A Walsh transform-neural network method for estimating the size distribution of bubbles in a liquid

An edge detected two-dimensional image of bubbles dispersed in a flowing liquid was captured in a 256-by-256 pixel window. The image produced was a binary image. Upon consideration of the merits of different spectral transform methods, a Manz sequency ordered Walsh transform was chosen to obtain the power spectrum of the bubble image. Using the spectrum as the input to a three-layer neural network the bubble size distribution was predicted. Histograms showing bubble size distributions were the target outputs corresponding to sets of inputs. Neural network training involved using backpropagation in conjunction with a wide range of deviations. Bubble positions within the photograph were also varied. The input-output training pairs were simulated from images generated with known distributions and used to train the backpropagation network. The trained network was then tested using unseen images and the results were excellent