Fourier-domain correlation approaches have been successful in a variety of image comparison approaches but fail when the scenes, patterns, or objects in the images are distorted. Here, we utilize the sequential training of shallow neural networks on Fourier-preprocessed video to infer 3-D movement. The bio-inspired pipeline learns x, y, and z-direction movement from high-frame-rate, low-resolution, Fourier-domain preprocessed inputs (either cross power spectra or phase correlation data). Our pipeline leverages the high sensitivity of Fourier methods in a manner that is resilient to the parallax distortion of a forward-facing camera. Via sequential training over several path trajectories, models generalize to predict the 3-D movement in unseen trajectory environments. Models with no hidden layer are less accurate initially but converge faster with sequential training over different flightpaths. Our results show important considerations and trade-offs between input data preprocessing (compression) and model complexity (convergence).
Here we elaborate on the edge-enhanced spectral components that are produced by the vortex Fourier trans- form, which are introduced in [1]. The vortex phase pattern imprinted on from an object breaks the spatial invariance of its Fourier representation is robust to noise. We report on new results related to the image classification of the MNIST digit dataset with no hidden layers. We show that the accuracy from one phase vortex mask is capable of achieving 0:95 validation accuracy and further show that the dynamic range of the phase modulation scheme significantly influences the classification accuracy and classification convergence rate.
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