Reliable semantic segmentation is essential for clinical decision making, yet deep models rarely provide explicit statistical guarantees on their errors. We introduce a simple post-hoc framework that constructs confidence masks with distribution-free, image-level control of false-positive predictions. Given any pretrained segmentation model, we define a nested family of shrunken masks obtained either by increasing the score threshold or by applying morphological erosion. A labeled calibration set is used to select a single shrink parameter via conformal prediction, ensuring that, for new images that are exchangeable with the calibration data, the proportion of false positives retained in the confidence mask stays below a user-specified tolerance with high probability. The method is model-agnostic, requires no retraining, and provides finite-sample guarantees regardless of the underlying predictor. Experiments on a polyp-segmentation benchmark demonstrate target-level empirical validity. Our framework enables practical, risk-aware segmentation in settings where over-segmentation can have clinical consequences. Code at https://github.com/deel-ai-papers/conseco.

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