A Semiautomatic Multi-Label Color Image Segmentation Coupling Dirichlet Problem and Colour Distances

Image segmentation is an essential but critical component in low level vision, image analysis, pattern recognition, and now in robotic systems. In addition, it is one of the most challenging tasks in image processing and determines the quality of the final results of the image analysis. Colour based segmentation could hence offer more significant extraction of information as compared to intensity or texture based segmentation. In this work, we propose a new local or global method for multi-label segmentation that combines a random walk based model with a direct label assignment computed using a suitable colour distance. Our approach is a semi-automatic image segmentation technique, since it requires user interaction for the initialisation of the segmentation process. The random walk part involves a combinatorial Dirichlet problem for a weighted graph, where the nodes are the pixel of the image, and the positive weights are related to the distances between pixels: in this work we propose a novel colour distance for computing such weights. In the random walker model we assign to each pixel of the image a probability quantifying the likelihood that the node belongs to some subregion. The computation of the colour distance is pursued by employing the coordinates in a colour space (e.g., RGB, XYZ, YCbCr) of a pixel and of the ones in its neighbourhood (e.g., in a 8-neighbourhood). The segmentation process is, therefore, reduced to an optimisation problem coupling the probabilities from the random walker approach, and the similarity with respect the labelled pixels. A further investigation involves an adaptive preprocess strategy using a regression tree for learning suitable weights to be used in the computation of the colour distance. We discuss the properties of the new method also by comparing with standard random walk and k-means approaches. The experimental results carried on the White Blood Cell (WBC) dataset and GrabCut datasets show the remarkable performance of the proposed method in comparison with state-of-the-art methods, such as normalised random walk and normalised lazy random walk, with respect to segmentation quality and computational time. Moreover, it reveals to be very robust with respect to the presence of noise and to the choice of the colourspace.