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MDL in Action

The following chooses to focus on the incorporation of MDL in shape models. The process aims to choose good landmarks along some curve without any human intervention.

At the start, correspondences across a set of examples are places quite arbitrarily. Usually, a path-length spread of the points is a sensible enough choice which means landmarks are equally-spaced. This allows maximum freedom of movements for all landmarks mutually. A model is then created for the whole set and its parameters $b_{i}$which can solely characterise it are used to evaluate its compactness. For good choice of correspondences across the set we expect low values of $b_{i}$as well as ones with low variance, that is, a small range of acceptable values. The correspondences are then shifted along the contour of the shape iteratively in a process known as continuous reparameterisation. It is not just mathematically continuous (as it is functionally defined so that it fits any scale), but it also potentially affects all landmarks along the curve in a ripple-like/cascading behaviour. The reparameterisation is kept diffeomorphic so that no landmarks move beyond the position of their successor (or more generally, one of their two neighbours), a step that could result in tearing and/or folding⁵.

Experience has discovered that examples within the training sets should be dealt with one at the time⁶, evaluating the whole set and the model at each stage. Reparameterisation is usually defined by some transformation rules that are vital to get good and fast results. The reparameterisation is usually applied to a number of adjacent landmarks at a time and different scales are chosen at random as well as the location being affected. At the later stages of the reparameterisation process, it is usually expected that no real improvements will be made for large scale alternation attempts and these will therefore be discarded fully in favour of small scale alternations that make the final fine adjustments. Experience has also shown that ultimately good choice of landmark can be made automatic mainly due to the ability of evaluating the model from information theoretic point-of-view, namely MDL.

MDL is well described by Rissanen in [16,17] and the world wide web at: http://www.mdl-research.org/.