Topic
Hat operator
About: Hat operator is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 111 citations.
Papers
Posted Content•
TL;DR: It is found that a spatial pattern that is damped in time in a deterministic system may be sustained and amplified by stochasticity, most strikingly at an optimal spatio-temporal noise level.
Abstract: The formation of pattern in biological systems may be modeled by a set of reaction-diffusion equations. A diffusion-type coupling operator biologically significant in neuroscience is a difference of Gaussian functions (Mexican Hat operator) used as a spatial-convolution kernel. We are interested in the difference among behaviors of \emph{stochastic} neural field equations, namely space-time stochastic differential-integral equations, and similar deterministic ones. We explore, quantitatively, how the parameters of our model that measure the shape of the coupling kernel, coupling strength, and aspects of the spatially-smoothed space-time noise, control the pattern in the resulting evolving random field. We find that a spatial pattern that is damped in time in a deterministic system may be sustained and amplified by stochasticity, most strikingly at an optimal spatio-temporal noise level. In addition, we find that spatially-smoothed noise alone causes pattern formation even without spatial coupling.
2 citations
1 Jan 1995
TL;DR: The quality of the results increases if Gaussian masks of larger width are used in the derivation process instead of simple 3 x 3 masks as suggested in the underlying papers, and multiresolution approaches can be applied to color images when usingGaussian masks with different standard deviations in the edge detection scheme.
Abstract: Several approaches of different complexity already exist to edge detection in color images. Nevertheless, the question remains of how different are the results when employing computational costly techniques instead of simple ones. This paper presents a comparative study on different approaches to color edge detection. The approaches are based on the Sobel operator, the Laplace operator, the Mexican Hat operator, different realizations of the Cumani operator, and the Alshatti-Lambert operator. Furthermore, we present an efficient algorithm for implementing the Cumani operator. All operators have been applied to several synthetic and real images. The results are presented in this paper. We show that the quality of the results increases if Gaussian masks of larger width are used in the derivation process instead of simple 3 x 3 masks as suggested in the underlying papers. Moreover, multiresolution approaches can be applied to color images when using Gaussian masks with different standard deviations in the edge detection scheme.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2018 | 1 |
| 1995 | 1 |