Optical analog computing based on flat optical structures offers significant advantages in system miniaturization, loss reduction, and computational speed compared to traditional systems requiring complex optical configurations. However, existing metasurface schemes for analog image processing suffer from critical limitations, including polarization dependence, bandwidth constraints, and restricted numerical aperture (NA). In this work, we demonstrate a robust and easy-to-fabricate nonlocal dielectric metasurface, which can readily perform polarization-independent edge detection with extended bandwidth and high NA. The isotropic two-dimensional second-order differentiation operations under arbitrary polarization conditions, including unpolarized illumination, are realized by leveraging the magnetic dipole resonance (MD). This scheme enables real-time, high-quality edge detection, featuring a bandwidth of 48 nm centered at 1064 nm and a NA of up to 0.5. This work provides a novel, to the best of our knowledge, approach for achieving polarization-independent edge detection, paving the way for practical applications in optical computing and imaging systems.