Polynomial edge reconstruction sensitivity, subpixel Sobel gradient kernel analysis

Abstract

Abstract In digital image processing the accuracy and precision of edge detectors within noisy temporal environments can be imperative. In this article, a report on the polynomial reconstruction of 22.5° Sobel kernels using additional points through imaging system noise are analyzed. In comparison to the accuracy of first‐order interval kernel masks, the first‐order 45° kernel approximation using 5‐points provides consistent stability in accuracy and precision across pixel and subpixel gradients. For a 22.5° sampling interval, a 3‐point polynomial evaluation minimizes the error of the subpixel orientation of the gradient. These characteristics are derived from the retention of kernel symmetry using noninteger coefficients. Critical to gradient precision is the distortion of the evaluated points due to system noise or their value away from second‐order symmetry. For a refined measurement estimate, sensitivity up to 10−5 is demonstrated.

Keywords

• gradient approximation
• image analysis
• reconstructive edge detection
• subpixel accuracy