VarSelect: A Statistically Guided Framework for QoS-Tunable Sparse Computation in Low-Level Vision Operators

Low-level vision pipelines often evaluate local operators densely, including homogeneous regions that contribute weak responses. We introduce VarSelect, a deterministic, training-free selective-computation framework that decouples constant-time local-statistical gating from the execution of compatible classical operators. We evaluated it under implementation-parity CPU conditions using BSDS500 validation and a frozen 200-image test set, with Sobel for calibration, transfer to Scharr and Laplacian, resolution/complexity analyses, refinement, and a controlled Sobel 3×3–5×5 operator-cost experiment. At the validation-selected operating point k = 7 (local-statistics window size) and κ = 0.5 (gate-threshold multiplier), 25.6% of test pixels were selected. Sobel and Scharr achieved native-C median speed-ups of 1.545×/1.549× (scalar-audit) and 1.149×/1.174× (optimized-native) for raw-response computation, whereas Laplacian remained below parity, exposing the break-even limit for very low-cost operators. At the frozen threshold, VarSelect-SR retained 87.4%, 87.1%, and 91.9% of Dense + SR F1 for Sobel, Scharr, and Laplacian; Sobel retention slightly missed the 90% target, while full-curve ODS F1 decreased by 1.66%. In separate secondary analyses, increasing Sobel cost from 18 to 50 nominal multiply–accumulate contributions per pixel increased speed-up from 1.50× to 2.68× and reduced gate contribution from 0.489 to 0.191. Across ten isotropic rescalings of one scene, speed-up remained stable without retuning. These results support a QoS-tunable framework with an operator-agnostic interface; quality and profitability remain operator-, threshold-policy-, and implementation-dependent.