Matrix-valued data sets arise in a number of applications including diffusion timberland sale sandals tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour

Consequently, there arises the need to filter and segment such tensor fields. In order to detect edge-like structures in tensor fields, we first generalise Di Zenzo’s concept of a structure tensor for vector-valued images to tensor-valued timberland outlet online data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We timberland boat shoes uk present both two-dimensional and three-dimensional formulations, timberland canada and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite.

We give an interpretation of tensorial mean curvature motion as a process… for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, timberland boots timberland earthkeepers sandals we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image.

Since tensorial active contours incorporate information from all channels, timberland boots canada they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts.

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