<p>Distance-based fuzzy rough set is a generalized rough set model with important theoretical and applied value. Semi-grouping functions are a novel type of aggregation operators that seamlessly integrate with distance functions in fuzzy rough set theory. To address the sensitivity of distance-based fuzzy rough sets to noise influence and enhance robustness of related algorithms, this paper proposes a variable-precision fuzzy rough set model by selecting semi-grouping functions as the truth value table. The properties of distance-based variable precision fuzzy rough set are investigated. The new model satisfies the comparable property, which is not met by most variable precision fuzzy rough sets. An application of this new model in digital image contour extraction is presented. We select six digital images and adjust different precision levels to achieve optimal results. Experiments demonstrate that through the variable precision mechanism and by selecting suitable semi-grouping functions, the proposed algorithm achieves up to 5.06% reduction in noise introduction rate compared to conventional methods. This approach provides a more flexible processing mechanism, thereby yielding clearer and more complete contours.</p>