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High-frequency oscillations and high surface aeration, induced by strong turbulence, make water depth measurement for hydraulic jumps a persistently challenging task. The investigation of hydraulic jump behaviour continues to be an important research theme, particularly with regards to the stilling basin design. Reliable knowledge of time-averaged and extreme values along a depth profile can help develop an adequate design of a stilling basin, improve safety, and aid the understanding of the jump phenomenon. This paper presents an attempt to mitigate certain limitations of existing depth measurement methods by adopting a non-intrusive computer vision-based approach to measuring the water depth profile of a hydraulic jump. The proposed method analyses video data in order to detect the boundary between the air-water mixture and the laboratory flume wall. This is achieved by coupling two computer vision methods: (1) analysis of the vertical image gradients, and (2) general-purpose edge detection using a deep neural network model. While the gradient analysis technique alone can provide adequate results, its performance can be significantly improved in combination with a neural network model which incorporates a 'human-like' vision within the algorithm. The model coupling reduces the likelihood of false detections and improves the overall detection accuracy. The proposed method is tested in two experiments with different degrees of jump aeration. Results show that the coupled model can reliably and accurately capture the instantaneous depth profile along the jump, with low sensitivity to image noise and flow aeration. The coupled model presented fewer false detections than the gradient-based model, and offered consistent performance in regions of high as well as low aeration. The proposed approach allows for automated detection of the free-surface interface and expands the potential of computer vision-based measurement methods in hydraulics. © 2020 IOP Publishing Ltd.