Multi-dimensional image processing

1. Background and motivation Multi-dimensional image processing is of paramount importance in areas such as multimedia, robotics, computer vision, graphics, biomedical engineering and industrial inspection. The growing interest in the development of multi-dimensional image processing techniques should be attributed primarily to the importance of color image and video processing and analysis. Practitioners and end-users deal with multi-dimensional data sets in emerging applications such as digital image indexing and archiving, web-based processing of color images and videos, virtual restoration of artworks, multimedia sequence mining and cDNA micro-array image processing. The surge of emerging applications and the proliferation of multimedia devices, as well as imaging-enabled consumer electronic devices suggest that the search for new, more efficient multi-dimensional image processing tools and solutions will continue. During the last two decades, technological advances in hardware and software have allowed for replacement of the two-dimensional (2D) image processing techniques with their three-dimensional (3D) or higher order (multi-dimensional) counter parts. For example, in the past 2D processing of image sequences or motion videos used to rely on processing the individual frames separately. However, motion videos represent a true 3D image signal or a time sequence of 2D images which exhibits significant correlation in both the spatial and temporal domain. By omitting the essential temporal correlation of the visual data, 2D solutions generate output videos with noticeable motion artifacts. To avoid visual impairments, spatiotem-poral techniques, such as various de-noising, enhancement and compression solutions, process the input video as a 3D image signal with emphasis on motion estimation and analysis. Coupled with feature extraction methods, multi-dimensional image processing concepts have been applied recently to video analysis, summarization, and retrieval with great success. In parallel with the development of new, efficient and cost effective processing of motion videos, the need for high-quality image output has boosted research in the general area of color image processing, image analysis, and perceptual image evaluation. It is well known that a digital RGB color image can be viewed as a two-dimensional array of the three-dimensional, vectorial samples. In the early days of color image processing, many of the solutions originally developed for processing monochrome (gray-scale) images were used extensively for processing color visual data since each individual channel in the RGB color image can be considered a monochrome image. However, by ignoring the essential spectral correlation that exists amongst the three color channels, these so-called component wise color processing techniques often generate images …