C2PD: Continuity-Constrained Pixelwise Deformation for Guided Depth Super-Resolution

Guided depth super-resolution (GDSR) has demonstrated impressive performance across a wide range of domains, with numerous methods being proposed. However, existing methods often treat depth maps as images, where shading values are computed discretely, making them struggle to effectively restore the continuity inherent in the depth map. In this paper, we propose a novel approach that maximizes the utilization of spatial characteristics in depth, coupled with human abstract perception of real-world substance, by transforming the GDSR issue into deformation of a roughcast with ideal plasticity, which can be deformed by force like a continuous object. Specifically, we firstly designed a cross-modal operation, Continuity-constrained Asymmetrical Pixelwise Operation (CAPO), which can mimic the process of deforming an isovolumetrically flexible object through external forces. Utilizing CAPO as the fundamental component, we develop the Pixelwise Cross Gradient Deformation (PCGD), which is capable of emulating operations on ideal plastic objects (without volume constraint). Notably, our approach demonstrates state-of-the-art performance across four widely adopted benchmarks for GDSR, with significant advantages in large-scale tasks and generalizability.