Research On Image Enlargement And Recovery Based On Rational Function And Mesh Generation

Image enlargement is the key problem in the field of image process, but how to combine graph and image with each other effectively is a challenge. In order to keep the geometric features of the image and the flexibility of process of image enlargement and recovery, this paper firstly construct the triangular mesh based on the locally geometric features. As is well known, it is not easy to construct a non-structural triangular mesh sensitive to the features of image while combine the geometric features of the image. In order to solve this problem, we proposed a flexible and greedy mesh-generation algorithm. The algorithm regards the rational interpolation function as an operator and combines it to the process of constructing the triangular mesh. Then we use a new edge-detection method and the primary component analysis to filter the seed points which are sensitive to the local features of the image. In order to construct a higher quality mesh which is sensitive to image feature, we proposed a new strategy for the filtering of the seed points. By using a greedy method to filter the seed points which can minimize the error growth, we reconstruct the triangular mesh dynamically. We also proposed a simplified version of algorithm which can be used to achieve a better trader-off between the quality and construction speed of the triangular mesh.Next, combined with the features of rational function, we do the process of image enlargement and recovery based on the triangular mesh which had already been constructed just now. Then, we proposed an adaptive rational surface fitting algorithm with local features as constraints. In consideration of that traditional edge detection methods can be only used to detect limited directions of the edge, we firstly proposed the concept of the primary component edge which we refer to it as PCE. We can quantize the edge direction by PCE. The advantage of such quantification is that it can estimate the edge direction accurately which can be used to correct the imperfections of the traditional edge detection methods. Meanwhile, with the consideration of the impact of the spatial distance and the generalized radiometric distance, we can figure out the adaptive weights which can be used to construct an optical and ideal rational surface. For the reason that there has a free parameter in the rational function, we can realize the optical surface fitting by parameter optimization that can minimize the error growth.Finally, we used the rational function mentioned above to process the remote sensing images. In the practical application, considering the objective problem that the resolution and the quality of the remote sensing images can’t meet the practical needs regularly, we proposed an adaptive surface fitting algorithm based on rational function. The enlargement of the remote sensing image can be realized by re-sampling from the continuous fitting surface. This paper has the following contributions:1. We replace the polynomial function to rational function to fit the original surface to construct the ideal surface. The key characteristic of the rational function is that it can reflect the essence of the image interpolation.2. We come up with the concept of PCE firstly which can be used to quantize the edge direction to improve the precision of the algorithm compared with the traditional methods.3. Based on the thesis that the re-sampled pixels and the estimated pixels should have the strong correlation properties, we can achieve it by the parameter optimization, this may be a strong hypothesis, but the experimental results show that our algorithm works well.4. Consider that the level of the continuity of the rational function is relatively low, we use a certain rule of rearranging the nodes of the triangle to fix such problem.