1. Level Set Segmentation 9.3.6 ~ 9.37 Ki-Chang Kwak

2. Laplacian Level Set Segmentation The itk::LaplacianSegmentationLevelSetImageFilter defines a speed term based on second derivative features in the image. The speed term is calculated as the Laplacian of the image values. The goal is to attract the evolving level set surface to local zero-crossings in the Laplacian image. The speed term for the LaplacianSegmentationLevelSetImageFilter is constructed by applying the itk::LaplacianImageFilter to the input feature image. One nice property of using the Laplacian is that there are no free parameters in the calculation.

3. Laplacian Level Set Segmentation

4. erf

5. LaplacianSegmentationLevelSetImageFilter level set equation can be weighted by scalars. For this application we will modify the relative weight of the propagation term. The curvature term is not used in this filter.

6. Results of applying LaplacianSegmentationLevelSetImageFilter Original imagemodel imageIteration : 10 Iteration : 20 Jagged edges are straightened and the small spur at the right-hand side of the mask has been removed.

7. Geodesic Active Contours Segmentation With Shape Guidance The source code for this section can be found in the file Examples/segmentation/GeodesicActiveContourShapePrioriLevelSetImageFilter.cxx In medical imaging applications, the general shape, location and orientation of an anatomical structure of interest is typically known a priori. This information can be used to aid the segmentation process especially when image contrast is low or when the object boundary is not distinct.

8. Geodesic Active Contours Segmentation With Shape Guidance

9. ShapePriorMAPCostFunction The cost fuunction is composed of composed of Four terms -Contour fit measures the likelihood of seeing the current evolving contour for a given set of shape/pose parameters. This is computed by Counting the number of pixels inside the current Contour but outside the current shape. -Image fit measures the likelihood of seeing Certain image features for a given set of shape/ pose parameters. This is computed by assuming that (1 – edge potential) approximates a zero- mean, unit variance Gaussian along the normal of the evolving contour.

10. ShapePriorMAPCostFunction Where G is a zero-mean, unit variance Gaussian and g is the edge potential feature image. The pose parameters are assumed to have a uniform distribution and hence do not contribute to the cost function. The shape parameters are assumed to have a Gaussian distribution. Maximum A Posteriori Estimation Goal : knowing a priori estimate p(θ) compute the posterior estimate p(θ|D)

11. OnePlusOneEvolutionaryOptimizer Strategy that simulates the biological evolution of a set of samples in the search space. This optimizer is mainly used in the process of bias Correction of MRI images.

12. Euler2DTransform -itk:Euler2DTransform implements a rigid transformation in 2D. It is composed of a plane Rotation and a two-dimensional translation. The first parameter is the angle in radians and the last two parameters are the translation in each dimension.

13. PCAShapeSignedDistance The itk::PCAShapeSignedDistanceFunction represents a statistical shape model defined by a mean signed distance and the first K principal components modes.

14. For debugging purposes it is quite helpful to track the evolution of the segmentation as it progresses. The following defines a custom itk::Command class for monitoring the RMS change and shape parameters at each iteration.

22. The input image to the GeodesicActiveContourShapePrioriLevelSetImageFilter is a Synthesized MR-T1 mid-sagittal slice (217 × 180 pixels, 1 × 1 mm spacing) of the Brain(left) and the initial best-fit shape(right) chosen to roughly overlap the corpus Callosum in the image to be segmented.

23. It can be observed that without shape guidance (left), segmentation using geodesic active contour leaks in the regions where the corpus callosum blends into the surrounding brain tissues. With shape guidance (center), the segmentation is constrained by the global shape model to prevent leaking.