Geometric methods have revolutionized the field of image processing and image analysis. I will review some of these classical methods including image snakes, total variation minimization, image segmentation methods based on curve minimization, diffuse interface methods, and state of the art fast computational algorithms that use ideas from compressive sensing. Recently some of these concepts have shown promise for problems in high dimensional data analysis and machine learning on graphs. I will briefly review the methods from imaging and then focus on the new methods for high dimensional data and network data.