This project is essentially about the idea of long-exposure photographs. (Actually, it is about the idea of any-exposure photographs, but everything will be more interesting when thought about in terms of longer exposure times.) To discuss the project, we should explore a few different ways of thinking about these types of images. First, we may speak very generally: Long-exposure photographs capture the visual changes in a subject over some span of time and represent the entire changing scene in a single image.
Example of a traditional long-exposure photograph, taken by Dan Bretl.
But how do you capture change in a subject over time? To "capture change" you essentially have to record the subject in each of its states as it does change. It is helpful here if we think of time as just a series of moments. These moments are "very very small" - so small in fact that no motion can occur during one. "Motion" in fact is just the visible phenomenon of an object being in a different location in one moment as compared to the last. (This is just a reiteration of our idea of "change" that we are trying to capture.) If we station our camera at some fixed point and in some fixed direction, it has a fixed frame on the world. Thus each moment presents a single static image in our camera's frame. A long-exposure photograph then can be thought of as simply a composite of the images presented by a number of consecutive moments. The traditional in-camera method of compositing that we're used to would essentially be to keep additively layering each successive image onto all the previous ones.
This idea is rather abstract though. We must think now a bit more about an actual camera, and how it records an image. We will talk specifically about a digital camera. Such a device has a sensor made up of a grid of light-sensitive pixels. Images are formed in the camera by photons striking the sensor and the camera recording these instances. The image formed is the final accumulation of all photons, or all light, that has struck the sensor during the specified amount of exposure time.
This method of actual photograph creation is elegant and simple and works very well in cameras, but it lacks any real flexibility except in the amount of exposure time (and in the positioning of the camera, but we will only be thinking of statically-positioned cameras for now). There is another important parameter though in the long-exposure creation process that a photographer should be able to control, and what this parameter is will be revealed when you combine the ideas of my previous two paragraphs.
How can we think of the way actual long-exposure photographs are created in a camera, in terms of our previous moment-image based idea? This actually isn't all that difficult. We can think of the moment-images for an actual camera (or more precisely, for an actual camera sensor) as just the pattern of photons that hit the sensor at each moment (and which came from the scene). Then the final image is quite literally the additive layering of all moment-images on top of each other.
To make this idea a little more visually accessible to our imagination however, let us think not just of a series of "moment-images" compositely making up a long-exposure photograph, but instead of a series of short-exposure-images (each of which, if you must do so to feel comfortable and complete, you may break down into composites of series of "moment-images") compositely making up a long-exposure photograph. In this way we can think of a 5-second exposure photograph being a composite of five consecutive 1-second exposure photographs. Nothing complicated goes on here; we just composite the five images as we've been compositing images always before, and for each pixel use the sum of the brightness values of that pixel for all five contributing images, resulting in a final five-second exposure image.
This is where the new possible element of flexibility on the photographer's part comes in, and where the idea for my entire project began. We keep talking of long-exposure photographs being the composite of a series of (shorter-exposure, or possibly "moment-exposure") images. But we also keep automatically assuming that that method of compositing should be a simple flat summation! This is certainly not the only way to composite a series of images. When we are talking about moment-images (patterns of photons) reaching a camera sensor, it may seem like the only way to go (although I will later argue against this), but when we talk about the compositing of say 1/30-second exposure images, or 1-second exposure images (types of images which have taken before and can see in front of us), it becomes quite apparent that there are many varying methods of compositing that we could use.
For example, we could average all contributing images, or we could take at full value certain parts of each image and take at zero value other parts of each image. We could use an endless array of methods of compositing, and this is what my project focuses on. I wrote a piece of software which takes in a series of consecutively-captured images, as well as a method of compositing, and gives back a long-exposure photograph. I found a way to express this process in a succinct mathematical form, and this is explained in the formalization section of this website.