Object Counting Across Modalities: Taxonomies, Benchmarks, Applications, and Open Challenges

Object-counting methods have rapidly shifted from class-specific density regression to open-vocabulary, foundation-model-backed counters. These methods now enumerate instances from various visual and textual prompts. While this shift marks major conceptual progress, our survey argues that claims of universal generality have outpaced the evaluative infrastructure. Most progress metrics rely on a few saturated benchmarks that models exploit for statistical regularities. Newly introduced diagnostic datasets reveal systematic failures in semantic grounding, temporal identity, and spatial reasoning with occlusion. To address these failures, we introduce a five-axis taxonomy (modality, mechanism, prompting, supervision level, and generalization setting). We use this taxonomy to audit the literature across application domains, including microscopy, remote sensing, crowd counting, and agriculture. This formalizes prevailing challenges into six structural contradictions. From these, we propose a roadmap for compositional scene understanding, active counting agents, and unified multimodal evaluation protocols. The main imperative is to build a robust evaluation infrastructure to distinguish open-world generalization from benchmark-specific optimization, rather than simple incremental engineering.