1,585 research outputs found
A Generalization of Otsu's Method and Minimum Error Thresholding
We present Generalized Histogram Thresholding (GHT), a simple, fast, and
effective technique for histogram-based image thresholding. GHT works by
performing approximate maximum a posteriori estimation of a mixture of
Gaussians with appropriate priors. We demonstrate that GHT subsumes three
classic thresholding techniques as special cases: Otsu's method, Minimum Error
Thresholding (MET), and weighted percentile thresholding. GHT thereby enables
the continuous interpolation between those three algorithms, which allows
thresholding accuracy to be improved significantly. GHT also provides a
clarifying interpretation of the common practice of coarsening a histogram's
bin width during thresholding. We show that GHT outperforms or matches the
performance of all algorithms on a recent challenge for handwritten document
image binarization (including deep neural networks trained to produce per-pixel
binarizations), and can be implemented in a dozen lines of code or as a trivial
modification to Otsu's method or MET.Comment: ECCV 202
Reparameterizing the Birkhoff Polytope for Variational Permutation Inference
Many matching, tracking, sorting, and ranking problems require probabilistic
reasoning about possible permutations, a set that grows factorially with
dimension. Combinatorial optimization algorithms may enable efficient point
estimation, but fully Bayesian inference poses a severe challenge in this
high-dimensional, discrete space. To surmount this challenge, we start with the
usual step of relaxing a discrete set (here, of permutation matrices) to its
convex hull, which here is the Birkhoff polytope: the set of all
doubly-stochastic matrices. We then introduce two novel transformations: first,
an invertible and differentiable stick-breaking procedure that maps
unconstrained space to the Birkhoff polytope; second, a map that rounds points
toward the vertices of the polytope. Both transformations include a temperature
parameter that, in the limit, concentrates the densities on permutation
matrices. We then exploit these transformations and reparameterization
gradients to introduce variational inference over permutation matrices, and we
demonstrate its utility in a series of experiments
Training Dynamic Exponential Family Models with Causal and Lateral Dependencies for Generalized Neuromorphic Computing
Neuromorphic hardware platforms, such as Intel's Loihi chip, support the
implementation of Spiking Neural Networks (SNNs) as an energy-efficient
alternative to Artificial Neural Networks (ANNs). SNNs are networks of neurons
with internal analogue dynamics that communicate by means of binary time
series. In this work, a probabilistic model is introduced for a generalized
set-up in which the synaptic time series can take values in an arbitrary
alphabet and are characterized by both causal and instantaneous statistical
dependencies. The model, which can be considered as an extension of exponential
family harmoniums to time series, is introduced by means of a hybrid
directed-undirected graphical representation. Furthermore, distributed learning
rules are derived for Maximum Likelihood and Bayesian criteria under the
assumption of fully observed time series in the training set.Comment: Published in IEEE ICASSP 2019. Author's Accepted Manuscrip
A Low Density Lattice Decoder via Non-Parametric Belief Propagation
The recent work of Sommer, Feder and Shalvi presented a new family of codes
called low density lattice codes (LDLC) that can be decoded efficiently and
approach the capacity of the AWGN channel. A linear time iterative decoding
scheme which is based on a message-passing formulation on a factor graph is
given.
In the current work we report our theoretical findings regarding the relation
between the LDLC decoder and belief propagation. We show that the LDLC decoder
is an instance of non-parametric belief propagation and further connect it to
the Gaussian belief propagation algorithm. Our new results enable borrowing
knowledge from the non-parametric and Gaussian belief propagation domains into
the LDLC domain. Specifically, we give more general convergence conditions for
convergence of the LDLC decoder (under the same assumptions of the original
LDLC convergence analysis). We discuss how to extend the LDLC decoder from
Latin square to full rank, non-square matrices. We propose an efficient
construction of sparse generator matrix and its matching decoder. We report
preliminary experimental results which show our decoder has comparable symbol
to error rate compared to the original LDLC decoder.%Comment: Submitted for publicatio
- …