Weakly Supervised Boundary Refinement for Artificial Intelligence Agriculture Field-Parcel Delineation Under Cadastral Map Obsolescence: A Computer Geometric-Error Evaluation

Cadastral maps in many agricultural regions are decades out of date, so parcel boundaries derived from them misalign with the fields that artificial-intelligence delineation systems are asked to recognise. the present analysis treats weakly supervised boundary refinement as a geometric-error problem rather than a segmentation-accuracy problem, and asks how much of the residual misalignment between a cadastral prior and a contemporary field can be removed when the only supervision available is image-level or sparse-point annotation. A formal model of boundary displacement is developed in which the cadastral polygon supplies a prior, a weak label supplies a directional constraint, and refinement is posed as minimisation of a geometric energy over admissible boundary deformations. Two propositions are proved: that the refined boundary is consistent under a Lipschitz condition on the image-derived edge field, and that the geometric-error reduction is bounded below by the cadastral displacement magnitude whenever the weak supervision is informative. The propositions are evaluated analytically against a declared variance structure with an intraclass correlation of 0.64, between-cluster standard deviation of 6.0 and residual standard deviation of 4.5, using a before-after-control-impact design across 8, 16, 24 and 32 clusters and effect sizes of 3, 5 and 8 percentage points with 2000 replications per cell. Power reaches conventional levels at 54 clusters for a 5-percentage-point effect. The contribution is a geometric-error formulation that separates cadastral obsolescence from annotation noise and specifies the conditions under which weakly supervised refinement is worth attempting.