M-J集的物理意义与增强图像生成算法的研究

【作者】 孟庆业；

【导师】 王兴元；

【作者基本信息】 大连理工大学 ， 计算机应用技术， 2004， 硕士

【摘要】 大多数的图像生成算法，都是按照从上到下从左到右的顺序扫描图像，计算每个像素点的颜色值。在图像的生成过程中，我们无法了解图像的整体特征，或者只能了解到图像的部分特征。这些传统的生成方法对于用户自主选择图像质量、修改生成参数的交互式应用中，是很不适用的。在本文中作者对现有的隔行扫描、四叉树、Baptista图像生成方法进行了分析，提出了一种新的基于交互式应用的图像生成方法：首先根据Baptista的思想对图像进行平均取样，然后基于待插像素点的邻域像素值分布的几何特征，对像素点进行评估以决定像素点的值。实验证明，采用此生成算法，仅提供较少的数据量，即可生成较清晰的图像。在减少数据传输量的同时，提高了图像的生成质量。 本文的另一部分是基于一个典型的Langevin问题——在双势井和变化的磁场中并受一恒冲量断续作用的运动带电粒子的动力学分析，利用频闪采样法，给出了描述粒子速度变化规律的复差分方程。选取适当的磁场强度和时间间隔(采样周期)，将这一差分方程简化为用来构造广义M-J(Mandelbrot-Julia)集的复映射，并基于粒子的动力学特征探讨了广义M-J集的物理意义。结果发现：(1)广义M-J集的分形结构特征可形象地反映出粒子速度的变化规律；(2)选取的时间间隔有、无意义，决定了广义M-J集的分形结构是否具有连续性；(3)广义M-J集的演化——即粒子速度的变化规律依赖于相角主值范围的不同选取；(4)若改变磁场强度和时间间隔的选取，如选取一随机波动的磁场，则此时广义J集可能会出现内部被填充的结构特征，即在速度空间中粒子的不稳定周期轨道的闭包出现“爆炸”现象。 本文首先对M-J集和增强图像生成算法所涉及的分形理论和图像处理概念进行了阐述。本文的重点是第四章和第五章，分别对M-J集在Langevin问题中的应用和交互式应用中的彩色图像生成算法进行了研究和探讨，本文的最后对实验的结果进行了分析和总结。本文关于M-J集的相关内容已经在SCI核心收录期刊《物理学报》上发表，并被SCI与EI收录。更多还原

【Abstract】 Most image generation algorithms scan image pixels according to top-to-bottom and left-to-right scanning; calculate the value of every pixel. It gives no idea of how the final image will be while it is being generated, or only part of image attribute can be known. Those traditional scanning is not a good method to interactive application where the user can choose image quality freely and interfere in the rendering modifying the generation parameters. In this paper the author analyzed interlaced image, quadtree and Baptista image generation method, and then presented a new interactive image generation method: Firstly, Sampling evenly for image pixels on the base of Baptista’s thinking, and evaluating the pixel’s value according to image pixel distribution’s geometry character of pixel’s neighborhood. The experimental results show that the interpolation algorithm can reconstruct high resolution images using less data. The quality of image generation is improved, while the quantity of data transmission is reduced greatly.Based on a dynamics research of the typical Langevin problem, i.e., a moving charged particle under the continuous influence of a constant impulse in a double-well potential and a time-dependent magnetic field, using the stroboscopic sampling, we propose complex difference equations which can describe the change rule of particle’s velocity. By selecting appropriate magnetic intensity and time intervals (sampling period), we reduce the difference equations to complex mapping which is used to construct the generalized M-J sets. Based on the particle’s dynamics characteristic, we discuss the physical meaning of the generalized M-J sets. The author found that: (1) The fractal structure of the generalized M-J sets may visually reflect the change rule of particle’s velocity; (2) Whether the selected time intervals is significative determine whether the fractal structure of the generalized M-J sets has the continuity; (3) The evolution of the generalized M-J sets, i.e., the change rule of particle’s velocity, depends on the different choices of the principal range of the phase angle; (4) If we change the choices of the magnetic intensity and time intervals, for example, choose a random fluctuant magnetic field, the generalized M-J sets may present the interior-filling structure feature, i.e., "explosion" phenomena appears in the closure of the particle’s instable periodic orbits in the velocity space.Firstly, paper explains some related fractal theory and concept of image processing about M-J Sets and incremental image generation. The emphasis of this paper is section four and section five, research and discuss over M-J Sets’ application in Langevin problem and interactive color image generation algorithm. Finally, paper summarizes the whole paper. Correlative content about M-J Sets in this paper is published in Acta Physica Sinica, which is indexed by SCI and EI.更多还原