3D reconstruction of single rising bubble in water using digital image processing and characteristic matrix

Reconstructing the shape of a bubble will lay a firm foundation for further description of the dynamic characteristics of bubbly flow, especially for a single rising bubble or separate bubbles whose interaction could be neglected. In this case, the rising bubble is usually simulated as an ellipsoid consisting of two semi-ellipsoids up and down. Thus the projected image of a bubble consists of two semi-ellipses. In this paper, a method for reconstructing the ellipsoid bubble model is described following digital image processing, using the Hough transform in 2D ellipse parameter extraction which could cover most of the bubble edge points in the image. Then a method based on characteristic symmetric matrix is described to detect 3D bubble ellipsoid model parameters from 2D ellipse parameters of projection planes. This method can be applied to bubbles rising with low-velocity in static flow field much in conformity with the projection theory and the shape variation of the rising bubble. This method does not need to solve nonlinear equation sets and provides an easy way to calculate the characteristic matrix of a space ellipsoid model for deformed bubble. For bubble application, two assumed conditions and a calibration factor are proposed to simplify calculation and detection. Errors of ellipsoid center and three axes are minor. Errors of the three rotation angles have no negative effect on further study on bubbly flow.