Centroidsshapesinverse problemsexistenceuniquenessstabilityAn inverse problem of determining the shape of a plane region from centroid information is an excellent vehicle for developing students'' physical intuition, honing their calculus skills, and exploring the fundamental mathematical notions of existence, ...
Specifically, we first recorded the spherical coordinates of centroids for each parcel in the Cammoun atlas43. Then, we randomly rotated the parcels while maintaining spatial autocorrelation and reassigned node values to the nearest parcels. This procedure was repeated 1000 times to create surrogate ...
Vec2Instance provides a framework for parametrization of instances, allowing convolutional neural networks to efficiently estimate the complex shapes of instances around their centroids. We demonstrate the feasibility of the proposed architecture with respect to instance segmentation tasks on satellite images,...
Participants were asked to draw shapes that were angry, sad, excited, or peaceful. The researchers then estimated the spectral centroids of the drawings by counting how many corners they had. The results revealed that angry and excited shapes had between 17 and 24 corners on average, while sad...
As in the case of the stream channel of Section 2.4, RibFill begins by discovering that each rib lay on a vertical section, but found that here the sections are not parallel. In such cases RibFill seeks a rib ordering principle based on the centroids of the ribs. These centroids are a...
. Points represent a single faecal sample from a single individual (n= 195). Sample sizes are specified in brackets in the legend, and colours indicate the presence (blue) or absence (yellow) of the MHC-I allele. Ellipses represent a 95% confidence interval around the cluster centroids...
Since the brain immunohistochemical images have stretched clusters that appear long and narrow in geometrical shape, we use centroids of straight lines instead of single points to approximate the clusters. An iterative, algorithm is developed to optimize the linear centroids by minimizing the ...
Partitions of similar views are obtained using a graph partitioning procedure and their "centroids" are considered to be their representative views. Finally, the views are ranked based on a saliency measure to form the objects representative views. This leads to a compact, human-oriented 2D ...
The final shape skeleton is obtained by joining centroidswhich are disjoint in the spanning tree, but have adjacent Voronoi regions. The skeletal descriptions obtained with the method are invariant to translation, rotation, and scale changes of the shape. The potential of the method is demonstrated...
Then the predicted centroids with size of 𝑁𝑝×3Np×3 is calculated by adding the offsets to the point cloud. The loss 𝐿𝑡0Lt0 considering foreground points only is 𝐿1L1 loss between predicted centroids and centroid labels: 𝐿𝑡0=1𝑁𝑓𝑔∑𝑖=1𝑁𝑓𝑔|𝒕𝒊−...