Centroid

About: Centroid is a research topic. Over the lifetime, 4110 publications have been published within this topic receiving 53637 citations. The topic is also known as: barycenter (geometry) & geometric center of a plane figure.

Contour registration by shape-specific points for shape matching

Abstract: The paper shows how registration of planar figures can be achieved using shape-specific points computed from the given figures. Registration makes the subsequent task of shape matching much easier. Examples are given, using the centroid and radius weighted mean, which yield reasonable results even for noisy images.

Interstellar cloud structure: the statistics of centroid velocities

Abstract: Context. The statistical properties of maps of line centroids have been used for almost 50 years, but there is still no general agreement on their interpretation. Aims. We have tried to quantify which properties of underlying turbulent velocity fields can be derived from centroid velocity maps, and we tested conditions under which the scaling behaviour of the centroid velocities matches the scaling of the three-dimensional velocity field. Methods. Using fractal cloud models we systematically studied the relation between three-dimensional density and velocity fields and the statistical properties of the resulting line centroid maps. We paid special attention to cases with large density fluctuations resembling supersonic interstellar turbulence. Starting from the ∆-variance analysis, we derived a new tool to compute the scaling behaviour of the three-dimensional velocity field from observed intensity and centroid velocity maps. Results. We provide two criteria to decide whether the information from the centroid velocities directly reflects the properties of the underlying velocity field. Applying these criteria allows us to understand the different results found so far in the literature for interpreting the statistics of velocity centroids. The new iteration scheme can be used to derive the three-dimensional velocity scaling from centroid velocity maps for arbitrary density and velocity fields, but it requires accurate knowledge of the average density of the interstellar cloud under consideration.

Semantically-grounded construction of centroids for datasets with textual attributes

Abstract: Centroids are key components in many data analysis algorithms such as clustering or microaggregation. They are considered as the central value that minimises the distance to all the objects in a dataset or cluster. Methods for centroid construction are mainly devoted to datasets with numerical and categorical attributes, focusing on the numerical and distributional properties of data. Textual attributes, on the contrary, consist of term lists referring to concepts with a specific semantic content (i.e., meaning), which cannot be evaluated by means of classical numerical operators. Hence, the centroid of a dataset with textual attributes should be the term that minimises the semantic distance against the members of the set. Semantically-grounded methods aiming to construct centroids for datasets with textual attributes are scarce and, as it will be discussed in this paper, they are hampered by their limited semantic analysis of data. In this paper, we propose a method that, exploiting the knowledge provided by background ontologies (like WordNet), is able to construct the centroid of multivariate datasets described by means of textual attributes. Special efforts have been put in the minimisation of the semantic distance between the centroid and the input data. As a result, our method is able to provide optimal centroids (i.e., those that minimise the distance to all the objects in the dataset) according to the exploited background ontology and a semantic similarity measure. Our proposal has been evaluated by means of a real dataset consisting on short textual answers provided by visitors of a natural park. Results show that our centroids retain the semantic content of the input data better than related works.

A Statistical Consistency Check for the Space Carving Algorithm.

Abstract: This paper investigates the use of the Space Carving algorithm with outdoor image sequences, using a lambertian lighting model. A new consistency function is proposed that uses a statistical comparison instead of the voxel centroid sampling that was initially proposed. This is important when there is more detail in the images than can be stored in a voxel representation. The new function is evaluated using synthetic data and real image sequences.

Method, apparatus, and system for building a compact language model for large vocabulary continuous speech recognition (lvcsr) system

Abstract: According to one aspect of the invention, a method is provided in which a set of probabilistic attributes in an N-gram language model is classified into a plurality of classes. Each resultant class is clustered into a plurality of segments to build a code-book for the respective class using a modified K-means clustering process which dynamically adjusts the size and centroid of each segment during each iteration in the modified K-means clustering process. A probabilistic attribute in each class is then represented by the centroid of the corresponding segment to which the respective probabilistic attribute belongs.