Studying large deformations with a Riemannian approach has been an efficient point of view to generate metrics between deformable objects, and to provide accurate, non ambiguous and smooth matchings between images. In this paper, we study the geodesics of such large deformation diffeomorphisms, and more precisely, introduce a fundamental property that they satisfy, namely the conservation of momentum. This property allows us to generate and store complex deformations with the help of one initial "momentum" which serves as the initial state of a differential equation in the group of diffeomorphisms. Moreover, it is shown that this momentum can be also used for describing a deformation of given visual structures, like points, contours or images, and that, it has the same dimension as the described object, as a consequence of the normal momentum constraint we introduce.
A gross datum of the Earth is a single measurable number describing some property of the whole Earth, such as mass, moment of inertia, or the frequency of oscillation of some id...
Abstract It is shown that the time-change of the natural perspective, due to the movement of rigid bodies relative to an observer, conveys information about geometrical properti...
While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, ...
The overall feasibility of 3-D color imaging is determined, taking into account display method, display options, and image processing system. The method is based on the display ...
When a rotating layer of fluid is heated uniformly from below and cooled from above, the onset of instability is inhibited by the rotation. The first part of this paper treats t...
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