Google can tell what it is for photo search well, but not for (patent) drawing search. Drawing-based search remains challenging because drawing images contain much less information compared with natural images; no color and texture, only shape and topology. In this talk, I will present remaining challenges in computer vision, and we will show how we overcome the obstacles by developing new image representation, methods and algorithms based on topological graphs and computational geometry. Our image representation, and methods are able to make machine learning and machine vision learn and see better. I will show the effectiveness of our topological graph-based image representation and methods using three applications: image classification, image denoising, and line segment detection, where patent image data are used in the second and third applications.