This paper introduces a smooth posterior density function for inferring shapes from silhouettes. Both the likelihood and the prior are modelled using kernel density functions and optimisation is performed using gradient ascent algorithms. Adding a prior allows for the recovery of concave areas of the shape that are usually lost when estimating the visual hull. This framework is also extended to use colour information when it is available in addition to the silhouettes. In these cases, the modelling not only allows for the shape to be recovered but also its colour information. Our new algorithms are assessed by reconstructing 2D shapes from 1D silhouettes and 3D faces from 2D silhouettes. Experimental results show that using the prior can assist in reconstructing concave areas and also illustrate the benefits of using colour information even when only small numbers of silhouettes are available.