A novel 3-D deformable model based on a geometrically induced external force field is proposed, which can be conveniently generalized to arbitrary dimensions. The external force field is based on hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradients. The evolution of the deformable model is solved using the level set method so that topological changes are handled automatically. The dynamic interaction forces between the geometries can greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and it gives the deformable model a high invariancy in initialization configurations. The bidirectionality of the external force field allows the new deformable model to handle arbitrary cross-boundary initializations, and facilitates the handling of weak edges and broken boundaries. In addition, the new deformable model can effectively overcome image noise, by enhancing the geometrical interaction field with a nonlocal edge-preserving algorithm.

Geometric Potential Force (GPF)

The external force field is called the geometric potential force (GPF) field as it is based on the hypothesized geometrically induced interactions between the relative geometries of the deforming surface and the object boundaries (characterized by image gradients).

GPF: (top) input image and initial deformable model, corresponding edge map, and computed geometric potential field; (middle) initial and evolving deformable models, and (bottom) associated GPF vector field.

Example results - rings segmentation from noisy image

EI model
Proposed GPF model

Example results - shape recovery from synthetic images

Isosurfaces of synthetic shapes
Initializations (yellow)
Geodesic
GGVF
Proposed GPF
Foreground (FG), background (BG) and overal segmentation accuracies of the above synthetic shapes using Geodesic, GGVF and the proposed GPF models.

Example results - shape recovery from weak edges

Example results - segmentation using GPF with arbitrary initialization

Example results - shape recovery from noisy image using GPF

Example results - segmentation of human aorta CT image

Geodesic
GGVF
proposed GPF

Example results - segmentation of cerebral artery MRI image

Geodesic
GGVF
Chan-Vese
proposed GPF

Example results - segmentation of femur CT image

Geodesic
GGVF
Chan-Vese
EI
proposed GPF

Example results - segmentation of multi-branch carotid artery CT image using GPF

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