cvamia 2004

A Multi-Scale Geometric Flow for Segmenting Vasculature in MRI: 

A Multi-Scale Geometric Flow for Segmenting Vasculature in MRI Maxime Descoteaux1, Louis Collins2, & Kaleem Siddiqi1 1Centre for Intelligent Machines & School of Computer Science 2Brain Imaging Center, Montreal Neurological Institute McGill University, Montréal, Canada

Blood vessel segmentation: 

Blood vessel segmentation Input: 3D medical data set Output: binary volume with 3D vascular tree Automatic Segmentation can be used for Visualization Registration between different modalities Image-guided neurosurgery Pre-surgical planning Large scale clinical studies

Angiographic data: 

Angiographic data Easier problem: sharp bright/dark contrast change only at vessel boundaries

Anatomical data: 

Proton density (PD) weighted MRI Anatomical data Harder problem: several bright/dark contrast changes at boundaries of non-vessel structures

Previous work: 

Previous work Aylward & Bullitt Koller et. al. Wink et. al. Wilson & Noble Krissian et. al. Lorigo et. al. Vasilevskiy & Siddiqi … most show promising results on angiographic data

Geometric flows: 

Geometric flows Work under restrictive assumptions: Initialization based on thresholding original volume No explicit term to model tubular structures Do not take into account the multi-scale nature of vasculature Gradient of image is assumed to be strong ONLY at vessel boundaries

A multi-scale geometric flow: 

A multi-scale geometric flow Introduce a tubular structure model incorporating local vessel centerline orientation and width Extend this measure to the implied vessel boundaries Apply a flux maximizing geometric flow

Local shape description: 

Hessian matrix Encodes shape information, i.e., how the normal to the iso-intensity manifold changes locally Local shape description

Frangi’s multi-scale extension: 

Consider the Hessian matrix at several scales covering the possible vessel widths Use derivatives of Lindeberg’s g-parametrized normalized Gaussian kernels over the different scales =>Compare responses over the different scales s Frangi’s multi-scale extension [Lindeberg, IJCV 98]

Local structure classification : 

blob vs others sheet vs others noise vs others Local structure classification

Frangi’s vesslness measure: 

Maximum along centerlines of tubular structures Close to zero outside vessel-like regions argmax( V(s) ) = radius of vessel Frangi’s vesslness measure [Frangi, MICCAI 98] for all s

Synthetic branch example: 

Synthetic branch example

Cropped MRA region: 

Cropped MRA region

Vesselness measure: 

Vesselness measure

Flux maximizing geometric flow: 

Used to direct the evolution of a curve/surface so that its normals are aligned with a given vector field Flux maximizing geometric flow [Vasilevkiy, Siddiqi, PAMI 02]

Vesselness extension: 

Vesselness extension Distribute the vesselness measure to vessel boundaries => j distribution

Multi-scale geometric flow: 

Consider the vector field The associated flux maximizing flow Multi-scale geometric flow

MRA segmentation: 

MRA segmentation

Gadolinium enhanced MRI: 

Gadolinium enhanced MRI

Qualitative validation: 

slice of PD slice of TOF slice of PC Qualitative validation

Phase contrast angiography: 

PC Vesselness of PC PC masked by segmentation Phase contrast angiography

Time of flight angiography: 

TOF Vesselness of TOF TOF masked by segmentation Time of flight angiography

Proton density weighted MRI : 

PD Vesselness of PD PD masked by segmentation (reversed contrast) Proton density weighted MRI

PC-PD-TOF comparison: 

PC-PD-TOF comparison

Contributions: 

Contributions A new geometric flow which can extract vasculature from standard MRI Visualization of the vasculature by an MIP of the original volume masked by the segmentation Qualitatively, the PD segmentation improves upon results obtained from TOF angiography and is very similar to that obtained from PC angiography Quantitatively…

Key references: 

Key references A. Frangi, W. Niessen, K.L. Vincken, M.A. Viergever. Multi-scale vessel enhancement filtering. Proc. MICCAI'98, pp.130-137, 1998. T. Lindeberg. Edge detection and ridge detection with automatic scale selection. International Journal of Computer Vision, vol 30(2), 1998. A. Vasilevskiy, K. Siddiqi. Flux maximizing geometric flows. IEEE Transactions On Pattern Analysis and Machine Intelligence, vol. 24, 2002. THANK YOU!

Initial curve: 

Initial curve

Final curve: 

Final curve

Key constructions: : 

synthetic tube vesselness measure j-distribution div(V ) Key constructions:

Eigen analysis of the Hessian: 

Eigen analysis of the Hessian We find the direction where there are extreme changes in the normal 1) smallest e-value is close to zero (low curvature along vessel) 2) other two e-values are high and very close (high curvature of circular cross-section)

Eigen analysis of the Hessian: 

Eigen analysis of the Hessian

MRA example: 

MRA example

Surface evolution: 

Surface evolution