Graph clustering, variational image segmentation methods and Hough transform scale detection for object measurement in images

We consider the problem of scale detection in images where a region of interest is present together with a measurement tool (e.g. a ruler). For the segmentation part, we focus on the graph based method by Flenner and Bertozzi which reinterprets classical continuous Ginzburg-Landau minimisation models in a totally discrete framework. To overcome the numerical difficulties due to the large size of the images considered we use matrix completion and splitting techniques. The scale on the measurement tool is detected via a Hough transform based algorithm. The method is then applied to some measurement tasks arising in real-world applications such as zoology, medicine and archaeology.