3D reconstruction of single rising bubble in water using digital image processing and characteristic matrix--颗粒学报PARTICUOLOGY

Bian, Y., Dong, F., Zhang, W., Wang, H., Tan, C., & Zhang, Z. (2013). 3D reconstruction of single rising bubble in water using digital image processing and characteristic matrix. Particuology, 11(2), 170–183. https://doi.org/10.1016/j.partic.2012.07.005

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

Yuchen Bian ^a, Feng Dong ^a *, Weida Zhang ^a, Hongyi Wang ^b, Chao Tan ^a, Zhiqiang Zhang ^a

a Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China
b School of Electrical Engineering and Automation, Tianjin Polytechnic University, Tianjin 300387, China

10.1016/j.partic.2012.07.005

Volume 11, Issue 2, April 2013, Pages 170-183

Received 26 November 2011, Revised 7 July 2012, Accepted 11 July 2012, Available online 26 December 2012.

E-mail: fdong@tju.edu.cn

Highlights

► 2D ellipse parameters were extracted from ellipse projection planes with Hough transform.

► Characteristic points between 2D projection ellipse and 3D space ellipsoid were matched.

► 3D bubble ellipsoid model was reconstructed with characteristic matrix method.

Abstract

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.

Graphical abstract

Keywords

Bubble; Digital image processing; Parameter extraction; Ellipsoid model; Reconstruction; Characteristic matrix

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