21-09-2017, 10:38 AM
Effective rendering of visual information is at the heart of many image processing tasks, including compression, denoise removal, feature extraction, and reverse problems. The efficiency of a representation refers to the ability to capture meaningful information about an object of interest using a short description. For image compression or content-based image retrieval, using an efficient rendering implies the compactness of the compressed file or the index entry for each image in the database. For practical applications such efficient representation must be obtained through structured transformations and fast algorithms. For unidimensional, smooth, part-like signals as scanning lines for an image, wavelets have been established as the proper tool because they provide an optimal representation for these signals in a sense. In addition, the wavelet representation is susceptible to efficient algorithms; in particular, leads to rapid transformations and suitable tree data structures. These are the key reasons for the success of wavelets in many signal processing and communications applications; for example, the wavelet transformation was adopted as the transformation for the new standard of image compression, JPEG-2000. However, natural images are not simply stacks of straight 1-D scanning lines; the points of discontinuity (ie, the edges) are typically located along smooth curves (ie contours) due to the smooth boundaries of the physical objects. Thus, natural images contain intrinsic geometric structures that are key features in visual information. As a result of a detachable extension of 1-D bases, 2-D wavelets are good for isolating discontinuities at edge points, but they will not "see" smoothness along the contours. In addition, separable wavelets can capture only limited directional information - an important and unique feature of multidimensional signals. These disappointing behaviors indicate that the most powerful representations are necessary in the higher dimensions.