Many natural images contain reflections and transparency, i.e., they contain mixtures of reflected and transmitted light. When viewed from a moving camera, these appear as the superposition of component layer imagesmoving relative to each other. The problem of multiple motion recovery has been previously studied by a number of researchers. However, no one has yet demonstrated how to accurately recover the component images themselves. In this paper we develop an optimal approach to recovering layer images and their associated motions from an arbitrary number of composite images. We develop two different techniques for estimating the component layer images given known motion estimates. The first approach uses constrained least squares to recover the layer images. The second approach iteratively refines lower and upper bounds on the layer images using two novel compositing operations, namely minimum- and maximum-composites of aligned images. We combine these layer extraction techniques with a dominant motion estimator and a subsequent motion refinement stage. This results in a completely automated system that recovers transparent images and motions from a collection of input images.