5,959 research outputs found
The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation
We generalize the SiZer of Chaudhuri and Marron (J. Amer. Statist. Assoc. 94
(1999) 807-823, Ann. Statist. 28 (2000) 408-428) for the detection of shape
parameters of densities on the real line to the case of circular data. It turns
out that only the wrapped Gaussian kernel gives a symmetric, strongly Lipschitz
semi-group satisfying "circular" causality, that is, not introducing possibly
artificial modes with increasing levels of smoothing. Some notable differences
between Euclidean and circular scale space theory are highlighted. Based on
this, we provide an asymptotic theory to make inference about the persistence
of shape features. The resulting circular mode persistence diagram is applied
to the analysis of early mechanically-induced differentiation in adult human
stem cells from their actin-myosin filament structure. As a consequence, the
circular SiZer based on the wrapped Gaussian kernel (WiZer) allows the
verification at a controlled error level of the observation reported by Zemel
et al. (Nat. Phys. 6 (2010) 468-473): Within early stem cell differentiation,
polarizations of stem cells exhibit preferred directions in three different
micro-environments.Comment: Published at http://dx.doi.org/10.3150/15-BEJ722 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Well-posedness of a nonlinear integro-differential problem and its rearranged formulation
We study the existence and uniqueness of solutions of a nonlinear
integro-differential problem which we reformulate introducing the notion of the
decreasing rearrangement of the solution. A dimensional reduction of the
problem is obtained and a detailed analysis of the properties of the solutions
of the model is provided. Finally, a fast numerical method is devised and
implemented to show the performance of the model when typical image processing
tasks such as filtering and segmentation are performed.Comment: Final version. To appear in Nolinear Analysis Real World Applications
(2016
A network for multiscale image segmentation
Detecting edges of objects in their images is a basic problem in computational vision. The scale-space technique introduced by Witkin [11] provides means of using local and global reasoning in locating edges. This approach has a major drawback: it is difficult to obtain accurately
the locations of the 'semantically meaningful' edges. We have refined the definition of scale-space, and introduced a class of algorithms for implementing it based on using anisotropic diffusion [9]. The algorithms involves simple, local operations replicated over the image making parallel
hardware implementation feasible. In this paper we present the
major ideas behind the use of scale space, and anisotropic diffusion for edge detection, we show that anisotropic diffusion can enhance edges, we suggest a network implementation of anisotropic diffusion, and provide
design criteria for obtaining networks performing scale space, and edge detection. The results of a software implementation are shown
- …