# Discrete-Constrained Regression for Local Counting Models

arXiv: https://arxiv.org/abs/2207.09865 · HTML: https://mlsanity.com/paper/2207.09865/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 20 Jul 2022.

## Builds on (most cited first, 19 of 19)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [Simple Baselines for Human Pose Estimation and Tracking](https://mlsanity.com/paper/1804.06208/) (2018)
- [CSRNet: Dilated Convolutional Neural Networks for Understanding the Highly Congested Scenes](https://mlsanity.com/paper/1802.10062/) (2018)
- [Composition Loss for Counting, Density Map Estimation and Localization in Dense Crowds](https://mlsanity.com/paper/1808.01050/) (2018)
- [Bayesian Loss for Crowd Count Estimation with Point Supervision](https://mlsanity.com/paper/1908.03684/) (2019)
- [Distribution Matching for Crowd Counting](https://mlsanity.com/paper/2009.13077/) (2020)
- [JHU-CROWD++: Large-Scale Crowd Counting Dataset and A Benchmark Method](https://mlsanity.com/paper/2004.03597/) (2020)
- [From Open Set to Closed Set: Counting Objects by Spatial Divide-and-Conquer](https://mlsanity.com/paper/1908.06473/) (2019)
- [Deep attention-based classification network for robust depth prediction](https://mlsanity.com/paper/1807.03959/) (2018)
- [Multi-Level Bottom-Top and Top-Bottom Feature Fusion for Crowd Counting](https://mlsanity.com/paper/1908.10937/) (2019)
- [Counting with Focus for Free](https://mlsanity.com/paper/1903.12206/) (2019)
- [Count-ception: Counting by Fully Convolutional Redundant Counting](https://mlsanity.com/paper/1703.08710/) (2017)
- [Adaptive Mixture Regression Network with Local Counting Map for Crowd Counting](https://mlsanity.com/paper/2005.05776/) (2020)
- [Uniformity in Heterogeneity:Diving Deep into Count Interval Partition for Crowd Counting](https://mlsanity.com/paper/2107.12619/) (2021)
- [PaDNet: Pan-Density Crowd Counting](https://mlsanity.com/paper/1811.02805/) (2018)
- [Quantifying Facial Age by Posterior of Age Comparisons](https://mlsanity.com/paper/1708.09687/) (2017)

## Built on by (most cited first, 19 of 19)

- [Zero-shot Object Counting](https://mlsanity.com/paper/2303.02001/) (2023)
- [CrowdCLIP: Unsupervised Crowd Counting via Vision-Language Model](https://mlsanity.com/paper/2304.04231/) (2023)
- [Improving Deep Regression with Ordinal Entropy](https://mlsanity.com/paper/2301.08915/) (2023)
- [Hierarchical Classification Auxiliary Network for Time Series Forecasting](https://mlsanity.com/paper/2405.18975/) (2024)
- [Improving Point-based Crowd Counting and Localization Based on Auxiliary Point Guidance](https://mlsanity.com/paper/2405.10589/) (2024)
- [Domain-General Crowd Counting in Unseen Scenarios](https://mlsanity.com/paper/2212.02573/) (2022)
- [Redesigning Multi-Scale Neural Network for Crowd Counting](https://mlsanity.com/paper/2208.02894/) (2022)
- [Regressor-Segmenter Mutual Prompt Learning for Crowd Counting](https://mlsanity.com/paper/2312.01711/) (2023)
- [CLIP-EBC: CLIP Can Count Accurately through Enhanced Blockwise Classification](https://mlsanity.com/paper/2403.09281/) (2024)
- [RGB-D Indiscernible Object Counting in Underwater Scenes](https://mlsanity.com/paper/2304.11677/) (2023)
- [Zero-Shot Object Counting with Language-Vision Models](https://mlsanity.com/paper/2309.13097/) (2023)
- [Deep Imbalanced Regression via Hierarchical Classification Adjustment](https://mlsanity.com/paper/2310.17154/) (2023)
- [Counting Like Human: Anthropoid Crowd Counting on Modeling the Similarity of Objects](https://mlsanity.com/paper/2212.02248/) (2022)
- [Improving Deep Regression with Tightness](https://mlsanity.com/paper/2502.09122/) (2025)
- [Virtual Classification: Modulating Domain-Specific Knowledge for Multidomain Crowd Counting](https://mlsanity.com/paper/2402.03758/) (2024)
- [Crowd Counting with Sparse Annotation](https://mlsanity.com/paper/2304.06021/) (2023)
- [Learning from Pseudo-labeled Segmentation for Multi-Class Object Counting](https://mlsanity.com/paper/2307.07677/) (2023)
- [RAD: Retrieval High-quality Demonstrations to Enhance Decision-making](https://mlsanity.com/paper/2507.15356/) (2025)
- [RepSFNet : A Single Fusion Network with Structural Reparameterization for Crowd Counting](https://mlsanity.com/paper/2601.20369/) (2026)

## Abstract (arXiv)

Local counts, or the number of objects in a local area, is a continuous value by nature. Yet recent state-of-the-art methods show that formulating counting as a classification task performs better than regression. Through a series of experiments on carefully controlled synthetic data, we show that this counter-intuitive result is caused by imprecise ground truth local counts. Factors such as biased dot annotations and incorrectly matched Gaussian kernels used to generate ground truth counts introduce deviations from the true local counts. Standard continuous regression is highly sensitive to these errors, explaining the performance gap between classification and regression. To mitigate the sensitivity, we loosen the regression formulation from a continuous scale to a discrete ordering and propose a novel discrete-constrained (DC) regression. Applied to crowd counting, DC-regression is more accurate than both classification and standard regression on three public benchmarks. A similar advantage also holds for the age estimation task, verifying the overall effectiveness of DC-regression.