I have a camera for a computer vision application that I know has e.g. a 60 degree field of view. It captures images that are 640 pixels wide.
My question then is if I crop the central half of pixels, at 320 pixels wide, is it fair to say that what is shown in this crop corresponds to a 30 degree field of view?
And would the ratios continue to work like that? Or am I missing some trigonometry here? I added a picture below to try and help explain my question.
Help much appreciated, thanks!
Using a coordinate system where the origin is along the image axis, $x$ coordinate and the angle $\theta$ are related by $$\tan\theta = \frac{x}{d} \quad \iff \quad x = d \tan\theta$$
If for $x = 320$ we have $\theta = 30^\circ$, then $$d = \frac{320}{\tan 30^\circ} = 320 \sqrt{3} \approx 554.256$$ and $$x = 320 \sqrt{3} \tan\left(\theta\right) \quad \iff \quad \theta = \arctan\left(\frac{x}{320 \sqrt{3}}\right)$$ In other words, if the $640$-pixel wide image corresponds to an angle of $60^\circ$, the $320$-pixel wide center part corresponds to an angle of approximately $32.2^\circ$.
This is based on the properties of 3D projection, assuming a perfect lens system (similar to a pinhole camera); and is not an approximation.