification Of Brain MRI Colm Elliott Mar 2014

2 Tissue Classification Tissue classification is part of many processing pipelines. We often want to classify each voxel in an MRI volume as one of white matter (wm), grey matter (gm) or cerebro-spinal fluid (csf).

3 Overview Unsupervised Clustering K-means, Expectation Maximization (EM) Markov Random Fields (MRFs) Atlas based Methods Bayesian Methods How these algorithms relate to available tools (SPM, FSL, Freesurfer)

4 Unsupervised Clustering Class of algorithms to automatically group data into coherent clusters. K-Means and EM are 2 such algorithms. Unsupervised clustering based on MRI intensities is used as a basis for many tissue classification tools.

5 Unsupervised Clustering Class of algorithms to automatically group data into coherent clusters. K-Means and EM are 2 such algorithms. Unsupervised clustering based on MRI intensities is used as a basis for many tissue classification tools.

6 Unsupervised Clustering Class of algorithms to automatically group data into coherent clusters. K-Means and EM are 2 such algorithms. Unsupervised clustering based on MRI intensities used as a basis for many tissue classification tools.

7 Unsupervised Clustering Class of algorithms to automatically group data into coherent clusters. K-Means and EM are 2 such algorithms. Unsupervised clustering based on MRI intensities used as a basis for many tissue classification tools.

8 K-means Clustering Algorithm to find K clusters Each cluster defined by mean value of samples in cluster Assign samples to clusters so as to minimize within-cluster variance For Healthy Brain MRI, usually K = 3, corresponding to white matter, grey matter and and csf.

9 K-means Clustering Begin by initializing clusters. Usually done by choosing K samples that are far away from each other.

10 K-means Clustering We assign samples (voxels) to each cluster based on minimum squared distance (in terms of intensity) to the cluster mean.

11 K-means Clustering We assign samples (voxels) to each cluster based on minimum squared distance (in terms of intensity) to the cluster mean.

12 K-means Clustering We assign samples (voxels) to each cluster based on minimum squared distance (in terms of intensity) to the cluster mean.

13 K-means Clustering Once all samples have been assigned to a cluster, we recompute cluster means

14 K-means Clustering And reassign samples to clusters based on new cluster means

15 K-means Clustering Once all samples have been assigned to a cluster, we recompute cluster means

16 K-means Clustering Once all samples have been assigned to a cluster, we recompute cluster means

17 K-means Clustering Process stops when sample assignments are the same over 2 iterations.

18 K-means Clustering Works well if clusters have similar variance and are well separated in terms of intensity. Computationally fast. Unsupervised. Generally too simplistic for real images.

19 Noisy MRI image K-means Clustering

20 Real MRI image K-means Clustering

21 K-means Clustering Pros Simple Fast Unsupervised Cons Too simple for real and/or noisy MRI images Not probabilistic Can depend on initialization Not generally used in practice

22 EM Expectation-Maximization Conceptually similar to K-means Model distribution of intensities by mixture of weighted Gaussians Each cluster described by Gaussian distribution (mean and std) Weight (frequency of occurrence)

23 EM Provides probabilistic tissue classification Probability of being csf, gm, wm at each voxel Allows for identification of high-confidence voxels Segmentation csf gm wm entropy

24 EM Assume K = 3 Initialize clusters using some reasonable approximate segmentation (e.g. K-Means)

25 EM Compute cluster weights based on frequency of occurrence of each tissue type csf = gm = wm = 0.442

26 EM Fit Gaussian distribution to each cluster

27 EM Fit Gaussian distribution to each cluster

28 EM Use iterative updating scheme similar to K- means E-step: Assign voxels to clusters M-step: Fit gaussian to voxels in each cluster

29 EM Expectation (E-step) Assign each sample to a cluster based on current Gaussian model parameters. Is probabilistic assignment

30 EM Maximization (M-step) Compute weights and fit Gaussians to each cluster based on current tissue probabilities

31 EM Iterate between E-step and M-step until convergence

32 EM Iterate between E-step and M-step until convergence

33 EM

34 EM What if we have a noisier image?

35 EM EM is an upgrade over K-means Models clusters with 3 parameters (mean, variance and weight) instead of 1 Provides probabilistic output Is more computationally expensive than K- means Serves as basis for tissue classification, but not robust to noise if used on its own.

36 Spatial Context Clustering approaches we have seen so far look only at local intensity Any image with same histogram would lead to same clusters Intensity overlap between clusters leads to misclassification No spatial awareness No information about brain

37 Spatial Context Markov Random Fields (MRFs) Incorporate information from neighbouring voxels Can mitigate effect of noise Brain Atlas Incorporate prior knowledge about brain anatomy Can help disambiguate classification when intensity insufficient

38 Markov Random Fields Random Field: undirected graph Connected nodes (voxels) will influence each other Influence is bi-directional Markovianity: Only influenced by immediate neighbours

39 Markov Random Fields

40 Markov Random Fields

41 Markov Random Fields

42 Markov Random Fields

43 Markov Random Fields

44 Markov Random Fields Models relationships between tissue classes of neighbouring voxels. Tissue classification at a given voxel takes into account tissue labels at neighbouring voxels as well as intensity. Favours smoother classification. EM EM + MRF

45 Markov Random Fields Optimization complicated by cyclical dependencies between neighbouring voxels Often use iterative scheme such as ICM (Iterated Conditional Modes) Generate MRF smoothing term based on current tissue class estimates Update tissue class estimates incorporating MRF smoothing term Requires initial solution to be close to correct solution

46 Markov Random Fields wm (intensity) wm (smoothing) wm (overall) Iteration 1 gm (intensity) gm (smoothing) gm (overall)

47 Markov Random Fields wm (intensity) wm (smoothing) wm (overall) Iteration 10 gm (intensity) gm (smoothing) gm (overall)

48 Markov Random Fields Can help reduce misclassification due to noise. Can provide local context when intensity is ambiguous. Simple models tend to oversmooth classifications. More complex models are non-trivial to implement and/or optimize. MRF parameters can tradeoff noise suppression / smoothness.

49 Brain Atlas Brain atlases are constructed by coregistering many individual template brains and constructing an average image. icbm152 is a widely used atlas. Provides model of average healthy brain anatomy. icbm2009c

50 Brain Atlas In addition to creating an average brain image, we can construct tissue probability maps for our atlas by combining tissue classifications from individual templates.

51 Atlas Based Methods By non-linearly registering a brain atlas to a specific subject (or vice versa) we can map our atlas information on to our subject.

52 Atlas Based Methods We can then apply our non-linear transformation to the atlas tissue probability maps to make them subject specific Resultant tissue maps can be used for classification or as a tissue prior.

53 Bayesian Methods Bayes Rule as applied to tissue classification: posterior likelihood prior derived from atlas

54 Bayesian Methods Bayes Rule as applied to tissue classification: posterior likelihood prior derived from intensities

55 Bayesian Methods Bayes Rule as applied to tissue classification: posterior likelihood prior

56 Bayesian Methods Atlas derived tissue prior provides anatomical context. Helps suppress noise induced classification errors that are not anatomically plausible. EM Bayesian

57 Atlas Based Methods Anatomical atlases can provide powerful segmentation tools. Some atlases provide segmentations of individual structures of the brain. Class of algorithms that perform segmentation solely based on atlas and/or pre-segmented templates. Require non-linear registration. Registration never perfect.

58 Bayesian Methods Can blur atlas derived tissue priors to provide robustness against registration errors. Can incorporate MRF on top of Bayesian classification. Bayesian Bayesian + MRF

59 FSL-FAST Uses EM + MRF. Does bias field estimation in tandem with tissue classification. Can incorporate additional sequences. Optional incorporation of atlas priors. Zhang, Y., Brady M. and Smith S.: Segmentation of Brain MR Images Through a Hidden Markov Random Field Model and the Expectation-Maximization Algorithm IEEE TMI 2001 Smith S. et al.: Advances in functional and structural MR image analysis and implementation as FSL NeuroImage 2004

60 SPM8 Uses EM + Atlas Prior Uses multiple Gaussians to model intensity distribution of each tissue class Does bias field correction in tandem with tissue classification Registration to atlas is done based on tissue probabilities (as opposed to intensities) and is part of optimization Ashburner, J. and Friston, K.J.: Unified Segmentation NeuroImage 2005

61 Freesurfer Atlas-based + Intensity + MRF. Considers 40+ structures and not just 3 tissue types. MRF encodes plausible spatial relationships between individual structures. Fischl, B. et al.: Whole Brain Segmentation: Automated Labeling of Neuroanatomical Structures in the Human Brain Neuron 2002 Fischl, B. et al.: Sequence-independent segmentation of magnetic resonance images NeuroImage 2004

62 Summary EM is an unsupervised clustering algorithm often used in tissue classification. MRFs allow us to encode local spatial relationships to suppress noise and provide a smoother tissue classification. Atlas based tissue priors allow us to encode prior anatomical information into our tissue classification.

63 Things I didn t talk about Brain masking NU correction Multi-sequence segmentation Segmentation of individual structures Multi-atlas methods Pathology