Bayesian Multiscale Modeling of Closed Curves in Point Clouds

Abstract

Modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy, to the classification of organisms based on their structural information. In low-contrast images or sparse and noisy point clouds, there is often insufficient data to recover local segments of the boundary in isolation. Thus, it becomes critical to model the entire boundary in the form of a closed curve. To achieve this, we develop a Bayesian hierarchical model that expresses highly diverse 2D objects in the form of closed curves. The model is based on a novel multiscale deformation process. By relating multiple objects through a hierarchical formulation, we can successfully recover missing boundaries by borrowing structural information from similar objects at the appropriate scale. Furthermore, the model’s latent parameters help interpret the population, indicating dimensions of significant structural variability and also specifying a ‘central curve’ that summarizes the collection. Theoretical properties of our prior are studied in specific cases and efficient Markov chain Monte Carlo methods are developed, evaluated through simulation examples and applied to panorex teeth images for modeling teeth contours and also to a brain tumor contour detection problem.

A rapid segmentation method of cell boundary for developing embryos using machine learning with a personal computer

“…Our application takes 4 s per image, which is fast enough edges. Another way is to set connective lines as output and construct corresponding a loss of function (Gu et al, 2014). This method would be promising since it directly outputs connective lines without postprocessing.…”

The Statistical Face of a Region Under Monsoon Rainfall in Eastern India

“…Whether the additional sophistication would bring any worthwhile benefit remains to be seen. One can also use parametric and/or Bayesian imputation (see Gu et al (2014)). Appropriate parametric models for the present application, once identified, may be used in future to look for better ways of handling censored data.…”

Robust and rate-optimal Gibbs posterior inference on the boundary of a noisy image

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