42,738 research outputs found
The shape of primordial non-Gaussianity and the CMB bispectrum
We present a set of formalisms for comparing, evolving and constraining
primordial non-Gaussian models through the CMB bispectrum. We describe improved
methods for efficient computation of the full CMB bispectrum for any general
(non-separable) primordial bispectrum, incorporating a flat sky approximation
and a new cubic interpolation. We review all the primordial non-Gaussian models
in the present literature and calculate the CMB bispectrum up to l <2000 for
each different model. This allows us to determine the observational
independence of these models by calculating the cross-correlation of their CMB
bispectra. We are able to identify several distinct classes of primordial
shapes - including equilateral, local, warm, flat and feature (non-scale
invariant) - which should be distinguishable given a significant detection of
CMB non-Gaussianity. We demonstrate that a simple shape correlator provides a
fast and reliable method for determining whether or not CMB shapes are well
correlated. We use an eigenmode decomposition of the primordial shape to
characterise and understand model independence. Finally, we advocate a
standardised normalisation method for based on the shape
autocorrelator, so that observational limits and errors can be consistently
compared for different models.Comment: 32 pages, 20 figure
Provably scale-covariant networks from oriented quasi quadrature measures in cascade
This article presents a continuous model for hierarchical networks based on a
combination of mathematically derived models of receptive fields and
biologically inspired computations. Based on a functional model of complex
cells in terms of an oriented quasi quadrature combination of first- and
second-order directional Gaussian derivatives, we couple such primitive
computations in cascade over combinatorial expansions over image orientations.
Scale-space properties of the computational primitives are analysed and it is
shown that the resulting representation allows for provable scale and rotation
covariance. A prototype application to texture analysis is developed and it is
demonstrated that a simplified mean-reduced representation of the resulting
QuasiQuadNet leads to promising experimental results on three texture datasets.Comment: 12 pages, 3 figures, 1 tabl
Statistical Model of Shape Moments with Active Contour Evolution for Shape Detection and Segmentation
This paper describes a novel method for shape representation and robust image segmentation. The proposed method combines two well known methodologies, namely, statistical shape models and active contours implemented in level set framework. The shape detection is achieved by maximizing a posterior function that consists of a prior shape probability model and image likelihood function conditioned on shapes. The statistical shape model is built as a result of a learning process based on nonparametric probability estimation in a PCA reduced feature space formed by the Legendre moments of training silhouette images. A greedy strategy is applied to optimize the proposed cost function by iteratively evolving an implicit active contour in the image space and subsequent constrained optimization of the evolved shape in the reduced shape feature space. Experimental results presented in the paper demonstrate that the proposed method, contrary to many other active contour segmentation methods, is highly resilient to severe random and structural noise that could be present in the data
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Shape-driven segmentation of the arterial wall in intravascular ultrasound images
Segmentation of arterial wall boundaries from intravascular images is an important problem for many applications in the study of plaque characteristics, mechanical properties of the arterial wall, its 3D reconstruction,
and its measurements such as lumen size, lumen radius, and wall radius. We present a shape-driven approach to segmentation of the arterial wall from intravascular ultrasound images in the rectangular domain. In a properly built
shape space using training data, we constrain the lumen and media-adventitia contours to a smooth, closed geometry, which increases the segmentation quality without any tradeoff with a regularizer term. In addition to a shape prior,
we utilize an intensity prior through a non-parametric probability density based image energy, with global image measurements rather than pointwise measurements used in previous methods. Furthermore, a detection step is included to address the challenges introduced to the segmentation process by side branches and calcifications. All these features greatly enhance our segmentation method. The tests of our algorithm on a large dataset demonstrate the effectiveness of our approach
Quantitative Analysis of Saliency Models
Previous saliency detection research required the reader to evaluate
performance qualitatively, based on renderings of saliency maps on a few
shapes. This qualitative approach meant it was unclear which saliency models
were better, or how well they compared to human perception. This paper provides
a quantitative evaluation framework that addresses this issue. In the first
quantitative analysis of 3D computational saliency models, we evaluate four
computational saliency models and two baseline models against ground-truth
saliency collected in previous work.Comment: 10 page
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