Segmentation

• Task: Assign a label to each pixel/voxel L(x) = S(f(x))

• Info at each pixel: intersity around and in different modalities

  
  

• useful and easy foreground-background substractin, preprocessing method for region of intrest

• Determine the peaks of histogram to get usful threshold

• Otsus threholding method using p: num of pixels in for- and background and intensity variances in groups:

• Global thresholding vs. local

• Multiple objects would require multiple thresholds

• Pixels are clustered by features: intensity, color etc.

• Idea: Automatically assign each pixel to one of N clusters

• + easy to implement

• choice of number of clusters has a main influence

• Methods exist to choose it automatically

• Same as k-means but probabilistic view

• Model intensities as Gaussian mixture model

• E-step: Assume likelihood parameters —> Soft assign labels

  • Compute p(c / I, params)

• M-step: Find thebest mean/std to fit the assigned points:

• Robust, outputs already useful

• - initialization important, num of components important

• Template at a reference frame; provides information

• Deterministic (world atlas); Probabilitic p(c(x)) brain atlas

• Step 1: Align atlas to image using registration

• Step 2: Start with a mixture model —> add atlas information

• Posterior takes into account the atlas and the image intensities

• Step 3: Optimize mean and standard deviation (no need to optimize for class probabilities anymore)

• Much better segmentation, no randomness in components, used commonly, easily generalized to other body parts, can be generalized for other modalities, outlier class added to detect outliers

• - lneeds an atlas for each body part, altlas is very important (diff. age, race, gender,…), image registration accuracy important

• Use many different atlases and aggregate over them —> during aggregate weight atlases based on quality of registration

• Many atlases reduces the importance of a single

• Less likely to have bas registration

• Slves some problems, highly accurate ,state-of-the-art

• Often rquires non-linear registration computationally very expensive

Perform local searches in a sliding window manner

• Dilation: fill gaps

• Erosion : remove islands

• Opening: Erosion followed by Dilation

• Closing: DIlation followed by Erosion

• Formulate neighborhood consistenc in a probabilitic model

• Punish inconsitency in labeling of neighboring voxels

• Joint distribution of labels and intensities:

• MRF: set up prior distribution based on Markovian property

• Defined through energy; d is distance between labels

• Probability distibution given the energy:

• Z is normalization constant —> lower —> enforces consistency

• Hammersley-Clifford Therore: Any probability distribution that satisfoes Markovian probertiy is a Gibbs distribution for an appropriate locally defined energy and vice versa

• Segmentation via posterior maximization:

• Simple implementation, effective

• Solution deends on paams, conitions, could convert slow, complicated optimization