The high volumes of data produced by state-of-the-art optical microscopes encumber research. We developed a method that reduces data size and processing time by orders of magnitude while disentangling signal by taking advantage of the laminar structure of many biological specimens. Our Image Surface Analysis Environment automatically constructs an atlas of 2D images for arbitrarily shaped, dynamic and possibly multilayered surfaces of interest. Built-in correction for cartographic distortion ensures that no information on the surface is lost, making the method suitable for quantitative analysis. We applied our approach to 4D imaging of a range of samples, including a Drosophila melanogaster embryo and a Danio rerio beating heart.