  The mixture of Gaussian distributions, a soft version of k-means , is
considered a state-of-the-art clustering algorithm. It is widely used in
computer vision for selecting classes, e.g., color, texture, and shapes. In
this algorithm, each class is described by a Gaussian distribution, defined by
its mean and covariance. The data is described by a weighted sum of these
Gaussian distributions. We propose a new method, inspired by quantum
interference in physics. Instead of modeling each class distribution directly,
we model a class wave function such that its magnitude square is the class
Gaussian distribution. We then mix the class wave functions to create the
mixture wave function. The final mixture distribution is then the magnitude
square of the mixture wave function. As a result, we observe the quantum class
interference phenomena, not present in the Gaussian mixture model. We show that
the quantum method outperforms the Gaussian mixture method in every aspect of
the estimations. It provides more accurate estimations of all distribution
parameters, with much less fluctuations, and it is also more robust to data
deformations from the Gaussian assumptions. We illustrate our method for color
segmentation as an example application.
