# Numerical Coordinate Regression with Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1801.07372 · HTML: https://mlsanity.com/paper/1801.07372/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2018.

## Built on by (most cited first, 30 of 72)

- [Human Pose Regression with Residual Log-likelihood Estimation](https://mlsanity.com/paper/2107.11291/) (2021)
- [Neural Localizer Fields for Continuous 3D Human Pose and Shape Estimation](https://mlsanity.com/paper/2407.07532/) (2024)
- [BARC: Learning to Regress 3D Dog Shape from Images by Exploiting Breed Information](https://mlsanity.com/paper/2203.15536/) (2022)
- [STAR Loss: Reducing Semantic Ambiguity in Facial Landmark Detection](https://mlsanity.com/paper/2306.02763/) (2023)
- [TFPose: Direct Human Pose Estimation with Transformers](https://mlsanity.com/paper/2103.15320/) (2021)
- [Sparse to Dense Motion Transfer for Face Image Animation](https://mlsanity.com/paper/2109.00471/) (2021)
- [DSC-PoseNet: Learning 6DoF Object Pose Estimation via Dual-scale Consistency](https://mlsanity.com/paper/2104.03658/) (2021)
- [Real-time Outdoor Localization Using Radio Maps: A Deep Learning Approach](https://mlsanity.com/paper/2106.12556/) (2021)
- [Localization with Sampling-Argmax](https://mlsanity.com/paper/2110.08825/) (2021)
- [Off The Grid: Detection of Primitives for Feed-Forward 3D Gaussian Splatting](https://mlsanity.com/paper/2512.15508/) (2025)
- [LSPnet: A 2D Localization-oriented Spacecraft Pose Estimation Neural Network](https://mlsanity.com/paper/2104.09248/) (2021)
- [Low-resolution Human Pose Estimation](https://mlsanity.com/paper/2109.09090/) (2021)
- [Heatmap Distribution Matching for Human Pose Estimation](https://mlsanity.com/paper/2210.00740/) (2022)
- [Distractor-aware Event-based Tracking](https://mlsanity.com/paper/2310.14194/) (2023)
- [Single-Shot Cuboids: Geodesics-based End-to-end Manhattan Aligned Layout Estimation from Spherical Panoramas](https://mlsanity.com/paper/2102.03939/) (2021)
- [Multi-modal Retinal Image Registration Using a Keypoint-Based Vessel Structure Aligning Network](https://mlsanity.com/paper/2207.10506/) (2022)
- [Ki-Pode: Keypoint-based Implicit Pose Distribution Estimation of Rigid Objects](https://mlsanity.com/paper/2209.09659/) (2022)
- [EDM: Efficient Deep Feature Matching](https://mlsanity.com/paper/2503.05122/) (2025)
- [Linear-Covariance Loss for End-to-End Learning of 6D Pose Estimation](https://mlsanity.com/paper/2303.11516/) (2023)
- [Cascaded Dual Vision Transformer for Accurate Facial Landmark Detection](https://mlsanity.com/paper/2411.07167/) (2024)
- [Single Person Pose Estimation: A Survey](https://mlsanity.com/paper/2109.10056/) (2021)
- [Accurate Scoliosis Vertebral Landmark Localization on X-ray Images via Shape-constrained Multi-stage Cascaded CNNs](https://mlsanity.com/paper/2206.02087/) (2022)
- [FCSN: Global Context Aware Segmentation by Learning the Fourier Coefficients of Objects in Medical Images](https://mlsanity.com/paper/2207.14477/) (2022)
- [ArtFacePoints: High-resolution Facial Landmark Detection in Paintings and Prints](https://mlsanity.com/paper/2210.09204/) (2022)
- [Bias-Compensated Integral Regression for Human Pose Estimation](https://mlsanity.com/paper/2301.10431/) (2023)
- [KeyPosS: Plug-and-Play Facial Landmark Detection through GPS-Inspired True-Range Multilateration](https://mlsanity.com/paper/2305.16437/) (2023)
- [Domain Generalization for In-Orbit 6D Pose Estimation](https://mlsanity.com/paper/2406.11743/) (2024)
- [landmarker: a Toolkit for Anatomical Landmark Localization in 2D/3D Images](https://mlsanity.com/paper/2501.10098/) (2025)
- [Pretrained equivariant features improve unsupervised landmark discovery](https://mlsanity.com/paper/2104.02925/) (2021)
- [Multi-Domain Multi-Definition Landmark Localization for Small Datasets](https://mlsanity.com/paper/2203.10358/) (2022)

## Abstract (arXiv)

We study deep learning approaches to inferring numerical coordinates for points of interest in an input image. Existing convolutional neural network-based solutions to this problem either take a heatmap matching approach or regress to coordinates with a fully connected output layer. Neither of these approaches is ideal, since the former is not entirely differentiable, and the latter lacks inherent spatial generalization. We propose our differentiable spatial to numerical transform (DSNT) to fill this gap. The DSNT layer adds no trainable parameters, is fully differentiable, and exhibits good spatial generalization. Unlike heatmap matching, DSNT works well with low heatmap resolutions, so it can be dropped in as an output layer for a wide range of existing fully convolutional architectures. Consequently, DSNT offers a better trade-off between inference speed and prediction accuracy compared to existing techniques. When used to replace the popular heatmap matching approach used in almost all state-of-the-art methods for pose estimation, DSNT gives better prediction accuracy for all model architectures tested.