Detecting branching structures using local Gaussian models

We present a method for modelling and estimating branching structures, such as blood vessel bifurcations, from medical images. We model branches as a superposition of Gaussian functions in a local region which describe the amplitude, position and orientations of linear features and also branches. The centroids of component features are separated by applying k-means to the local Fourier phase and the covariances and amplitudes subsequently estimated by a likelihood maximisation. We apply a penalised likelihood test (AIC) to select the best fit model in a region. Results are presented on synthetic and representative 2D retinal images which show the estimation to be robust and accurate in the presence of noise. We compare our results with a scale-space operator method.