Pixcavator is a new kind of image analysis software. It does not assume anything about what is or is not important in the image. That's for the user to decide. The goal is lossless analysis - there is no loss of information, no approximation, and no round-up errors. Pixcavator first captures (and counts) all objects in the image and then simplifies it by removing objects indicated by the user. The output is completely context independent. This program was written to illustrate and test how an elementary tool of algebraic topology, homology theory, can be used in image processing. The idea is to build more advanced image analysis applications on this simple platform. These applications are in the areas of image recognition and search. Pixcavator removes objects from images. But what is an object in a gray scale image? Our approach follows human perception - a dark region on a light background may be an object and so is a light region on a darker background. This approach is also valid for color images; for example, one may have a dark red object on a light red background. A green object on a red background has no red and, therefore, is also detectable by this method.