英文摘要 | Multiwavelets theory has received great attention of researchers in recent years, and it is an important branch of wavelet theory. With the profound mathematics foundation, multiwavelets has been applied into physics, chemistry, biology, electrical engineering and other areas. Both in theoretical and in application aspects, multiwavelets is well worth of study. Due to the limitation of time and ability, I put my focus on how to apply multiwavelets into image registration and image mosaic. During the work on multiwavelets and its application, I conducted some research on the key problems as following: 1. From the point view of digital signal processing(image processing, pattern recognition), it is pointed that wavelets has some disadvantage although it has advantage and has been applied into many areas. Multiwavelets, which has compact support and symmetry, can get rid of those drawbacks. Furthermore, the design of filter banks and the preprocessing methods are discussed. 2. Based on multiwavelets, we proposed a multiresolution diagonal algorithm. Firstly, we present multi-resolution model for image registration, and its iteration formulas; Secondly, after careful comparation among kinds of optimization methods, we choose Broyden-Fletcher-Goldfarb-Shanno algorithm and give the formulas for derivatives which are required in the optimization; Finally, based on multiwavelets, we propose a multiresolution diagonal algorithm. Our experimental results indicate that our algorithm converges very rapidly, needs less computation and has high robustness which is less-sensible to noise and is not likely to get trapped in a local minimum. 3. Carefully analyze two problems which are common in image mosaic, sharp edge and double-exposure effect. To overcome the problems, we propose a multiresolution approach with weight function. Experimental results indicate that this method can product perfect vision effect. 4. We generalize the concept of mosaic, and discuss the field of arbitrary view generation(AVG). We firstly point out the drawbacks of geometry modeling and illumination modeling in the traditional methods, and then give a survey of image-based approach. Based on Lumigraph, we present a capturing-viewpoint limited way to construct the lumigraph, which can simplify the calibration procedure. The computation formulas and system blocks are also presented. Currently, there are still many problems left open for multiwavelet, such as its construction, choice of the best basis, and its applications in image processing and computer vision. We believe that with the advancement of this field and other related fields, multiwavelet will become a more developed theory and find its applications in computer vision. |
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