Dominant Orientation using Fourier Power Spectrum
Subtract from the 8x8 image the mean value of its pixels, which should not affect the dominant orientation. This will remove artifacts due to windowing in the next step.
Window the image with a circularly symmetric window function that eliminates artifacts aligned with the image axes. Make sure you have chosen a window function that is sufficiently smooth to be sampled with a 8x8 grid without frequency domain aliasing.
Pad the image to 32x32 with zeros to increase the image size and thus the discrete Fourier transform (DFT) resolution. This makes the DFT result smoother and thus easier to interpolate.
Calculate for each angle an integral of the squared magnitude of the DFT result over a line corresponding to the angle. All angles must be treated equally; use same length lines. 4x4 piece-wise bicubic polynomial interpolation should suffice if you approximate the integral by a sum of point samples at the axis-aligned resolution of the DFT.


If you want to make the computation faster you can take advantage of that the integral will change quite smoothly as function of the angle, so you can first sample at the coarse resolution of at least $\text{atan}(1/8)\times 360\unicode{xb0}/(2\pi) \approx 7\unicode{xb0}$ to find where the highest peak might be, and then sample more finely around that angle.