# DCTM: Discrete-Continuous Transformation Matching for Semantic Flow

arXiv: https://arxiv.org/abs/1707.05471 · HTML: https://mlsanity.com/paper/1707.05471/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2017.

## Built on by (most cited first, 12 of 12)

- [Convolutional Hough Matching Networks](https://mlsanity.com/paper/2103.16831/) (2021)
- [Multi-scale Matching Networks for Semantic Correspondence](https://mlsanity.com/paper/2108.00211/) (2021)
- [Deep Matching Prior: Test-Time Optimization for Dense Correspondence](https://mlsanity.com/paper/2106.03090/) (2021)
- [Diffusion Model for Dense Matching](https://mlsanity.com/paper/2305.19094/) (2023)
- [Learning Part Segmentation through Unsupervised Domain Adaptation from Synthetic Vehicles](https://mlsanity.com/paper/2103.14098/) (2021)
- [Do It Yourself: Learning Semantic Correspondence from Pseudo-Labels](https://mlsanity.com/paper/2506.05312/) (2025)
- [Convolutional Hough Matching Networks for Robust and Efficient Visual Correspondence](https://mlsanity.com/paper/2109.05221/) (2021)
- [Learning Contrastive Representation for Semantic Correspondence](https://mlsanity.com/paper/2109.10967/) (2021)
- [Learning 3D Scene Analogies with Neural Contextual Scene Maps](https://mlsanity.com/paper/2503.15897/) (2025)
- [Semantic Correspondence: Unified Benchmarking and a Strong Baseline](https://mlsanity.com/paper/2505.18060/) (2025)
- [Towards Geometry-Grounded Dense Semantic Matching with VGGT Priors](https://mlsanity.com/paper/2509.21263/) (2025)
- [Learning Space-Time Semantic Correspondences](https://mlsanity.com/paper/2306.10208/) (2023)

## Abstract (arXiv)

Techniques for dense semantic correspondence have provided limited ability to deal with the geometric variations that commonly exist between semantically similar images. While variations due to scale and rotation have been examined, there lack practical solutions for more complex deformations such as affine transformations because of the tremendous size of the associated solution space. To address this problem, we present a discrete-continuous transformation matching (DCTM) framework where dense affine transformation fields are inferred through a discrete label optimization in which the labels are iteratively updated via continuous regularization. In this way, our approach draws solutions from the continuous space of affine transformations in a manner that can be computed efficiently through constant-time edge-aware filtering and a proposed affine-varying CNN-based descriptor. Experimental results show that this model outperforms the state-of-the-art methods for dense semantic correspondence on various benchmarks.