  In coronary angiography the condition of myocardial blood supply is assessed
by analyzing 2-D X-ray projections of contrasted coronary arteries. This is
done using a flexible C-arm system. Due to the X-ray immanent dimensionality
reduction projecting the 3-D scene onto a 2-D image, the viewpoint is critical
to guarantee an appropriate view onto the affected artery and, thus, enable
reliable diagnosis. In this work we introduce an algorithm computing optimal
viewpoints for the assessment of coronary arteries without the need for 3-D
models. We introduce the concept of optimal viewpoint planning solely based on
a single angiographic X-ray image. The subsequent viewpoint is computed such
that it is rotated precisely around a vessel, while minimizing foreshortening.
Our algorithm reduces foreshortening substantially compared to the input view
and completely eliminates it for 90 degree rotations. Rotations around
iso-centered foreshortening-free vessels passing the isocenter are exact. The
precision, however, decreases when the vessel is off-centered or foreshortened.
We evaluate worst case boundaries, providing insight in the maximal
inaccuracies to be expected. This can be utilized to design viewpoints
guaranteeing desired requirements, e.g. a true rotation around the vessel of at
minimum 30 degree.
