Course Instructor: Florica Moldoveanu

The course is structured in two parts. The first part is a continuation of the "Computer Graphics" course. It introduces the parametric representation of freeform curves and surfaces that are used for modeling and rendering of surfaces in any contemporary CAD system for architecture or other graphic design applications. Chapter 2 covers the fundamentals of solid modeling, also used in the CAD systems. Chapter 3 presents two approaches which are presently used in the synthesis of photorealistic images: texturing and global illumination. The course presents different texture mapping techniques and their implementation using the modern Graphical Processing Units. The well-known "Ray tracing" method is presented and analyzed, as a global illumination technique. The second part of the course introduces the fundamentals of image processing and low level analysis of images: digital image formation, correction of geometrical distortions, noise modeling and its reduction from images by applying different types of filters both in the spatial and in the frequency domain, feature detection using discrete operators that implement the first or the second derivative of the image function, different image segmentation algorithms, region contours extraction and their polygonal approximation, thinning and skeletonization algorithms that help in shape recognition, shape description and analysis methods.

Syllabus:

• Modeling and rendering three-dimensional free-form curves and surfaces.
• Free-form curves: Hermite, Bezier, B-spline, Nurbs.
• Sweep surfaces.
• Free-form surfaces: Hermite, Bezier, B-spline, Nurbs, ruled surfaces, cylindrical surfaces.
• Solid modeling.
• Topology notions, formal modeling criteria, Euler operators.
• Solid representation: Boundary representations, Cell decomposition, Regular and adaptive decomposition (Octree representation), Constructive Solid Geometry, Sweep Representations. Advanced rendering techniques.
• Textures based techniques.
• Standard mapping functions.
• Exact mapping.
• Two-stage mapping.
• Mapping textures on polygon interior points.
• Environment mapping techniques: reflective and refractive environment mapping, Fresnel Effect and Chromatic Dispersion.
• Bump mapping.
• Ray tracing.
• The global illumination model.
• The basic recursive ray tracing.
• Antialiasing methods for ray tracing.
• Optimization methods for ray intersections.
• Image enhancement and restoration techniques.
• Image histogram.
• Noise modeling.
• Spatial filters.
• Rank filters.
• Discrete Fourier Transform.
• Color image processing.
• Feature detection.
• Edge detectors using image Gradient.
• Edge detectors using image Laplacian.
• Canny edge detector.
• Hough transform.
• Image segmentation algorithms.
• Linear regions detection.
• Extracting region contours.
• Polygonal approximation of contours.
• Thinning and skeletonization.
• Shape description and analysis.