Systems, methods, and media for providing interactive refocusing are provided, the systems comprising: a lens; an image sensor; and a processor that: causes the image sensor to capture a plurality of images over a predetermined period of time, wherein each of the plurality of images represents a scene at a different point in time; changes a depth of field between at least a pair of the plurality of images; concatenates the plurality of images to create a duration focal volume in the order in which the images were captured; computes a space-time in-focus image that represents in-focus portions from each of the plurality of images based on the duration focal volume; and computes a space-time index map that identifies an in-focus image for each location of the scene from among the plurality of images based on the duration focal volume and the space-time in-focus image.