Abstract
Extraction of the cardiac surfaces of interest from multidetector computed tomographic (MDCT) data is a prerequisite step for cardiac analysis, as well as for image guidance procedures. Most of the existing methods need manual corrections, which is timeconsuming. We present a fully automatic segmentation technique for the extraction of the right ventricle, left ventricular endocardium and epicardium from MDCT images. The method consists in a 3D level set surface evolution approach coupled to a new stopping function based on a multiscale directional second derivative Gaussian filter, which is able to stop propagation precisely on the real boundary of the structures of interest. We validated the segmentation method on 18 MDCT volumes from healthy and pathologic subjects using manual segmentation performed by a team of expert radiologists as gold standard. Segmentation errors were assessed for each structure resulting in a surfacetosurface mean error below 0.5 mm and a percentage of surface distance with errors less than 1 mm above 80%. Moreover, in comparison to other segmentation approaches, already proposed in previous work, our method presented an improved accuracy (with surface distance errors less than 1 mm increased of 8–20% for all structures). The obtained results suggest that our approach is accurate and effective for the segmentation of ventricular cavities and myocardium from MDCT images.
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Abbreviations
 O :

Original MDCT volume
 t :

Number of iterations
 c :

Conductance parameter
 U :

Membership function matrix
 C :

Number of classes
 q _{ i } :

Pixel to be processed
 i :

Pixel counts (1 to N)
 l :

Counts of the classes
 v _{l} :

Cluster centroids
 V :

Vector of the cluster centroids (v _{l})
 w :

Weighting exponent
 I :

Anisotropic filtered MDCT volume
 M :

Mean of intensity
 \( \sigma \) :

Standard deviation
 r :

Constant value that controls the capture range
 as :

Alpha shape constant of the concave hull algorithm
 \( \phi 1 \) :

Level set function of the first propagation
 \( \phi 2 \) :

Level set function of the second propagation
 g _{1} :

Stopping function of the first propagation
 g _{2} :

Stopping function of the second propagation
 p _{1} :

Propagation constant of the first evolution
 p _{2} :

Propagation constant of the second evolution
 a _{2} :

Advection constant of the second evolution
 R :

Rotational matrix
 b ^{θ} :

Directional filter
 \( B^{\varTheta } \) :

Battery of 6 directional filters (b ^{θ}) in 6 different directions \( \left\{ {0,\frac{\pi }{6},\frac{\pi }{3},\frac{\pi }{2},\frac{2\pi }{3},\frac{5\pi }{6}} \right\} \)
 \( j_{z}^{\theta } \) :

Result of filtering each slice with b ^{θ}
 J _{ z } :

Image containing in each pixel (x,y) the maximum value in that position among the 6 directions \( \left\{ {0,\frac{\pi }{6},\frac{\pi }{3},\frac{\pi }{2},\frac{2\pi }{3},\frac{5\pi }{6}} \right\} \) of j ^{θ}_{ z }
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Acknowledgements
The work was partially supported by the Italian Ministry of Health GR20091594705. Sofia Antunes is grateful to the Portuguese Foundation for Science and Technology (FCT) by generous funding through the Grant SFRH/BD/69488/2010.
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Associate Editor Joel D. Stitzel oversaw the review of this article.
Appendix
Appendix
Implementation Details
In the following is the list of classes, with brief descriptions, that we used within our method within Python:
Preprocessing

Curvature anisotropic diffusion image filter function from the ITK library was used to compute anisotropic filtering, in order to enhance the local properties of MDCT volumes.
Initialization of the Segmentation Algorithm

Scikitfuzzy toolkit for the Fuzzy C Mean algorithm implementation.

Skeletonize function from Scikitimage toolkit for the skeletonization and point extraction.

Confidence connected image filter implementation of ITK was used to obtain the initial rough segmentation from the seeds extracted in the previously point.
The 3D Level Set Algorithm

Geodesic active contour image filter function from ITK was used for the surface GAC evolution approach.

Numpy and Scipy packages were used to implement the multiscale and directional stopping function g that was given in input to the previously point.
Final Processing

3d alpha shape function from the CGAL library was used to implement the Convex and Concave Hull (Table 4).
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Antunes, S., Esposito, A., Palmisano, A. et al. Cardiac Multidetector CT Segmentation Based on Multiscale Directional Edge Detector and 3D Level Set. Ann Biomed Eng 44, 1487–1501 (2016). https://doi.org/10.1007/s1043901514224
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DOI: https://doi.org/10.1007/s1043901514224