Learning Three-Dimensional Shape Models for Sketch Recognition

Artifacts made by humans, such as items of furniture and houses, exhibit an enormous amount of variability in shape. In this paper, we concentrate on models of the shapes of objects that are made up of fixed collections of sub-parts whose dimensions and spatial arrangement exhibit variation. Our goals are: to learn these models from data and to use them for recognition. Our emphasis is on learning and recognition from three-dimensional data, to test the basic shape-modeling methodology. In this paper we also demonstrate how to use models learned in three dimensions for recognition of two-dimensional sketches of objects.

Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape

In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.