Core topics include sorting, binary search trees, red-black trees, dynamic programming, greedy algorithms, graph algorithms, linear programming and string matching. Advanced examples connect algorithmic thinking with graph-cut texture synthesis and surface registration.

涵盖排序、二叉搜索树、红黑树、动态规划、贪心算法、图算法、线性规划和字符串匹配，并通过基于图割的纹理合成、曲面配准等专题展示算法思想在视觉与图形学中的应用。

An introduction to Fourier analysis and transforms, Gabor transforms and wavelet transforms. The course covers Mallat's multiresolution analysis, Daubechies orthogonal wavelets and wavelet packets, followed by applications in image and geometry processing.

介绍傅里叶分析与变换、Gabor 变换和小波变换，涵盖 Mallat 多分辨率分析、Daubechies 正交小波构造和小波包，并讨论小波在图像与几何处理中的基础应用。

A mathematical and computational introduction to three-dimensional surfaces from the viewpoint of discrete differential geometry. Topics span surface representation, 3D scanning, registration, reconstruction, mesh smoothing, parameterization and deformation.

从离散微分几何的视角介绍三维曲面的数学与计算基础，覆盖曲面表示、三维扫描、配准、曲面重建、网格平滑、参数化与曲面变形等完整几何处理流程。

Classical optimization methods—including line search, trust-region, quasi-Newton, penalty and augmented Lagrangian methods—together with split Bregman and alternating-direction methods for sparse optimization.

讲授线搜索、信赖域、拟牛顿、罚函数和增广拉格朗日等经典优化方法，并介绍用于稀疏优化问题的 Split Bregman、交替方向法等算法。

Classical image-processing methods, partial-differential-equation approaches to image processing, and selected advanced topics that connect mathematical models with visual applications.

介绍经典数字图像处理方法、基于偏微分方程的图像处理方法，以及若干连接数学模型与视觉应用的前沿专题。