Detection of bubbles as Concentric Circular Arrangements

A method for the detection of bubble-like transparent objects with multiple interfaces in a liquid is proposed. Depending on the lighting conditions, bubble appearance varies significantly, including contrast reversal and multiple inter-reflections. We formulate the bubble detection problem as the detection of Concentric Circular Arrangements (CCA). The CCAs are recovered in a hypothesize-optimize-verify framework. The hypothesis generation proceeds by sampling from the components of the non-maximum suppressed responses of oriented ridge filters followed by CCA parameter estimation. Parameter optimization is carried out by minimizing a novel cost-function by the simplex method. The proposed method for bubble detection showed good performance in an industrial application requiring estimation of gas volume in pulp suspension, achieving 1.5% mean absolute relative error.

1. Introduction

The present paper proposes a method for the detection of bubbles or, more generally, transparent roughly spherical objects with multiple interfaces, in a liquid. Under different lighting conditions, the appearance of bubbles varies from a pair of ring-like, bright ridge edges to blurred dark edges with contrast reversal and multiple inter-reflections. Experiments showed that oriented filter responses induced by the presence of such objects are well modelled by concentric arrangements of circular arcs, as can be seen in Fig. 1. Figure 1. Examples of images of bubbles and local maxima (in spatial and orientation domains) of oriented ridge filters.