A Precise Flotation Bubble Size Measurement Method Based on Boundary Probability Regression

The visual characteristics of flotation froth surfaces, particularly the bubble size distribution, provide real-time insights into flotation conditions, playing a crucial role in monitoring and optimizing the flotation process. However, inherent issues in flotation froth images, such as blurred boundaries, uneven illumination, and shadow interference, pose challenges for existing segmentation methods to effectively address the boundary disconnection problem, thus affecting the accuracy of bubble size measurements. To address this challenge, this study proposed an innovative flotation bubble size measurement method based on boundary probability regression, transforming the segmentation task from a traditional “pixel-level boundary classification” problem to a “continuous boundary probability regression” problem. The core of this method lies in introducing boundary probability maps to replace binary boundary masks as labels for supervised boundary generation and designing a corresponding boundary regression network. Building upon this foundation, the method enhances gradient information in the boundary probability map and preliminarily locates boundary positions based on gradient changes. In addition, it incorporates an adaptive mechanism to flexibly adjust the distance threshold of breakpoints’ connection according to real-time bubble density information, thereby optimizing the quality of segmentation results. Experimental results demonstrated that this method exhibits significant advantages over existing flotation froth image segmentation methods in three key indicators: bubble count, boundary disconnections number, and bubble size distribution. Furthermore, tests on flotation froth datasets from other regions validated the method’s cross-scenario generalization ability, while applications on general segmentation datasets in other domains further confirmed its potential in addressing complex boundary segmentation tasks. This approach provides new research directions for improving the accuracy of bubble size measurement and image segmentation tasks in related fields.