GEOMETRIC AND 3D COMPUTER VISION

This course provides an in-depth study of the theory and techniques of modern computer vision, focusing on the non-trivial process of recovering geometric information of a scene from its 2-dimensional image representation.
The course develops in a bottom-up fashion, starting from the fundamental concepts of "early vision" and progressing with the classical methods to detect geometrical primitives, like curves and point-based features. Finally, the mathematical framework of projective geometry is discussed in the context of recovering the 3D structure of a scene.

Knowledge:
- Basic and advanced image processing algorithms
- Techniques for identifying objects and shapes in images or videos
- General concepts of projective geometry
- Relevant 3D reconstruction methodologies and technologies

Skills:
- Implement programs using simple and advanced image processing algorithms
- Know how to implement algorithms for the detection of linear and punctual features
- Develop algorithms for the 3D reconstruction of objects from images

Linear algebra and calculus are suggested to understand the lectures better.

Early vision
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- Introduction to vision
- The image formation process
- Intensity transformations
- Color vision
- Spatial filtering
- Filtering in frequency domain
- Morphological image processing
- Edge detection


Mid-level vision
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- Fitting of curves and Hough transform.
- Detection and matching of point features
- Tracking


Projective geometry
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- Elements of Analytical Euclidean Geometry
- Geometric primitives
- 2D and 3D projective transformations


Camera models
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- Affine and projective cameras
- Intrinsic calibration
- Pose estimation


Two-view geometry
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- Epipolar geometry
- Stereopsis
- 3D Reconstruction and triangulation


Laboratory activities: Development of algorithms in Python, Numpy and the OpenCV library

[1] R. C. Gonzalez, R.E. Woods. Digital Image Processing (3rd edition). Pretience Hall
[2] R. Szeliski. Computer Vision Algorithms and Applications. Springer
[3] D. Forsyth, J. Ponce. Computer Vision: A Modern Approach (2nd edition). Pearson
[4] R. Hartley, A. Zisserman. Multiple View Geometry in Computer Vision (2nd edition). Cambridge University Press, New York, NY, USA.

The verification of learning involves the development of Python programs using algorithms and methods studied along the course. These programs can be in the form of a final project work (details given at the end of the course) or as a set of assignments to be developed along the course. In both cases, students' implementation will be discussed by oral examination.

The grading scale (how grades will be assigned) is defined as follows:

A. Scores in the range of 18-22 will be assigned when:
- sufficient knowledge and applied understanding of the programme;
- limited ability to implement algorithmic solutions to the given problems.
- sufficient communication skills, especially regarding specific terminology used in computer vision.
B. Scores in the range of 23-26 will be assigned when:
- good knowledge and applied understanding of the programme;
- fair ability to implement algorithmic solutions to the given problems.
- adequate communication skills, especially regarding specific terminology used in computer vision.
C. Scores in the range of 27-30 will be assigned when:
- good knowledge and applied understanding of the programme;
- reasonable ability to implement algorithmic solutions to the given problems.
- fully appropriate communication skills, especially regarding specific terminology used in computer vision.
D. Honors will be awarded in the presence of excellent understanding and development skills of advanced computer vision algorithms.

oral

The course is composed of frontal lessons, typically comprising practical examples to better understand all the studied concepts. Together with the referral texts, additional material will be provided by means of PowerPoint slides and source code.

English