Advances in Computational Vision and Medical Image by Chandrajit Bajaj, Samrat Goswami (auth.), João Manuel R. S.

By Chandrajit Bajaj, Samrat Goswami (auth.), João Manuel R. S. Tavares, R. M. Natal Jorge (eds.)

The current e-book comprises prolonged models of papers provided within the foreign convention VIPIMAGE 2007 – ECCOMAS Thematic convention on Computational imaginative and prescient and scientific picture, held in Faculdade de Engenharia da Universidade do Porto, in 17-19 of October 2007. This convention was once the 1st ECCOMAS thematic convention on computational imaginative and prescient and scientific picture processing. It covers issues comparable with photograph processing and research, scientific imaging and computational modeling and simulation, contemplating their multidisciplinary.

This e-book collects the state of the art examine, equipment and new rules with regards to computational imaginative and prescient and scientific snapshot processing contributing for the improvement of those parts of knowledge.

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Additional resources for Advances in Computational Vision and Medical Image Processing: Methods and Applications

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In this chapter, we give a more general framework that is illustrated by different important applications. This section introduces some basic definitions about local metric (a tensor field) on a Riemannian manifold and the associated notion of geodesic distance and minimal paths. The important point is that the geodesic distance to a set of starting points G. D. S. N. V. 2009 29 30 G. D. Cohen satisfies a non-linear differential equation, the Eikonal equation, which is solved to compute numerically the geodesic distance.

1, is a geodesic between x0 and x1 . Over a continuous domain, one can invoke a similar (but weaker) theorem. 2 Geodesic Methods for Shape and Surface Processing 47 Fig. 9 Theorem 7 (Explored area). If the heuristic satisfies V (x) ≤ d(x1 , x), then the geodesic γ ∈ P1 (x0 , x1 ) between x0 and x1 satisfies {γ (t) \ t ∈ [0, 1]} ⊂ {x \ P(x) = U(x) +V (x) ≤ P(x1 )} . This theorem shows why it is important to estimate the geodesic distance by below, since otherwise the region explored by the algorithm might not contain the true geodesic.

For other applications to computer graphics and image processing one can see [6] and [7]. The recent book [8] treats all the details of the geometry of non-rigid surfaces, including geodesic distance computation and shape comparison. One can also see the two books [9,10] that contain review articles with some applications of Fast Marching and geodesic methods and in particular [1]. 1 Front Propagation Algorithms Depending on the properties of the metric, one needs to consider several algorithms, that all rely on the idea of front propagation.

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