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- W2762458441 abstract "Transporting deformations from a template to a different one is a typical task of the shape analysis. In particular, it is necessary to perform such a kind of transport when performing group-wise statistical analyses in Shape or Size and Shape Spaces. A typical example is when one is interested in separating the difference in function from the difference in shape. The key point is: given two different templates (mathscr {B}_X) and (mathscr {B}_Y) both undergoing its own deformation, and describing these two deformations with the diffeomorphisms (varPhi _X) and (varPhi _Y), then when it is possible to say that they are experiencing the same deformation? Given a correspondence between the points of (mathscr {B}_X) and (mathscr {B}_Y) (i.e. a bijective map), then a naive possible answer could be that the displacement vector (mathbf {u}), associated to each corresponding point couple, is the same. In this manuscript, we assume a different viewpoint: two templates undergo the same deformation if for each corresponding point couple of the two templates the condition (mathbf {C}_X := nabla ^T varPhi _X nabla varPhi _X = nabla ^T varPhi _Y nabla varPhi _Y =: mathbf {C}_Y) holds or, in other words, the local metric (non linear strain) induced by the two diffeomorphisms is the same for all the corresponding points." @default.
- W2762458441 created "2017-10-20" @default.
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- W2762458441 date "2017-10-13" @default.
- W2762458441 modified "2023-09-27" @default.
- W2762458441 title "Transporting Deformations via Integration of Local Strains" @default.
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- W2762458441 doi "https://doi.org/10.1007/978-3-319-68195-5_126" @default.
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