Summary: Existing edge detection filters work well on straight edges but make significant errors near sharp corners by producing rounded corners. This is due to the fact that the edge maps produced by these filters are scale variant. We enhance Canny’s optimality criteria to incorporate detection performance near corners as an explicit design objective. The resulting optimal filter, termed ‘Bessel integral filter’, can be derived analytically and exhibits superior performance over recent alternatives, both in terms of numerical accuracy and experimental fidelity. A noise-free localization index is also derived here to account for the detection accuracy of discontinuities forming sharp corners in the absence of noise. We prove here that edges detected by the filters that are not optimal with respect to this noise-free localization index are scale variant. However, the Bessel integral filter proposed here is optimal with respect to the noise-free localization index and therefore it is a scale-invariant filter.