Problem #1: (marker-less scaling) Poikos ltd. has created algorithms for matching photographs of humans to three-dimensional body scans. Due to variability in camera lenses and body sizes, the resulting three-dimensional data is normalised to have unit height and has no absolute scale. The problem is to assign an absolute scale to normalised three-dimensional data.
Prior Knowledge: A database of similar (but different) reference objects with known scales. An imperfect 1:1 mapping from the input coordinates to the coordinates of each object within the reference database. A projection matrix mapping the three-dimensional data to the two-dimensional space of the photograph (involves a non-linear and non-invertible transform; x=(M*v)_x/(M*v)_z, y=(M*v)_y/(M*v)_z).
Problem #2: (improved silhouette fitting) Poikos ltd. has created algorithms for converting RGB photographs of humans in (approximate) poses into silhouettes. Currently, a multivariate Gaussian mixture model is used as a first pass. This is imperfect, and would benefit from an improved statistical method. The problem is to determine the probability that a given three-component colour at a given two-component location should be considered as "foreground" or "background".
Prior Knowledge: A sparse set of colours which are very likely to be skin (foreground), and their locations. May include some outliers. A (larger) sparse set of colours which are very likely to be clothing (foreground), and their locations. May include several distributions in the case of multi-coloured clothing, and will probably include vast variations in luminosity. A (larger still) sparse set of colours which are very likely to be background. Will probably overlap with skin and/or clothing colours. A very approximate skeleton for the subject.
Limitations: Sample colours are chosen "safely". That is, they are chosen in areas known to be away from edges. This causes two problems; highlights and shadows are not accounted for, and colours from arms and legs are under-represented in the model. All colours may be "saturated"; that is, information is lost about colours which are "brighter than white". All colours are subject to noise; each colour can be considered as a true colour plus a random variable from a gaussian distribution. The weight of this gaussian model is constant across all luminosities, that is, darker colours contain more relative noise than brighter colours.