ANNE: adaptive neuron network expansion for 2D medical image segmentation

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Accurate 2D medical image segmentation requires both fine-scale boundary modeling and long-range contextual reasoning, yet architectures that provide both capabilities are often computationally expensive. We present ANNE, a compact encoder–decoder that combines Mamba-based state-space blocks for efficient global-context modeling with Adaptive Progressive Expansion Neurons (A-PEN) for nonlinear local feature refinement. A-PEN extends prior progressively expanded neuron formulations by introducing learnable normalized gates over a fixed bank of polynomial expansion terms, together with trainable expansion coefficients and a parametric activation. The normalized gates provide a coupled parameterization of the candidate expansion branches rather than a uniquely identifiable measure of individual term importance. Remez approximation is used as approximation-theoretic motivation for compact polynomial representations; ANNE does not execute the classical Remez exchange algorithm or claim a minimax approximation guarantee. We evaluate ANNE on eight public 2D datasets covering dermoscopic lesion, colonoscopic polyp, and retinal-vessel segmentation. Across these benchmarks, ANNE provides competitive overlap and boundary accuracy while using approximately 2.77 million trainable parameters. Component ablations indicate that A-PEN and Mamba make complementary contributions, and resolution profiling identifies a favorable accuracy–cost operating point at $$\varvec{256\times 256}$$ 256 × 256 pixels. To ensure transparent interpretation, controlled reproductions are distinguished from literature-reported comparisons. The results support ANNE as a parameter-efficient segmentation architecture within the evaluated 2D benchmark setting, while external-domain, volumetric, and clinical validation remain important directions for future work.