Discrete-Constrained Regression for Local Counting Models

TL;DR

This paper introduces a discrete-constrained regression approach for local counting models, addressing inaccuracies in ground truth data that cause regression to underperform compared to classification.

Contribution

The paper proposes a novel discrete-constrained regression method that improves local counting accuracy by reducing sensitivity to annotation errors.

Findings

DC-regression outperforms classification and standard regression on crowd counting benchmarks.

The approach is also effective for age estimation tasks.

Addressing ground truth errors enhances counting model performance.

Abstract

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.