Aerospace thin-walled components， such as aircraft skins， commonly use chemical milling techniques to create complex surface patterns. Therefore， accurately inspecting the processed patterns is crucial in ensuring the machining quality of the thin-walled parts. However， due to factors such as gravity and clamping forces， these parts are susceptible to bending and deformation during the inspection process， leading to inconsistent detection results. Traditional methods often rely on custom fixtures that conform to the curved surface of the parts， which is both costly and inefficient， and may not meet the rapid detection demands of industrial environments. To address these challenges， this paper proposes a novel chemical milling contour detection method for aircraft skins based on point cloud dimensionality reduction. This method innovatively reduces the dimensionality of the 3D surface contour to a 2D plane， thereby mitigating part deformation and enabling high-precision detection of complex surface patterns. Initially， the CAD standard contour of the skin surface is obtained as the reference data， and the pattern contour point cloud of the actual part is captured using structured light technology as the initial data. The geodesic distance matrix is then calculated based on the measured contour model and the CAD model. Finally， both the measured and standard contours are synchronously reduced to a 2D plane using the geodesic distance matrix， facilitating error analysis of the processed contour pattern. Experimental results demonstrate that the proposed method can achieve fixture-free detection of aircraft skin milling patterns with an accuracy of 0.039 mm.