GeoSelect: Spatial-Program Execution for Training-Free Referring Remote Sensing Image Segmentation

Referring remote sensing image segmentation segments the object named by a natural-language expression in an aerial image. Existing training-free methods resolve the expression through implicit vision-language activations or region-text similarity, which gives weak control over the spatial, superlative, and ordinal relations that dominate aerial referring, such as the rightmost ship or the second court from the left. We propose GeoSelect, a training-free pipeline that reframes referring as the execution of a typed spatial program. A frozen, text-only language model synthesises the expression into a small domain-specific language, a well-formedness checker accepts the program, and a deterministic executor runs it. The central abstraction is a single scored candidate set type under which every operator composes: continuous geometric fields realise position and proximity, while discrete set and order operators add the extremum, ordinal, top-k, and relational constructions that fields alone cannot express. Execution is explicit, so every intermediate is inspectable, and a reliability ladder degrades any failing program to the field-only special case. GeoSelect achieves 58.86 mIoU on RRSIS-D test and 55.27 mIoU on RISBench test, more than twice the best prior training-free method on RRSIS-D, with no referring supervision and on a single GPU. Under a fixed detector and segmenter, explicit execution improves over implicit selectors under the same backbone; the best-box-IoU and outcome-partition diagnostics motivate complementary tests of proposal recall and program-path behaviour, with the program path the clearer priority on RISBench, and an exposure audit shows comparable accuracy on the audited unseen subset. Code and configurations are available at https://github.com/Avalon-S/GeoSelect.