Conclusion

Medioni, Gérard; Lee, Mi-Suen; Tang, Chi-Keung

doi:10.1016/b978-044450353-4/50010-x

Cited by 5 publications

(11 citation statements)

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“…The proposed method is built upon the tensor voting framework [ 11 ]. We have extended it by introducing the evaluation of multiple scales and by using complementary sources of information to reduce noisy structures and to improve the connectivity of voxels.…”

Section: Discussionmentioning

confidence: 99%

“…The tensor voting framework [ 11 ] is a robust technique for extracting structures from a cloud of points. It is based on the principle that a set of unconnected tokens (i.e.…”

Section: Methodsmentioning

confidence: 99%

“…A common approach is to assign an isotropic, ball-shaped tensor to each of the tokens [ 11 , 12 ]. All three eigenvalues of a token’s tensor have the same value, .…”

Section: Methodsmentioning

confidence: 99%

“…We therefore only present their formulation (see Appendix 6 ), mentioning that the tensor voting procedure can be regarded as a tensor convolution with a voting kernel which itself produces a tensor. The interested reader is referred to [ 11 , 12 ] for further details.…”

Section: Methodsmentioning

confidence: 99%

“…For the sake of completeness, we present in this section the expressions for SV, PV and BV, the stick, plate and ball votes. Further details on the mathematical derivation of the three expressions can be found in [ 11 , 12 ].…”

Section: Appendix: Stick Plate and Ball Tensor Votingmentioning

confidence: 99%

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Stability, structure and scale: improvements in multi-modal vessel extraction for SEEG trajectory planning

et al. 2015

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PurposeBrain vessels are among the most critical landmarks that need to be assessed for mitigating surgical risks in stereo-electroencephalography (SEEG) implantation. Intracranial haemorrhage is the most common complication associated with implantation, carrying significantly associated morbidity. SEEG planning is done pre-operatively to identify avascular trajectories for the electrodes. In current practice, neurosurgeons have no assistance in the planning of electrode trajectories. There is great interest in developing computer-assisted planning systems that can optimise the safety profile of electrode trajectories, maximising the distance to critical structures. This paper presents a method that integrates the concepts of scale, neighbourhood structure and feature stability with the aim of improving robustness and accuracy of vessel extraction within a SEEG planning system.MethodsThe developed method accounts for scale and vicinity of a voxel by formulating the problem within a multi-scale tensor voting framework. Feature stability is achieved through a similarity measure that evaluates the multi-modal consistency in vesselness responses. The proposed measurement allows the combination of multiple images modalities into a single image that is used within the planning system to visualise critical vessels.ResultsTwelve paired data sets from two image modalities available within the planning system were used for evaluation. The mean Dice similarity coefficient was , representing a statistically significantly improvement when compared to a semi-automated single human rater, single-modality segmentation protocol used in clinical practice ().ConclusionsMulti-modal vessel extraction is superior to semi-automated single-modality segmentation, indicating the possibility of safer SEEG planning, with reduced patient morbidity.

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Section: Discussionmentioning

confidence: 99%

“…The tensor voting framework [ 11 ] is a robust technique for extracting structures from a cloud of points. It is based on the principle that a set of unconnected tokens (i.e.…”

Section: Methodsmentioning

confidence: 99%

“…A common approach is to assign an isotropic, ball-shaped tensor to each of the tokens [ 11 , 12 ]. All three eigenvalues of a token’s tensor have the same value, .…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Appendix: Stick Plate and Ball Tensor Votingmentioning

confidence: 99%

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Stability, structure and scale: improvements in multi-modal vessel extraction for SEEG trajectory planning

et al. 2015

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Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2)

et al. 2013

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To model association fields that underly perceptional organization (gestalt) in psychophysics we consider the problem Pcurve of minimizing for a planar curve having fixed initial and final positions and directions. Here κ(s) is the curvature of the curve with free total length ℓ. This problem comes from a model of geometry of vision due to Petitot (in J. Physiol. Paris 97:265–309, 2003; Math. Inf. Sci. Humaines 145:5–101, 1999), and Citti & Sarti (in J. Math. Imaging Vis. 24(3):307–326, 2006). In previous work we proved that the range of the exponential map of the underlying geometric problem formulated on SE(2) consists of precisely those end-conditions (xfin,yfin,θfin) that can be connected by a globally minimizing geodesic starting at the origin (xin,yin,θin)=(0,0,0). From the applied imaging point of view it is relevant to analyze the sub-Riemannian geodesics and in detail. In this article we show that is contained in half space x≥0 and (0,yfin)≠(0,0) is reached with angle π,show that the boundary consists of endpoints of minimizers either starting or ending in a cusp,analyze and plot the cones of reachable angles θfin per spatial endpoint (xfin,yfin),relate the endings of association fields to and compute the length towards a cusp,analyze the exponential map both with the common arc-length parametrization t in the sub-Riemannian manifold and with spatial arc-length parametrization s in the plane . Surprisingly, s-parametrization simplifies the exponential map, the curvature formulas, the cusp-surface, and the boundary value problem,present a novel efficient algorithm solving the boundary value problem,show that sub-Riemannian geodesics solve Petitot’s circle bundle model (cf. Petitot in J. Physiol. Paris 97:265–309, [2003]),show a clear similarity with association field lines and sub-Riemannian geodesics.

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