The indicator of contact boundaries for an integral geometry problem

We pose and study a rather particular integral geometry problem. In the two-dimensional space we consider all possible straight lines that cross some domain. The known data consist of the integrals over every line of this kind of an unknown piecewise smooth function that depends on both points of the domain and the variables characterizing the lines. The object we seek is the discontinuity curve of the integrand. This problem arose in the author's previous research in X-ray tomography. In essence, it is a generalization of one mathematical aspect of flaw detection theory, but seems of interest in its own right. The main result of this article is the construction of a special function that can be unbounded only near the required curve. Precisely for this reason we call the function the indicator of contact boundaries. A uniqueness theorem for the solution follows rather easily from the property of indicators.