Introduction to the theory of fundamental problems in computer vision, synopsis of evidences from biological vision, mathematical models and computational algorithms for their solution, and description of selected applications. Visual sensors and image formation. Spatio-temporal processing of visual signals: Multidimensional linear filters and Fourier/Gabor analysis. Morphological operators and nonlinear filters. Multiscale image analysis with linear (Gaussian scale-space) and nonlinear methods (geometric diffusion). Detection of edges and other geometric features. Analysis of shape and texture. Motion estimation. Stereopsis and multiview geometry. Curve/surface evolution, active contours, and levelsets. Graph-theoretic methods. Image segmentation. 3D reconstruction. Object recognition. Applications in artificial intelligence, biomedicine, robotics, digital arts, and internet.