## Two New Approaches to Depth of Field Post-Processing: Pyramid Spreading and Tensor Filtering

### Abstract

Depth of field refers to the swath that is imaged in sharp focus through an optics system, such as a camera lens. Control over depth of field is an important artistic tool, which can be used, for example, to emphasize the subject of a photograph. The most efficient algorithms for simulating depth of field are post-processing methods. Post-processing can be made more efficient by making various approximations. We start with the assumption that the point spread function (PSF) is Gaussian. This assumption introduces structure into the problem which we exploit to achieve speed. Two methods will be presented. In our first approach, which we call pyramid spreading, PSFs are spread into a pyramid. By writing larger PSFs to coarser levels of the pyramid, the performance remains constant, independent of the size of the PSFs. After spreading all the PSFs, the pyramid is then collapsed to yield the final blurred image. Our second approach, called the tensor method, exploits the fact that blurring is a linear operator. The operator is treated as a large tensor which is compressed by finding structure in it. The compressed representation is then used to directly blur the image. Both methods present new perspectives on the problem of efficiently blurring an image.

### Citation

Todd J. Kosloff and Brian A. Barsky.
"**Two New Approaches to Depth of Field Post-Processing: Pyramid
Spreading and Tensor Filtering**".
In *International Joint Conference on Computer Vision, Imaging and Computer
Graphics Theory and Applications*, pages IS–9–IS–18, May 2010.