We introduce theoretically and demonstrate experimentally the performance of a Guided-Path Tomography sensor head and a complete system for imaging of physical parameters on non-planar and possibly flexible surfaces. Novel in our approach is to employ waveguiding sensor elements, strategically arranged on the imaged surface, to allow tomography measurements and the inverse problem solution. In the reported particular implementation we image deformation over ∼1sq.m., which is achieved by sensitizing the sensor elements to bending. The problem of severely limited number of measurements is addressed by an original method for sinogram recovery, followed by the application of well established methods for solving the hard-field tomography inverse problem. We show that the sensor is capable of distinguishing objects of different mass and shape of footprint. It also calculates the coordinates of the centre of mass of the imaged objects, which facilitates integration with control systems. \circledC 2009 IOP Publishing Ltd.