2,014 research outputs found
Performing edge detection by difference of Gaussians using q-Gaussian kernels
In image processing, edge detection is a valuable tool to perform the
extraction of features from an image. This detection reduces the amount of
information to be processed, since the redundant information (considered less
relevant) can be unconsidered. The technique of edge detection consists of
determining the points of a digital image whose intensity changes sharply. This
changes are due to the discontinuities of the orientation on a surface for
example. A well known method of edge detection is the Difference of Gaussians
(DoG). The method consists of subtracting two Gaussians, where a kernel has a
standard deviation smaller than the previous one. The convolution between the
subtraction of kernels and the input image results in the edge detection of
this image. This paper introduces a method of extracting edges using DoG with
kernels based on the q-Gaussian probability distribution, derived from the
q-statistic proposed by Constantino Tsallis. To demonstrate the method's
potential, we compare the introduced method with the traditional DoG using
Gaussians kernels. The results showed that the proposed method can extract
edges with more accurate details.Comment: 5 pages, 5 figures, IC-MSQUARE 201
The Burbea-Rao and Bhattacharyya centroids
We study the centroid with respect to the class of information-theoretic
Burbea-Rao divergences that generalize the celebrated Jensen-Shannon divergence
by measuring the non-negative Jensen difference induced by a strictly convex
and differentiable function. Although those Burbea-Rao divergences are
symmetric by construction, they are not metric since they fail to satisfy the
triangle inequality. We first explain how a particular symmetrization of
Bregman divergences called Jensen-Bregman distances yields exactly those
Burbea-Rao divergences. We then proceed by defining skew Burbea-Rao
divergences, and show that skew Burbea-Rao divergences amount in limit cases to
compute Bregman divergences. We then prove that Burbea-Rao centroids are
unique, and can be arbitrarily finely approximated by a generic iterative
concave-convex optimization algorithm with guaranteed convergence property. In
the second part of the paper, we consider the Bhattacharyya distance that is
commonly used to measure overlapping degree of probability distributions. We
show that Bhattacharyya distances on members of the same statistical
exponential family amount to calculate a Burbea-Rao divergence in disguise.
Thus we get an efficient algorithm for computing the Bhattacharyya centroid of
a set of parametric distributions belonging to the same exponential families,
improving over former specialized methods found in the literature that were
limited to univariate or "diagonal" multivariate Gaussians. To illustrate the
performance of our Bhattacharyya/Burbea-Rao centroid algorithm, we present
experimental performance results for -means and hierarchical clustering
methods of Gaussian mixture models.Comment: 13 page
Detecting self-similarity in surface microstructures
The relative configurational entropy per cell as a function of length scale
is a sensitive detector of spatial self-similarity. For Sierpinski carpets the
equally separated peaks of the above function appear at the length scales that
depend on the kind of the carpet. These peaks point to the presence of
self-similarity even for randomly perturbed initial fractal sets. This is also
demonstrated for the model population of particles diffusing over the surface
considered by Van Siclen, Phys. Rev. E 56 (1997) 5211. These results allow the
subtle self-similarity traces to be explored.Comment: 9 pages, 4 figures, presented at ECOSS18 (Vienna) Sept. 199
Information theoretic thresholding techniques based on particle swarm optimization.
In this dissertation, we discuss multi-level image thresholding techniques based on information theoretic entropies. In order to apply the correlation information of neighboring pixels of an image to obtain better segmentation results, we propose several multi-level thresholding models by using Gray-Level & Local-Average histogram (GLLA) and Gray-Level & Local-Variance histogram (GLLV). Firstly, a RGB color image thresholding model based on GLLA histogram and Tsallis-Havrda-Charv\u27at entropy is discussed. We validate the multi-level thresholding criterion function by using mathematical induction. For each component image, we assign the mean value from each thresholded class to obtain three segmented component images independently. Then we obtain the segmented color image by combining the three segmented component images. Secondly, we use the GLLV histogram to propose three novel entropic multi-level thresholding models based on Shannon entropy, R\u27enyi entropy and Tsallis-Havrda-Charv\u27at entropy respectively. Then we apply these models on the three components of a RGB color image to complete the RGB color image segmentation. An entropic thresholding model is mostly about searching for the optimal threshold values by maximizing or minimizing a criterion function. We apply particle swarm optimization (PSO) algorithm to search the optimal threshold values for all the models. We conduct the experiments extensively on The Berkeley Segmentation Dataset and Benchmark (BSDS300) and calculate the average four performance indices (Probability Rand Index, PRI, Global Consistency Error, GCE, Variation of Information, VOI and Boundary Displacement Error, BDE) to show the effectiveness and reasonability of the proposed models
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