The Roofline model offers a compact way to reason about whether an image-processing kernel is limited by floating-point throughput or by memory bandwidth. This article applies the Roofline framework to canonical filters—generic 3×3 convolution, Sobel edge detection with gradient magnitude, and separable Gaussian blurs (5×5 and 7×7)—to map their computational intensity and predict performance on representative CPU and GPU profiles. We formalize arithmetic intensity under transparent assumptions for single-channel 32-bit images and two-pass separable pipelines, and we derive bandwidth-bound ceilings and compute-bound plateaus for each architecture. Using an illustrative device pair (CPU with 500 GFLOP/s peak and 50 GB/s bandwidth; GPU with 10 TFLOP/s peak and 300 GB/s bandwidth), we show that the studied filters occupy the bandwidth-limited region with intensities between ≈0.38 and ≈1.25 FLOPs/byte, which implies that improving blocking, reuse, and data movement often dominates raw FLOP optimization. A Roofline chart and a comparative table report predicted ceilings in GFLOP/s and converted pixel-throughput ceilings for each kernel. We discuss implications for schedule design, separability, and pipeline organization and argue that Roofline-guided reasoning helps prioritize cache tiling, fusion, and memory-traffic reduction before micro-optimizing scalar FLOPs.

Roofline model, arithmetic intensity, memory bandwidth

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