Investigation of cardinality classification for bacterial colony counting using explainable artificial intelligence

Automated bacterial colony counting from images is an important technique to obtain data required for the development of vaccines and antibiotics. However, bacterial colonies present unique machine vision challenges that affect counting, including (1) small physical size, (2) object clustering, (3) high data annotation cost, and (4) limited cross-species generalisation. While FamNet is an established object counting technique effective for clustered objects and costly data annotation, its effectiveness for small colony sizes and cross-species generalisation remains unknown. To address the first three challenges, we propose ACFamNet, an extension of FamNet that handles small and clustered objects using a novel region of interest pooling with alignment and optimised feature engineering. To address all four challenges above, we introduce ACFamNet Pro, which augments ACFamNet with multi-head attention and residual connections, enabling dynamic weighting of objects and improved gradient flow. Experiments show that ACFamNet Pro achieves a mean normalised absolute error (MNAE) of 9.64% under 5-fold cross-validation, outperforming ACFamNet and FamNet by 2.23% and 12.71%, respectively.

When a bacterial sample is exposed to several antibiotics, not every applied drug necessarily acts: if the organism is resistant to one of them, that drug leaves no morphological trace. The clinically meaningful quantity is therefore not which antibiotics were applied, but which ones were active. We show that these two are sharply decoupled in real E. coli microscopy - naively assuming the applied combination equals the active one is correct only about 37% of the time - yet existing computational tools are ill-suited to recovering the active set. Forward perturbation models such as scGen, CPA, and IMPA are designed to predict appearance from treatment, not the reverse, and inverting them degrades sharply; discriminative image classifiers tend to memorise strain- and batch-specific texture and fail to transfer across experimental replicates. We introduce AURA, which reframes the task as constrained, energy-based inverse attribution. Its central inductive bias is that the active set must be a subset of the applied set; this collapses the candidate space and lets AURA infer the active subset of applied antibiotics by decomposing residual morphology into antibiotic response atoms and selecting the subset with the lowest reconstruction energy, using no strain label at test time. AURA-E adds evidence-aware abstention, withholding a prediction when candidate explanations remain near-equally plausible. On cross-replicate transfer in an E. coli cytological profiling dataset, AURA recovers the active antibiotic combination with 95.47% exact-match accuracy.

Interpretability in object detection provides crucial confidence support for clinical auxiliary diagnosis. However, in tiny bacteria detection, traditional explanation methods often suffer from blurred foreground boundaries and diffuse feature attribution due to the extreme sparsity of target morphological features and severe interference from complex backgrounds. Such limitations hinder the provision of logically coherent morphological evidence. To bridge this gap, we propose a novel eXplainable AI (XAI) framework, SAM-Sode. The framework innovatively transforms initial feature attribution maps into geometry-aware prompts, leveraging the prior knowledge of the foundation model (SAM3) to achieve spatial refinement and morphological reconstruction of the explanatory mappings. Furthermore, we introduce a dual-constraint mechanism based on physical significance and geometric alignment to perform instance-level denoising, generating coherent explanations that better align with human expert intuition. Experimental results on our self-constructed bacteria dataset with complex circuit backgrounds (containing 2,524 images) and other public datasets demonstrate that the proposed method effectively suppresses background redundancy and significantly enhances the decision-making transparency of tiny object detection.