# PDC-Net+: Enhanced Probabilistic Dense Correspondence Network

arXiv: https://arxiv.org/abs/2109.13912 · HTML: https://mlsanity.com/paper/2109.13912/

## Key facts

- Cited by 80 papers in the map (data through 14 Oct 2026).
- Builds on 78 of its 118 references that are in the map.
- First posted on arXiv 28 Sep 2021.

## Builds on (most cited first, 30 of 78)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [Semantic Understanding of Scenes through the ADE20K Dataset](https://mlsanity.com/paper/1608.05442/) (2016)
- [Two-Stream Convolutional Networks for Action Recognition in Videos](https://mlsanity.com/paper/1406.2199/) (2014)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [The 2017 DAVIS Challenge on Video Object Segmentation](https://mlsanity.com/paper/1704.00675/) (2017)
- [NetVLAD: CNN architecture for weakly supervised place recognition](https://mlsanity.com/paper/1511.07247/) (2015)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [MegaDepth: Learning Single-View Depth Prediction from Internet Photos](https://mlsanity.com/paper/1804.00607/) (2018)
- [Albumentations: fast and flexible image augmentations](https://mlsanity.com/paper/1809.06839/) (2018)
- [Direct Sparse Odometry](https://mlsanity.com/paper/1607.02565/) (2016)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [HPatches: A benchmark and evaluation of handcrafted and learned local descriptors](https://mlsanity.com/paper/1704.05939/) (2017)
- [Large-Scale Image Retrieval with Attentive Deep Local Features](https://mlsanity.com/paper/1612.06321/) (2016)
- [Probabilistic Regression for Visual Tracking](https://mlsanity.com/paper/2003.12565/) (2020)
- [R2D2: Repeatable and Reliable Detector and Descriptor](https://mlsanity.com/paper/1906.06195/) (2019)
- [UnFlow: Unsupervised Learning of Optical Flow with a Bidirectional Census Loss](https://mlsanity.com/paper/1711.07837/) (2017)
- [COTR: Correspondence Transformer for Matching Across Images](https://mlsanity.com/paper/2103.14167/) (2021)
- [Learning to Find Good Correspondences](https://mlsanity.com/paper/1711.05971/) (2017)

## Built on by (most cited first, 30 of 80)

- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [RoMa: Robust Dense Feature Matching](https://mlsanity.com/paper/2305.15404/) (2023)
- [SPARF: Neural Radiance Fields from Sparse and Noisy Poses](https://mlsanity.com/paper/2211.11738/) (2022)
- [DKM: Dense Kernelized Feature Matching for Geometry Estimation](https://mlsanity.com/paper/2202.00667/) (2022)
- [SEA-RAFT: Simple, Efficient, Accurate RAFT for Optical Flow](https://mlsanity.com/paper/2405.14793/) (2024)
- [ASpanFormer: Detector-Free Image Matching with Adaptive Span Transformer](https://mlsanity.com/paper/2208.14201/) (2022)
- [XFeat: Accelerated Features for Lightweight Image Matching](https://mlsanity.com/paper/2404.19174/) (2024)
- [Local All-Pair Correspondence for Point Tracking](https://mlsanity.com/paper/2407.15420/) (2024)
- [PF3plat: Pose-Free Feed-Forward 3D Gaussian Splatting](https://mlsanity.com/paper/2410.22128/) (2024)
- [DreamMatcher: Appearance Matching Self-Attention for Semantically-Consistent Text-to-Image Personalization](https://mlsanity.com/paper/2402.09812/) (2024)
- [OmniGlue: Generalizable Feature Matching with Foundation Model Guidance](https://mlsanity.com/paper/2405.12979/) (2024)
- [RoMa v2: Harder Better Faster Denser Feature Matching](https://mlsanity.com/paper/2511.15706/) (2025)
- [Dens3R: A Foundation Model for 3D Geometry Prediction](https://mlsanity.com/paper/2507.16290/) (2025)
- [Composed Image Retrieval with Text Feedback via Multi-grained Uncertainty Regularization](https://mlsanity.com/paper/2211.07394/) (2022)
- [Binocular-Guided 3D Gaussian Splatting with View Consistency for Sparse View Synthesis](https://mlsanity.com/paper/2410.18822/) (2024)
- [DeDoDe v2: Analyzing and Improving the DeDoDe Keypoint Detector](https://mlsanity.com/paper/2404.08928/) (2024)
- [Unifying Correspondence, Pose and NeRF for Pose-Free Novel View Synthesis from Stereo Pairs](https://mlsanity.com/paper/2312.07246/) (2023)
- [UFM: A Simple Path towards Unified Dense Correspondence with Flow](https://mlsanity.com/paper/2506.09278/) (2025)
- [PATS: Patch Area Transportation with Subdivision for Local Feature Matching](https://mlsanity.com/paper/2303.07700/) (2023)
- [Refign: Align and Refine for Adaptation of Semantic Segmentation to Adverse Conditions](https://mlsanity.com/paper/2207.06825/) (2022)
- [Probabilistic Warp Consistency for Weakly-Supervised Semantic Correspondences](https://mlsanity.com/paper/2203.04279/) (2022)
- [OMNI-DC: Highly Robust Depth Completion with Multiresolution Depth Integration](https://mlsanity.com/paper/2411.19278/) (2024)
- [Cross-View Completion Models are Zero-shot Correspondence Estimators](https://mlsanity.com/paper/2412.09072/) (2024)
- [PMatch: Paired Masked Image Modeling for Dense Geometric Matching](https://mlsanity.com/paper/2303.17342/) (2023)
- [Local Feature Matching Using Deep Learning: A Survey](https://mlsanity.com/paper/2401.17592/) (2024)
- [Adaptive Spot-Guided Transformer for Consistent Local Feature Matching](https://mlsanity.com/paper/2303.16624/) (2023)
- [Diffusion Model for Dense Matching](https://mlsanity.com/paper/2305.19094/) (2023)
- [Relative Pose Estimation through Affine Corrections of Monocular Depth Priors](https://mlsanity.com/paper/2501.05446/) (2025)
- [Towards Generalizable Scene Change Detection](https://mlsanity.com/paper/2409.06214/) (2024)
- [Improving Transformer-based Image Matching by Cascaded Capturing Spatially Informative Keypoints](https://mlsanity.com/paper/2303.02885/) (2023)

## Abstract (arXiv)

Establishing robust and accurate correspondences between a pair of images is a long-standing computer vision problem with numerous applications. While classically dominated by sparse methods, emerging dense approaches offer a compelling alternative paradigm that avoids the keypoint detection step. However, dense flow estimation is often inaccurate in the case of large displacements, occlusions, or homogeneous regions. In order to apply dense methods to real-world applications, such as pose estimation, image manipulation, or 3D reconstruction, it is therefore crucial to estimate the confidence of the predicted matches. We propose the Enhanced Probabilistic Dense Correspondence Network, PDC-Net+, capable of estimating accurate dense correspondences along with a reliable confidence map. We develop a flexible probabilistic approach that jointly learns the flow prediction and its uncertainty. In particular, we parametrize the predictive distribution as a constrained mixture model, ensuring better modelling of both accurate flow predictions and outliers. Moreover, we develop an architecture and an enhanced training strategy tailored for robust and generalizable uncertainty prediction in the context of self-supervised training. Our approach obtains state-of-the-art results on multiple challenging geometric matching and optical flow datasets. We further validate the usefulness of our probabilistic confidence estimation for the tasks of pose estimation, 3D reconstruction, image-based localization, and image retrieval. Code and models are available at https://github.com/PruneTruong/DenseMatching.