The discrete ordered median problem for clusteringSTEM-image intensities

Resumen

Electron tomography is a technique for imaging three-dimensional structures of materials at nanometer scale. This technique consists on reconstructing nano-objects thanks to projections provided by a electron microscope from different tilt angles. The Scanning-Transmission Electron Microscope images obtained are used for identifying the elements that constitute the nano-objects under study. This recognition procedure is knownas segmentation which consists of classifying the image intensities into different clusters. Classical segmentation models stand out for their ability to provide one segmentation of the original image very quickly and with low computational burden [1]. However, they do not usually achieve high quality segmentations with a small number of clusters to classify the different elements which compose the structures represented in the image.The main idea behind this work is to apply the ordered median problem to locate p intensities as the representatives of p different clusters andallocate every intensity to one cluster representative [2]. The advantage ofusing this function is its good adaptability to the different types of particlesto be studied due to the wide range of vector weights that can be cast [3]. Moreover, to reduce the computational time needed to solve these problems, some improvements are introduced for the formulations by taking advantage of the vector weight structure. These alternative improvements are based on the idea developed in [4]. Finally, we propose different ways of analysing the quality of the segmentations provided by our approach using different choices of the vector weights in some real instances.