Curvilinear structures are common in medical imaging, which typically require dedicated processing techniques. We present a new structure to process these, that we call the polygonal path image, denoted $\mathfrak{P}$. We derive from $\mathfrak{P}$ some curvilinear structure enhancement and analysis algorithms. We show that $\mathfrak{P}$ has some interesting properties: it generalizes several concepts found in other methods; it makes it possible to control the smoothness and length of the structures under study; and it can be computed efficiently. We estimate quantitatively its performance in the context of interventional cardiology for the detection of guide-wires in X-ray images. We show that $\mathfrak{P}$ is particularly well suited for this task where it appears to outperform previous state of the art techniques.