This study presents an enhanced mean curvature image registration model designed to handle displacement fields with varying degrees of smoothness while effectively preventing grid folding. Our approach utilizes a multi-level strategy that integrates the Lagrangian multiplier method and damped Newton's method employing Armijo line search for the efficient solution of the proposed model. Convergence analysis of the algorithm is also conducted. Both synthetic and real image experiments produced results demonstrate that our model achieves visually superior registration outcomes and robustly prevents grid folding.

The mean curvature model is one of the efficient higher-order models for image denoising, and its Euler-Lagrange equation is a fourth-order nonlinear equation which makes the development of efficient numerical methods very difficult. In this paper, on the one hand, it is proposed to replace the gradient in the nonlinear terms other than the mean curvature with the gradient obtained by convolving the image with a Gaussian low-pass filter. This modification leads to a new Euler-Lagrange equation that retains the structure of the original equation, but with a reduced degree of nonlinearity. On the other hand, we also develop a novel fixed point curvature method to solve this new equation. Numerical experiments show that our method not only recovers high-quality images from highly noisy images, but is also 10 times faster than the nonlocal means (NLM) method and 6-10 times faster than the the augmented Lagrangian method.

为了理想化物体表面反射模型,通过辐射度学和球面三角公式推导出条形光源、均匀光源和半球均匀光源照射下的朗伯体场景辐射亮度,进而得到了 3种光源下的朗伯体表面反射模型.

首先使用双边滤波法对粗糙深度图作平滑处理,该方法在保持边缘细节的同时可以很好地去噪;然后针对偏振法线的歧义问题,以深度信息作为先验条件,采用 自定义阈值分割方法校正;最后构造以深度约束为拟合项、偏振法线约束为光滑项的罚函数方法,并利用最小二乘法进行计算,以实现融合重建.选取4幅不同偏振角度的偏振图像与单幅粗糙深度图进行实验,结果表明,相对于单一模态,深度与偏振的多模态融合能恢复更好的表面细节,达到更优的几何形状效果.

The normal major has a strong career orientation, and practical teaching. As an important part of the talent training of the normal professional, it is a necessary condition to ensure that the normal students can meet the graduation requirements. It also plays a vital role in improving the quality of talent training in colleges and universities to meet the certification standard of normal major. However, there are still some problems in the content arrangement, time planning, specific implementation, process management and evaluation in the process of practical teaching in some normal universities. In order to give full play to the acquisition function of practical teaching in normal skills, we need to implement all links of practical teaching based on the certification standard of normal major. In this paper, we will discuss from the local education department, university level, department level and teacher level, and put forward some specific suggestions and measures to implement practical teaching.

自适应全变分(adaptive total variation,ATV)模型可以利用差分曲率自适应地选择基于Lp范数的正则项,并且能自适应调节正则项与保真项的权重,能够有效地去除噪声和保持图像边缘.使用半隐式梯度下降法求解ATV模型时,误差的高频分量会快速衰减而低频分量却衰减缓慢,从而导致收敛速度缓慢.为了加快低频误差衰减的速度,利用半隐式梯度下降法设计了光滑化方法,构造了求解ATV模型的非线性多重网格法,并通过与不动点迭代法、半隐式梯度下降法的对比实验,验证了新方法的去噪效果更好且计算速度更快.

设计了一种简化的p函数以简化TVp配准模型,以滞后不动点迭代和Gauss?Seidel松弛迭代相结合构造光滑化方法,给出了一种有效的非线性多重网格(NMG)算法.数值实验表明该算法与不动点迭代方法(FP)相比具有更好的配准速度和配准精度.

通过对差分曲率设置有效的限制算子和插值算子,构造了 一种新的非线性多重网格法,并将此方法应用于基于差分曲率的TVP模型.新方法与不动点迭代法的对比实验结果表明,新方法处理的图像峰值信噪比明显高于不动点迭代法,且收敛速度是不动点迭代法的2～3倍.

教学技能是师范生发展的必备要素,完备的教学技能培训体系和有效的教学技能训练是提高师范生质量的重要保证.从师资力量、教育类课程的教学和教育实践三个方面分析了高等师范院校师范生技能培训中存在的问题.针对这些问题,结合近年来吉首大学数学与应用数学专业的师范生技能培训工作展开分析,希望对高校师范生技能培训有一定的借鉴意义.

引入超曲面函数作为图像配准正则项的核函数,建立了位移兼顾全局平滑与保留不连续性的改进全变分(TV)配准模型.为了快速有效地求解该模型,在一般的非线性多重网格(NMG)算法中,使用滞后扩散不动点迭代与逐次超松弛迭代相互作用构造新的平滑方法,并在限制过程中采用层析技术将粗网格上的误差插值回细网格,设计出一种优化NMG算法.仿真实验结果表明,优化NMG算法与NMG算法相比,配准精度更高,收敛速度更快;改进TV配准模型与TV配准模型相比,配准误差更小,耗时更少,配准效果更好.

引入符号函数建立了兼顾位移场光滑与不连续的自适应全变分配准模型,并给出了有效的不动点迭代方法.实验表明,由自适应全变分模型得到的图像比全变分配准模型的效果更好,花费时间更少.

提出了一种改进的LLT去噪模型,并给出有效的不动点迭代方法.数值实验结果表明,改进的LLT模型不仅能保持图像的细节,而且能避免阶梯效应.

Developing a variational model that is capable of restoring both smooth (no edges) and non-smooth (with edges) images is still a valid challenge at the image processing. In this paper, we present two methods for image denoising problems based on the use of the LLT model (see [14]) and TV model (see [20]). The idea of our methods is, add the texture which is separated from the cartoon and noisy, back to the original noisy image or the texture plus noisy part, and the sum then processed. In order to obtain the texture, we first separate texture plus noise from cartoon by LLT model, and then use TV model to remove some noisy from texture. Numerical experiments show our method is able to maintain some important information such as small details in the image, and at the same time to get a better visualization.

提出了运用具有全局收敛性的同伦方法求解Lysaker-Lundervold-Tai (LLT)模型,构造了一种逐步减小光滑化参数的同伦方程,并给出了有效的路径跟踪方法.实验表明,该方法收敛速度是不动点方法的2倍.

Several important theorems in variation principle are introduced,and the derivation of Euler-La-grange equation for the mean curvature model and the boundary conditions are presented based on these theorems.

TV model is one of the models with the quality of preserving edges in image denoising.In order to avoid the staircasing effect from the TV model,and make the restored image have a better visualiza-tion,the L2-model is used to extract a smooth primal sketch from the observed image and then to obtain other meaningful signal by the TV model from the removed noise image.

Abstract. Developing a variational model that is capable of restoring both smooth (no edges) and non-smooth (with edges) images is still a valid challenge in the image processing. In this paper, we present two methods for image denoising problems based on the use of the LLT model (see [14]) and iterated total variation refinement. The idea of our methods is, first make use of the LLT model to get a smooth primal sketch, and then get some meaningful signal by iterated total variation refinement from the removed noise image. Numerical experiments show that our method is able to maintain some important information such as small details in the image, and at the same time to get a better visualization.

Mean curvature-based energy minimization denoising model by Zhu and Chan offers one approach for restoring both smooth (no edges) and non-smooth (with edges) images. The resulting fourth-order partial differential equations arising from minimization of this model is non-trivial to solve due to appearance of a high nonlinearity and stiffness term, because simple alternative methods such as the fixed point method and the primal dual method do not work. In this paper, we first present a relaxed fixed point method for solving such equations and further to combine with a homotopy algorithm to achieve fast convergence. Numerical experiments show that our method is able to maintain all important information in the image, and at the same time to filter out noise.

The total variation (TV) minimization problem is widely studied in image restoration.Although many alternative methods have been proposed for its solution, the Newton method remains not usable for the primal formulation due to no convergence.A previous study by Chan, Zhou and Chan [15] considered a regularization parameter continuation idea to increase the domain of convergence of the Newton method with some success but no robust parameter selection schemes.In this paper, we consider a homotopy method for the same primal TV formulation and propose to use curve tracking to select the regularization parameter adaptively.It turns out that this idea helps to improve substantially the previous work in efficiently solving the TV Euler-Lagrange equation.The same idea is also considered for the two other methods as well as the deblurring problem, again with improvements obtained.Numerical experiments show that our new methods are robust and fast for image restoration, even for images with large noisy-to-signal ratio.

The Rudin, Osher, and Fatemi model [20] (ROF) for image restoration has been extensively studied due to its edge preserving capability, but for images without edges (jumps), the solution to this model has the undesirable staircasing effect. To improve the model, Lysaker, Lundervold and Tai [14] (LLT) proposed a better second-order functional suitable for restoring smooth images but it is difficult to preserve discontinuities for non-smooth images. It turns out that results from convex combinations of ROF model and LLT model can preserve the main advantages of both models (see [16, 9]). In this paper, we first propose an applicable homotopy algorithm based fixed point method for the LLT model. We then propose two new variants of convex combination models. Numerical experiments are shown to demonstrate the advantages of these combination models and the robustness of our homotopy algorithm.