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.

Real-time image stabilization

Abstract: An apparatus and method for stabilizing image frames in a video data stream. A weighted average or centroid of the intensity or hue associated with pixels vs. the horizontal and vertical position of each pixel is calculated for a reference frame in the video data stream. A corresponding centroid is calculated for a subsequent frame in the stream. This image frame is then translated so that the centroid of the subsequent frame and the centroid of the reference frame coincide, reducing artifacts from shaking of the video capture device. Alternatively, the video stream frames may be divided into tiles and centroids calculated for each tile. The centroids of the tiles of a subsequent frame are curve fit to the centroids of tiles in a reference frame. An affine transform is then performed on the subsequent frame to reduce artifacts in the image from movements of the video capture device.

Triangle Centers as Functions

Abstract: We consider a kind of problem that appears to be new to Euclidean geometry, since it depends on an understanding of a point as a function rather than a position in a two-dimensional plane. Certain special points we call centers, including the centroid, incenter, circumcenter, and orthocenter. For example, the centroid, as a function of the class of triangles with sidelengths in the ratio a1 : a2 : a3, is given by the formula 1/a1 : 1/a2 : 1/a3. The kind of problem introduced here leads to functional equations whose solutions are centers.

Functional Decomposition for Bundled Simplification of Trail Sets

Abstract: Bundling visually aggregates curves to reduce clutter and help finding important patterns in trail-sets or graph drawings. We propose a new approach to bundling based on functional decomposition of the underling dataset. We recover the functional nature of the curves by representing them as linear combinations of piecewise-polynomial basis functions with associated expansion coefficients. Next, we express all curves in a given cluster in terms of a centroid curve and a complementary term, via a set of so-called principal component functions. Based on the above, we propose a two-fold contribution: First, we use cluster centroids to design a new bundling method for 2D and 3D curve-sets. Secondly, we deform the cluster centroids and generate new curves along them, which enables us to modify the underlying data in a statistically-controlled way via its simplified (bundled) view. We demonstrate our method by applications on real-world 2D and 3D datasets for graph bundling, trajectory analysis, and vector field and tensor field visualization.

Deep Clustering with a Dynamic Autoencoder: From Reconstruction towards Centroids Construction

Abstract: In unsupervised learning, there is no apparent straightforward cost function that can capture the significant factors of variations and similarities. Since natural systems have smooth dynamics, an opportunity is lost if an unsupervised objective function remains static during the training process. The absence of concrete supervision suggests that smooth dynamics should be integrated. Compared to classical static cost functions, dynamic objective functions allow to better make use of the gradual and uncertain knowledge acquired through pseudo-supervision. In this paper, we propose Dynamic Autoencoder (DynAE), a novel model for deep clustering that overcomes a clustering-reconstruction trade-off, by gradually and smoothly eliminating the reconstruction objective function in favor of a construction one. Experimental evaluations on benchmark datasets show that our approach achieves state-of-the-art results compared to the most relevant deep clustering methods.

Gossip-Based Centroid and Common Reference Frame Estimation in Multiagent Systems

Abstract: In this study, the decentralized common reference frame estimation problem for multiagent systems in the absence of any common coordinate system is investigated. Each agent is deployed in a 2-D space and can only measure the relative distance of neighboring agents and the angle of their line of sight in its local reference frame; no relative attitude measurement is available. Only asynchronous and random pairwise communications are allowed between neighboring agents. The convergence properties of the proposed algorithm are characterized, and its sensitiveness against additive noise on the relative distance measurements is investigated. An experimental validation of the effectiveness of the proposed algorithm is provided.