Grouping ., -, ->, [formula], into Regions, Curves, and Junctions

We address the problem of extracting segmented, structured information from noisy data obtained through local processing of images. A unified computational framework is developed for the inference of multiple salient structures such as junctions, curves, regions, and surfaces from any combinations of points, curve elements, and surface patch elements inputs in 2D and 3D. The methodology is grounded in two elements: tensor calculus for representation and nonlinear voting for data communication. Each input site communicates its information (a tensor) to its neighborhood through a predefined (tensor) field and, therefore, casts a (tensor) vote. Each site collects all the votes cast at its location and encodes them into a new tensor. A local, parallel routine such as a modified marching cube/square process then simultaneously detects junctions, curves, regions, and surfaces. The proposed method is noniterative, requires no initial guess or thresholding, can handle the presence of multiple curves, regions, and surfaces in a large amount of noise while it still preserves discontinuities, and the only free parameter is scale. We present results of curve and region inference from a variety of inputs.

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