CANONICAL ORIENTATION

In order to obtain a reference frame for computing the descriptor of a keypoint a local reference frame is needed, one solution is to chose the direction in which most of the gradient is found

DOG CANONICAL ORIENTATION

Given a keypoint the orientation $\theta$ and magnitude $m$ is given by

$$m(x,y)=\sqrt{(L(x+1,y)-L(x-1,y){)}^2+(L(x,y+1)-L(x,y-1){)}^2}$$ $$\theta (x,y)={\tan }^{-1}\frac{L(x,y+1)-L(x,y-1))}{L(x+1,y)-L(x-1,y))}$$

Then an orientation histogram is computed with a bin size of $10^{°}$ with the contributions of each pixel of the belonging to a neighborhood of the keypoint.

The contribution of a single point is obtained by the gradient magnitude weighted by a Gaussian with $\sigma =1.5{\sigma }_S$ to account for the scale of the keypoint

then the highest peak of the histogram is considered for the canonical orientation with the 2 neighbors

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