Pyramid-based Computer Graphics the Pyramid Representation and Computer Graphics

Pyramid-based graphics techniques can provide realistic computer graphics on small systems without the complexities of physics simulations. Human beings have an intuitive feel for graphics. Graphics problems such as blending two images smoothly, interpolating to fill in missing image data, or creating realistic looking images are routinely solved by artists using traditional media. It i s much more difficult to perform these tasks mathematically. A major step in solving a computer graphics problem is choosing an appropriate numerical representation for the image, one which allows us to use our visual and artistic intuition in a natural way. Artists often tend to separate the spatial scales of an image when creating or altering a picture. When an artist paints a landscape, the coarse scale (low spatial frequency) information is filled in first, as a wash of color in a large region. Intermediate size details can be added next with a medium-size brush. As a last step, the artist draws the fine details with a small brush. The image can be considered a sum of overlays of increasingly fine detail. When an artist touches up a damaged picture, both the large and small scale variations are considered in filling in the missing pieces. In synthesizing and combining images, we would like to imitate the artist's ability to see an image on both large and small scales by representing the image mathematically on many different spatial scales simultaneously. The simplest way to represent an image is to set the numerical value of each pixel proportional to the image intensity. This representation is useful when we want to paint or draw directly one pixel at a time, or when simple manipulations of contrast or color are desired. But it becomes cumbersome when we want to look at an image at several spatial resolutions. Abstract: This paper describes pyramid solutions to graphics problems that have proven difficult in other image representations. The "physics simulation" approach grows more out of the physics and mathematical modelling traditions. Greater realism can be achieved by using the physics simulation approach but the complexity and computation time are vastly increased over the multiresolution pyramid approaches described here. A Fourier transform representation can be used to separate the various spatial scales of an image. Unfortunately, when we leave the familiar spatial domain for the spatial frequency domain our intuitive feel for the problem is lost. Operating o n the Fourier transform …