The methodology of marching phase-space transformations has been previously considered for slowly varying media. The present work implements the approach for a medium with a planar wave velocity discontinuity. It is shown that propagation in the water column can be systematically separated from the scattering events at the discontinuity. The latter take place in a narrow interaction zone, out of which the previously invoked local homogeneity assumption can be used again. The width of the interaction zone is obtained by the investigation of the recently developed evolution equation of the local spectra. The associated phase-space propagators and the isolation of phenomena such as reflection, refraction, and head waves in phase space are demonstrated. Computations are performed and compared to reference solutions.

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Autonomous vehicles are a promising solution to traffic congestion, air pollution, accidents, and wasted time and resources. However, remote driver intervention may be necessary for extreme situations to ensure safe roadside parking or complete remote takeover. In such cases, high-quality real-time video streaming is crucial for practical remote driving. In a preliminary study, we already presented a region of interest (ROI) HEVC data compression where the image was segmented into two categories of ROI and background, allocating more bandwidth to the ROI, yielding an improvement in the visibility of the classes that essential for driving while transmitting the background with lesser quality. However, migrating bandwidth to the large ROI portion of the image doesn't substantially improve the quality of traffic signs and lights. This work categorized the ROIs into either background, weak ROI, or strong ROI. The simulation-based approach uses a photo-realistic driving scenario database created with the Cognata self-driving car simulation platform. We use semantic segmentation to categorize the compression quality of a Coding Tree Unit (CTU) according to each pixel class. A background CTU can contain only sky, trees, vegetation, or building classes. Essentials for remote driving include significant classes such as roads, road marks, cars, and pedestrians. And most importantly, traffic signs and traffic lights. We apply thresholds to decide if the number of pixels in a CTU of a particular category is enough to declare it as belonging to the strong or weak ROI. Then, we allocate the bandwidth according to the CTU categories. Our results show that the perceptual quality of traffic signs, especially textual signs and traffic lights, improves significantly by up to 5.5 dB compared to the only background and foreground partition, while the weak ROI classes at least retain their original quality.

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