A new method is presented for tomographic reconstruction of objects with homogeneous attenuation. The method is based on parametric representation with Non-Uniform Rational B-Splines (NURBS) and statistical inversion with a Markov Chain Monte Carlo (MCMC) algorithm. The method recovers the approximate boundary curve shape and the attenuation value of two-dimensional homogeneous objects. The boundary can be represented by NURBS with few parameters, reducing the number of degrees of freedom. However, this leads to a nonlinear inverse problem, and therefore statistical inversion is used. One of the benefits of the approach is that the reconstruction is automatically in the form of the geometrical representation in industrial CAD format or CNC configuration. Computational results are presented with two different simulated homogeneous geometric models and sparsely sampled tomographic data. The new method outperforms the baseline method (filtered back-projection) in image quality but not in computational speed.