Enhancing the Teaching of Linear Algebra with Digital Image Processing

数学科学(21)。这个“概念验证”项目正在开发包含数字图像处理(DIP)范例的教材，以加强线性代数的教与学。其关键思想是，处理一幅图像(或一系列图像，如电影)等效于对矩阵进行数学运算。由于这些运算的结果本质上是可视化的，学生们受到越来越复杂的可视化的指导，从而提供了一个机会来激发对数学概念和理论的理解。学生首先探索拉伸、旋转或翻转图像，然后自然地继续学习对比度增强、在被噪声破坏的数据中检测图像、特征提取、边缘检测和数据压缩技术-这些技术都依赖于使用线性代数中的概念。

Mathematical Sciences (21). This "proof-of-concept" project is developing instructional materials that incorporate examples from Digital Image Processing (DIP) to enhance the teaching and learning of linear algebra. The key idea is that processing an image (or a sequence of images, i.e. a movie) is equivalent to operating mathematically on matrices. Since the results of such operations are inherently visual, students are guided by increasingly sophisticated visualizations, thus providing an opportunity to motivate the understanding of mathematical concepts and theory. Students first explore stretching, rotating, or flipping images, then proceed naturally to the study of contrast enhancement, detecting images in data corrupted by noise, feature extraction, edge detection, and techniques of data compression - techniques that all rely on using concepts from linear algebra.