This work is devoted to describe a potential use of the 1-Dimensional Kohonen Networks in the automatic non-supervised classification of tissue in the human brain. Possible perspectives of application include the automatic delineation of areas on the cerebral map. One of the main aspects considered in this work is related to the fact that tissue classification obtained through Kohonen Networks is achieved by taking in account the tissue and its associated neighborhood. By this way, it is possible to argue that the obtained characterizations are sustained in the topology and geometry of the human cranium.
We describe the application of 1-Dimensional Kohonen Networks in the classification of color 2D images which has been evaluated in Popocatépetl Volcano's images. The Popocatépetl, located in the limits of the State of Puebla in México, is active and under monitoring since 1997. We will consider one of the problems related with the question if our application of the Kohonen Network classifies according to the total intensity color of an image or well, if it classifies according to the connectivity, i.e. the topology, between the pixels that compose an image. In order to give arguments that support our hypothesis that our procedures share the classification according to the topology of the pixels in the images, we will present two approaches based a) in the evaluation of the classification given by the network when the pixels in the images are permuted; and,b) when an additional metric to the Euclidean distance is introduced.
This work is devoted to present a methodology for the computation of Discrete Compactness in -dimensional orthogonal pseudo-polytopes. The proposed procedures take in account compactness' definitions originally presented for the 2D and 3D cases and extend them directly for considering the D case. There are introduced efficient algorithms for computing discrete compactness which are based on an orthogonal polytopes representation scheme known as the Extreme Vertices Model in the -Dimensional Space (D-EVM). It will be shown the potential of the application of Discrete Compactness in higher-dimensional contexts by applying it, through EVM-based algorithms, in the classification of video sequences, associated to the monitoring of a volcano's activity, which are expressed as 4D orthogonal polytopes in the space-color-time geometry.
This article will describe Pólya's Countings as a methodology for determining the number of configurations to be present in the nD Orthogonal Pseudo-Polytopes. Banks et al have used this methodology for counting configurations, in 1D to 4D spaces, under the context of the dual problem. We will describe a concise and simple representation for the configurations that provides the elements to reach the 5D and 6D cases and therefore to obtain their corresponding countings.
This work is devoted to contribute with two algorithms for performing, in an efficient way, connected components labeling and boundary extraction from orthogonal pseudo-polytopes. The proposals are specified in terms of the extreme vertices model in the -dimensional space (D-EVM). An overview of the model is presented, considering aspects such as its fundamentals and basic algorithms. The temporal efficiency of the two proposed algorithms is sustained in empirical way and by taking into account both lower dimensional cases (2D and 3D) and higher-dimensional cases (4D and 5D).
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