We present an approach to structure inference that is model-free,
efficient and capable of simultaneously inferring multiple structures of
different dimensionalities, even from datasets severely contaminated by
noise. Our work so far has focused mostly in perceptual organization in
2-, 3- and 4-D, but we have shown that Tensor Voting can be applied to
problems in higher dimensions, while keeping the computational complexity
at reasonable levels. Regardless of the dimensionality of the space, the
input data are encoded as second-order, symmetric, non-negative definite
tensors that cast votes to their neighboring points. These votes convey
the amount of support of the voter for a structure (such as a curve or a
hyper-surface) that goes through the voter and receiver. No parametric
models are assumed for the underlying structure and the criteria for
determining whether a structure goes through the data are proximity and
good continuation. The accumulation of votes at each input location
results in new tensors, which provide information about the presence of a
structure, as well as its dimensionality and local orientation. Since the
tensors can represent all possible structure types, which range from 0-D
junctions to hyper-volumes, multiple structures of different
dimensionality can be inferred at the same time and interact with each
other. Furthermore, structures of varying dimensionality, which may prove to be
hard for many other methods, can also be handled. Our
experiments have shown that Tensor Voting is very robust to outliers.
Recently, we have investigated multiple-scale implementations of the
framework with promising results in the field of medical imaging. A scale
is considered adequate for a region of the dataset according to local
criteria. Since all processing is local, the computational complexity depends
on the number of neighbors of each input point and remains manageable for
very large numbers of input tokens in high dimensions.
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