Nested Topology-preserving geometric deformable model (TGDM)

This implementation of geometric deformable models (GDM) has been designed primarily for cortical surface reconstruction as part of the CRUISE pipeline [2]. It evolves three nested surfaces, maintains the topology of all three, and ensures that the surfaces nest properly (i.e., that the inner surfaces is contained in the central is contained in the outer).

Input Types

This algorithm requires volumes from the "TOADS," "ACE" and "GVF" algorithms as input. The "Output" options for TOADS should be "cruise_input"

Nested TGDM Input: data related parameters

Initial level set	The level set that initializes the GDM. In CRUISE, is typically a topology-corrected white matter mask.
Initial Volume is Membership [0,255]	This option should be true if the initial level set's scale is from 0 to 255 Default: true
White matter membership	The white matter fill membership from TOADS.
Gray matter membership	The gray matter membership from TOADS.
ACE Gray matter membership	The enhanced gray matter membership from ACE.
Thinned ACE Skeleton	The thinned skeleton from ACE.
Gradient Vector Field	The GVF field produced from the ACE enhanced GM membership.
Brain Mask Level Set	Serves as a boundary for the outer surface. Notes: not mandatory
Embedded Inner Surface	Used for tracking if "" option is true. Notes: not mandatory
Tracking	Used for tracking if "Tracking" option is not "Off".
Generate Inner Surface	Will estimate an inner surface if checked.
Generate Central Surface	Will estimate a central surface if checked.
Generate Outer Surface	Will estimate an outer surface if checked.

Nested TGDM Input: other parameters

Initial iso level	Iso level to be used for the initial surface (on a [0,255] scale. Default: 126.9
White matter iso level	Default: 0.6 (on a [0,1] scale)
Gray matter iso level	Default: 0.4 (on a [0,1] scale)
Initial smoothing curvature force	The initial surface is first evolved under a curvature force with the weight specified for regularization purposes. Default: 1.0
Iterations for initial smoothing	The initial surface is first evolved under a curvature force for a number of iterations specified here for regularization purposes. Default: 6
Inner Surface Curvature Force	The inner surface is evolved first using the specified curvature force weight. Default: 0.5
Inner Surface Pressure Force	The inner surface is evolved first using the specified pressure force weight. Default: 1.0
Inner Surface External Force	The inner surface is evolved first using the specified external force weight. Default: 0.0
Iterations for Inner Surface	The inner surface is evolved first using the specified number of iterations. Default: 4
Central Surface Curvature Force	The central surface is evolved next using the specified curvature force weight. Default: 0.15
Central Surface Pressure Force	The central surface is evolved next using the specified pressure force weight. Default: 1.5
Central Surface External Force	The central surface is evolved next using the specified external force weight. Default: 1.0
Iterations for Central Surface	The central surface is evolved next using the specified number of iterations. Default: 7
Outer Surface Curvature Force	The outer surface is evolved last using the specified curvature force weight. Default: 1.0
Outer Surface Pressure Force	The outer surface is evolved last using the specified pressure force weight. Default: 1.0
Outer Surface External Force	The outer surface is evolved last using the specified external force weight. Default: 0.0
Iterations for Outer Surface	The outer surface is evolved last using the specified number of iterations. Default: 7
Connectivity (Foreground,Background)	The digital connectivity rule used in topology preservation. Default: (18,6)
Generate Iso-Surfaces	If true, triangulated meshes representing the iso-surfaces will be generated. Default: true

---

Nested TGDM Outputs

Inner Level Set	The level set volume for the inner surface.
Central Level Set	The level set volume for the central surface.
Outer Level Set	The level set volume for the outer surface.
Signed volume
Sphere Inner Map
Sphere Central Map
Sphere Outer Map
Inner Surface	Triangle mesh for the inner surface.
Central Surface	Triangle mesh for the central surface.
Outer Surface	Triangle mesh for the outer surface.

---

Example Usage
ntgdm_in_gvfx.png

Example input images from TOADS.	Initial Level Set (WM mask)	WM membership	GM membership	CSF membership
Example input images from ACE.	Thinned ACE Skeleton	ACE Enhanced GM membership
Example input images from GVF.	Gradient Vector Field (x component)
Output images	Inner Levelset	Central Levelset	Outer Levelset
Output surfaces	Inner Surface	Central Surface	Outer Surface

---

References

[1] X. Han, C. Xu, and J. L. Prince, "A Topology Preserving Level Set Method for Geometric Deformable Models," IEEE Trans. Patt. Anal. Machine Intell., vol. 25, no. 6, pp. 755-768, 2003.

[2] X. Han, D. L. Pham, D. Tosun, M. E. Rettmann, C. Xu, and J. L. Prince, "CRUISE: cortical reconstruction using implicit surface evolution.," NeuroImage, vol. 23, no. 3, pp. 997-1012, 2004.