Optical imaging is a fundamental method for detecting plasma phenomena, such as plasma bubbles, plasma streamers, and self-organized plasma patterns. Therefore, data mining of images is crucial in plasma diagnostics. This work presents image processing methods for extracting substructures in plasma bubbles, streamers, and patterns. In our experiment, plasma-liquid interfaces between atmospheric pressure argon-plasma jets and NaCl solutions are quantitatively captured. After extracting accurate plasma-liquid interfaces, traditional analytic functions and machine learning approaches are used to fit curves of interfaces. Regression of machine learning method based on Gaussian process reveals many details of interfaces, but neural networks present smooth and accurate regressions. The gravitational and surface tension forces are calculated using experimental plasma-liquid interfaces. The plasma forces are estimated to be several tens of Pa. However, they increased to several hundred Pa around the inflection points of interfaces. This study extends the application of image processing to plasma diagnostics and provides target data of gas-liquid interfaces for numerical simulations.