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

arXiv: https://arxiv.org/abs/2501.07688 · HTML: https://mlsanity.com/paper/2501.07688/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 13 Jan 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Drop an Octave: Reducing Spatial Redundancy in Convolutional Neural Networks with Octave Convolution](https://mlsanity.com/paper/1904.05049/) (2019)
- [Learning Rich Features from RGB-D Images for Object Detection and Segmentation](https://mlsanity.com/paper/1407.5736/) (2014)
- [Pixel-Adaptive Convolutional Neural Networks](https://mlsanity.com/paper/1904.05373/) (2019)
- [3D Sketch-aware Semantic Scene Completion via Semi-supervised Structure Prior](https://mlsanity.com/paper/2003.14052/) (2020)
- [Bi-directional Cross-Modality Feature Propagation with Separation-and-Aggregation Gate for RGB-D Semantic Segmentation](https://mlsanity.com/paper/2007.09183/) (2020)
- [Deep Convolutional Neural Network for Multi-modal Image Restoration and Fusion](https://mlsanity.com/paper/1910.04066/) (2019)
- [Discrete Cosine Transform Network for Guided Depth Map Super-Resolution](https://mlsanity.com/paper/2104.06977/) (2021)
- [Towards Fast and Accurate Real-World Depth Super-Resolution: Benchmark Dataset and Baseline](https://mlsanity.com/paper/2104.06174/) (2021)
- [Deformable Kernel Networks for Joint Image Filtering](https://mlsanity.com/paper/1910.08373/) (2019)
- [Joint Image Filtering with Deep Convolutional Networks](https://mlsanity.com/paper/1710.04200/) (2017)
- [RoutedFusion: Learning Real-time Depth Map Fusion](https://mlsanity.com/paper/2001.04388/) (2020)
- [Guided Depth Super-Resolution by Deep Anisotropic Diffusion](https://mlsanity.com/paper/2211.11592/) (2022)
- [Dual-Camera Super-Resolution with Aligned Attention Modules](https://mlsanity.com/paper/2109.01349/) (2021)
- [Joint Implicit Image Function for Guided Depth Super-Resolution](https://mlsanity.com/paper/2107.08717/) (2021)
- [BridgeNet: A Joint Learning Network of Depth Map Super-Resolution and Monocular Depth Estimation](https://mlsanity.com/paper/2107.12541/) (2021)
- [Spherical Space Feature Decomposition for Guided Depth Map Super-Resolution](https://mlsanity.com/paper/2303.08942/) (2023)
- [SGNet: Structure Guided Network via Gradient-Frequency Awareness for Depth Map Super-Resolution](https://mlsanity.com/paper/2312.05799/) (2023)
- [Guided Depth Map Super-resolution: A Survey](https://mlsanity.com/paper/2302.09598/) (2023)
- [Symmetric Uncertainty-Aware Feature Transmission for Depth Super-Resolution](https://mlsanity.com/paper/2306.00386/) (2023)
- [A Deep Primal-Dual Network for Guided Depth Super-Resolution](https://mlsanity.com/paper/1607.08569/) (2016)
- [Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-Spectral Image Fusion](https://mlsanity.com/paper/2308.16083/) (2023)

## Built on by (most cited first, 8 of 8)

- [DuCos: Duality Constrained Depth Super-Resolution via Foundation Model](https://mlsanity.com/paper/2503.04171/) (2025)
- [SpatioTemporal Difference Network for Video Depth Super-Resolution](https://mlsanity.com/paper/2508.01259/) (2025)
- [Multi-Order Matching Network for Alignment-Free Depth Super-Resolution](https://mlsanity.com/paper/2511.16361/) (2025)
- [Robust Depth Super-Resolution via Adaptive Diffusion Sampling](https://mlsanity.com/paper/2602.09510/) (2026)
- [Robust Self-Supervised Cross-Modal Super-Resolution against Real-World Misaligned Observations](https://mlsanity.com/paper/2602.18822/) (2026)
- [DegBins: Degradation-Driven Binning for Depth Super-Resolution](https://mlsanity.com/paper/2605.09628/) (2026)
- [WAVE: Reversing the Guidance Hierarchy for Coarse-to-Fine Guided Depth Super-Resolution](https://mlsanity.com/paper/2608.25302/) (2026)
- [FoundDSR: A Generalizable Foundation Model with Guided 2D Gaussian Splatting for Depth Super-Resolution](https://mlsanity.com/paper/2609.32323/) (2026)

## Abstract (arXiv)

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.