Autonomous Operators for Direct use on Irregular Image Data

Standard image processing algorithms for digital images require the availability of complete, and regularly sampled, image data. This means that irregular image data must undergo reconstruction to yield regular images to which the algorithms are then applied. The more successful image reconstruction techniques tend to be expensive to implement. Other simpler techniques, such as image interpolation, whilst cheaper, are usually not adequate to support subsequent reliable image processing. This paper presents a family of autonomous image processing operators constructed using the finite element framework that enable direct processing of irregular image data without the need for image reconstruction. The successful use of reduced data (as little as 10% of the original image) affords rapid, accurate, reliable, and computationally inexpensive image processing techniques.