Density codes and shape spaces

This paper presents an algorithm that allows for encoding probability density functions associated to samples of points of Rn. The resulting code is a sequence of points of Rn whose density function approximates that of the set of data points. However, contrarily to sampled data points, code points associated to two different density functions can be matched, which allows to efficiently compare such functions. Moreover, the comparison of two codes can be made invariant to a wide variety of geometrical transformations of the support coordinates, provided that the Jacobian matrix of the transformation be everywhere triangular, with a strictly positive diagonal. Such invariances are commonly encountered in visual shape recognition, for example. Thus, using this tool, one can build spaces of shapes that are suitable input spaces for pattern recognition and pattern analysis neural networks. Moreover, a parallel neural implementation of the encoding algorithm is available for 2D image data.