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In recent years there have been advances in the theory of nonlinear eigenvalue problems related to image processing and computer vision. The formulations of nonlinear transforms, related to one-homogeneous functionals, such as total-variation, has opened way to various applications of image decomposition, face fusion, denoising and more. Theory related to 1-Laplacian eigenvectors on graphs has contributed to better understanding of classification, segmentation and clustering methods. In addition, new numerical methods for solving these hard problems have been proposed. In this two-part minisymposium researchers will present their latest results and discuss future trends in this emerging field.