We often face the problem of extracting salient and structured information from a noisy data set. We
must handle the presence of multiple structures, and the interaction between them, in noisy, irregularly
clustered data sets. The successful solution relies on the proper implementation of constraints,
particularly the continuity constraint.
We present a unified computational framework that makes use of the continuity constraint to generate
descriptions in terms of surface, regions, curves, and labelled junctions, from sparse, noisy, binary
data in 2-D or 3-D. Each input site can be a point, a point with an associated tangent direction, a point
with an associated tangent vector, or any combination of the above. The methodology is grounded on
two elements: tensor calculus for representation, and voting for communication: each input site
communicates its information (a tensor) to its neighborhood through a predefined (tensor) field, and
therefore casts a (tensor) vote. Each site collects all the votes cast at its location and encodes them into
a new tensor. A local, parallel routine such as a modified marching squares process then
simultaneously detects junctions, curves and region boundaries. The proposed approach is very
different from traditional variational approaches, as it is non-iterative. Furthermore, the only free
parameter is the size of the neighborhood, related to the scale.
We will presents results and demonstrations in 2-D and 3-D, although the formalism is applicable to
higher dimensions.
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