Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Computational Modeling of Objects Presented in Images, CompIMAGE 2014, held in Pittsburgh, PA, USA, in September 2014. The 29 revised full papers presented together with 10 short papers and 6 keynote talks were carefully reviewed and selected from 54 submissions. The papers cover the following topics: medical treatment, imaging and analysis; image registration, denoising and feature identification; image segmentation; shape analysis, meshing and graphs; medical image processing and simulations; image recognition, reconstruction and predictive modeling; image-based modeling and simulations; and computer vision and data-driven investigations.