稳定场图像重建中的传递函数研究

目的 针对2维图像重建（或修复）的准确性和效率问题，以传递函数为核心并提出相关重建算法。方法 在图像局部纹理稳定场模型的基础上，针对每一个缺损像素点，考虑其周围已知区域的像素点都对它进行能量传递，且在重建过程中首先将能量传递到最近邻域内，由此构造传递函数并引入标量场的二阶泰勒展开来完成，最终依据最近邻域内的能量值，以插值完成重建。结果 采用重新构造的传递函数并结合不同的插值方法分别对缺损的几何图形、灰度图像及彩色图像进行重建，结果与图像场方向导数的局部区域重建算法、典型的CDD（curvature driven diffusion）、BSCB（Bertalmio Sapiro Caselles Ballester）、TV（total variation）重建算法相比，重建准确率分别提高了6%、10%、15%、13%，峰值信噪比（PSNR）分别提高了2 dB、1 dB、3 dB、2.5 dB，并且图像缺损边缘及纹理细节的重建更加清晰。结论 对2维图像重建的传递函数的研究及所提出的相关重建算法，对于不同类型图像不同程度的缺损，以保持较好的整体视觉效果和重建效率为前提，较大地提高了重建准确性和PSNR，尤其在图像缺损区域边缘及纹理细节的重建上表现出色。

Transfer function research of stable field reconstruction

Objective Reconstructing defective images accurately and efficiently has become increasingly important nowadays. With the development of image analysis and recognition, many reconstructed images have been used for feature extraction, and few algorithms can realize accurate and efficient reconstruction effect. This study reconstructs local image regions based on the directional derivative of a field and proposes a stable field model of image local texture to achieve accuracy and reconstruction efficiency. The point source effect function is chosen as the transfer function of the pixel information relationship between the known region and the defect region. However, the designed point source effect function only considered the function of the gradient in the process of energy transfer. The energy transfer value of pixels in the defective region is calculated. The weighted summation is realized by average filtering. Experimental data show that the reconstruction of the edge of the geometry is not fine enough to greatly improve the accuracy of the actual image reconstruction. Given the problem of the accuracy and efficiency of the two-dimensional image reconstruction (or inpainting), this study designed the transfer function as the core function, proposed a new relative reconstruction algorithm, and mainly introduced the transfer function because this function involved energy transformation. Method Stationary images can be regarded as a stable energy field because of the stable result of the interaction between the surface and structure of object and light. Several studies have reconstructed defect images based on a stable field and have proven that the reconstruction effects can achieve the desired visual effect and high accuracy rate. Thus, the stable field model is used in this paper to describe the image local region. The energy value of the defect points is almost the same as that of the points in the nearest neighborhood. Thus, considering the value of these points is of great importance. In view of each pixel in the defect region, a reconstruction model considers the pixels in the known region as transmitting energy to each known pixel. During the reconstruction process, the energy is first transmitted into the nearest neighborhood, the transfer function is then constructed, and second-order Taylor expansion is introduced to achieve this process. Finally, the reconstruction is completed by interpolation according to the energy value in the nearest neighbor domain. Result This study reconstructed defect typical geometric graphs, gray images, and color images by using an algorithm that contains the transfer function and different interpolation methods. The interpolation methods include nearest neighbor interpolation, bilinear interpolation, and cubic convolution interpolation. Reconstruction results obtained by different interpolation methods are different. Compared with studies on reconstructing image local regions based on the directional derivative of a field, the typical curvature-driven diffusion, Bertalmio-Sapiro-Caselles-Ballester method, and total variation reconstruction algorithms, the reconstruction accuracy increased by approximately 6%, 10%, 15%, and 13% respectively, and the peak signal-to-noise ratio (PSNR) increased by approximately 2, 1, 3, and 2.5 dB, respectively. The reconstruction of the damaged edges and texture is clearer than that of the relative reconstruction models. Results improved considerably compared with traditional models because the proposed algorithm differs from traditional algorithms in certain aspects. For traditional algorithms, the main research idea is to use the information around the image defect area to transfer the inside of the region through several iterations. Once an iteration is performed, the value of the transfer function is updated to satisfy the visual effect of human visual observation. However, our algorithm does not involve iterations and transfers the energy value only once. Conclusion An improved algorithm based on the foundation of the image local region''s stable field model and the inpainting algorithms based on the stable field is proposed in this study, which investigates the transfer function of two-dimensional image reconstruction and the related reconstruction algorithms and shows the reconstruction of image edge and texture details. To maintain a good visual effect, the proposed method greatly improved reconstruction accuracy and PSNR, especially in the image defect region edge, and performs well in reconstructing texture details. Experimental results show that the proposed algorithm obtains good effects and has universal applicability to different types of images with varying degrees of defect.