Learning Enhanced Structural Representations with Block-Based Uncertainties for Ocean Floor Mapping

TL;DR

The paper addresses the challenge of producing high-resolution bathymetric maps with reliable uncertainty quantification across heterogeneous data sources. It introduces a Vector Quantized Variational Autoencoder (VQ-VAE) augmented with residual attention and a block-based uncertainty mechanism that leverages EMA-calibrated per-block confidence to guide learning. Empirical results show that the proposed UA-VQ-VAE significantly improves reconstruction quality (e.g., higher SSIM and PSNR) and produces tighter, more calibrated uncertainty estimates compared to traditional interpolation and other deep-learning baselines. This approach preserves critical structural features of the seafloor and yields spatially adaptive uncertainty, enhancing the reliability of ocean/climate modeling and coastal hazard assessments.

Abstract

Accurate ocean modeling and coastal hazard prediction depend on high-resolution bathymetric data; yet, current worldwide datasets are too coarse for exact numerical simulations. While recent deep learning advances have improved earth observation data resolution, existing methods struggle with the unique challenges of producing detailed ocean floor maps, especially in maintaining physical structure consistency and quantifying uncertainties. This work presents a novel uncertainty-aware mechanism using spatial blocks to efficiently capture local bathymetric complexity based on block-based conformal prediction. Using the Vector Quantized Variational Autoencoder (VQ-VAE) architecture, the integration of this uncertainty quantification framework yields spatially adaptive confidence estimates while preserving topographical features via discrete latent representations. With smaller uncertainty widths in well-characterized areas and appropriately larger bounds in areas of complex seafloor structures, the block-based design adapts uncertainty estimates to local bathymetric complexity. Compared to conventional techniques, experimental results over several ocean regions show notable increases in both reconstruction quality and uncertainty estimation reliability. This framework increases the reliability of bathymetric reconstructions by preserving structural integrity while offering spatially adaptive uncertainty estimates, so opening the path for more solid climate modeling and coastal hazard assessment.

Figures (6)

• Figure 1: Learning Enhanced Structural Representations with Block-Based Uncertainties
• Figure 2: Uncertainty Comparison of Models (3D)
• Figure 3: 2D Comparison of Models based on Error Map and Uncertainty Blocks
• Figure 4: High Resolution Bathymetry produced by Uncertainty-Aware SRCNN. This visualization comprises two rows of plots. The upper row presents the progression from low-resolution input ($32\times32$) to high-resolution prediction ($64\times64$), culminating in a prediction with uncertainty bounds visualized as translucent gray bands encompassing the predicted surface. The lower row provides the ground truth high-resolution terrain alongside a spatial map of uncertainty widths, where the scale ($0.1793$-$0.3855$) indicates the magnitude of uncertainty for each block in the prediction space.
• Figure 5: High Resolution Bathymetry produced by Uncertainty-Aware ESRGAN. Following the same layout convention, the upper row shows the pipeline from input through prediction, with the rightmost plot displaying the prediction bounds. The lower row shows comparison of the ground truth with a detailed block-wise uncertainty width distribution map. The uncertainty values, ranging from $0.1706$ to $0.3290$, demonstrate the model's confidence across different spatial regions, with particular attention to areas of complex topographical features.

Theorems & Definitions (14)

• Definition A.1: Block Partition
• Lemma A.4: Block-wise Error Distribution
• proof
• Theorem A.5: Block-wise vs Global Loss Optimization
• proof
• Lemma A.6: Block Size Trade-off
• proof
• Theorem A.7: Fixed Block Size Optimality
• proof
• Remark A.8