Using statistical moments is popular in computer vision since they provide a compact description and known performance attributes. Of particular interest is their often-cited property for reconstruction. Recent research using moments to describe moving shapes through an image sequence has led to an interest in reconstructing moving shapes from their moment description. This thesis follows two distinct lines of inquiry in order to elicit methods by which this might be achieved. Firstly, an investigation of the reconstruction of binary objects has been performed with particular emphasis on the use of orthogonal moments. Novel approaches to minimise the number of moments required in reconstruction are presented. A new adaptive thresholding technique is introduced aimed at the problem of thresholding reconstructions from limited moment sets by effecting a self-selecting parameter from the moment data itself. It has also been proposed that the Fourier Transform can be considered as an additional type of moment, offering particular benefits for computer represented objects in that there is a finite set that can provide complete reconstruction. The second strand of the thesis presents research where the changing shape of an object through a sequence is considered. It is hypothesised that by following moment 'history' (the changes of moment values through an object sequence) a novel temporal view of the object can be constructed at any point within the sequence (and outside the sequence for periodic motions). This is investigated using three different interpolation methods to predict moment values for missing frames in gait sequences and (re)constructing the frame using the predicted moment value set. The work highlights the need for an interpolation method to be non-linear in nature, otherwise the interpolation could be performed more efficiently in the object space rather than the moment space. Whilst linear interpolation is clearly linear, it is demonstrated that in the context of this application cubic spline interpolation should also be considered as a linear method. The third interpolation method, trigonometric interpolation, is non-linear in this context. In principle, it is demonstrated that interpolation in this way offers an approach to novel temporal views of objects.