--- title: Introductory Session to Machine Learing --- # Reading + Ma 2004 Chapter 1. # Session 1. **Briefing** Overview and History 2. Install and Test Software - Simple tutorials 3. **Debrief** questions and answers - recap of linear algebra # 1 Briefing ## Practical Information ### Information + Wiki - living document - course content + BlackBoard - announcements - discussion fora + Questions - either - in class - in discussion fora + Email will only be answered when there are good reasons not to use public fora. ### Taught Format + Sessions 4h twice a week - normally 1h briefing + 2h exercise + 1h debrief (may vary) + Exercises vary from session to session + mathematical exercises + experimental exercises + implementational exercises + **No** Compulsory Exercises + **Feedback in class** - please ask for feedback on partial work + Keep a diary. Make sure you can refer back to previous partial solution and reuse them. ### Learning Outcomes + Knowledge - The candidate can explain fundamental mathematical models for digital imaging, 3D models, and machine vision - The candidate are aware of the principles of digital cameras and image capture + Skills - The candidate can implemented selected techniques for object recognition and tracking - The candidate can calibrate cameras for use in machine vision systems + General competence - The candidate has a good analytic understadning of machine vision and of the collaboration between machine vision and other systems in robotics - The candidate can exploit the connection between theory and application for presenting and discussing engineering problems and solutions ### Exam + Oral exam $\sim 20$ min. + First seven minutes are *yours* - make a case for your grade wrt. learning outcomes - your own implementations may be part of the case - essentially that you can explain the implementation analytically + The remaing 13-14 minutes is for the examiner to explore further + More detailed assessment criteria will be published later ## Vision ![Eye Model from *Introduction to Psychology* by University of Minnesota](Images/eye.jpg) + Vision is a 2D image on the retina + Each cell perceives the light intencity of colour of the light projected thereon + Easily replicated by a digital camera + Each pixel is light intencity sampled at a given point on the image plane ## Cognition ![1912 International Lawn Tennis Challenge](Images/tennis.jpg) + Human beings see 3D objects - not pixels of light intencity + We *recognise* objects - *cognitive schemata* - we see a *ball* - not a round patch of white - we remember a *tennis match* - more than four people with white clothes and rackets + We observe objects arranged in depth - in front of and behind the net - even though they are all patterns in the same image plane + 3D reconstruction from 2D retina image - and we do not even think about how ## Applications - Artificial systems interact with their surroundings - navigate in a 3D environment - Simpler applications - face recognition - tracking in surveillance cameras - medical image diagnostics (classification) - image retrieval (topics in a database) - detecting faulty products on a conveyor belt (classification) - aligning products on a conveyor belt - Other advances in AI creates new demands on vision - 20 years ago, walking was a major challenge for robots - now robots walk, and they need to see where they go ... ## Focus - Artificial systems interact with their surroundings - navigate in a 3D environment - This means - Geometry of multiple views - Relationship between theory and practice - ... between analysis and implementation - Mathematical approach - inverse problem; 3D to 2D is easy, the inverse is hard - we need to understand the geometry to know what we program ## History - 1435: *Della Pictura* - first general treatise on perspective - 1648 Girard Desargues - projective geometry - 1913 Kruppa: two views of five points suffice to find - relative transformation - 3D location of the points - (up to a finite number of solutions) - mid 1970s: first algorithms for 3D reconstruction - 1981 Longuet-Higgins: linear algorithm for structure and motion - late 1970s E. D. Dickmans starts work on vision-based autonomous cars - 1984 small truck at 90 km/h on empty roads - 1994: 180 km/h, passing slower cars ## Python - Demos and tutorials in Python - you can use whatever language you want - we avoid Jupyter to make sure we can use camera and interactive displays easily - Demos and help on Unix-like system (may or may not include Mac OS) - In the exercise sessions - install necessary software - use the tutorials to see that things work as expected - In the debrief, we will start briefly on the mathematical modelling # 2 Tutorials + [Introduction]() # 3 Debrief 1. Discuss problems arising from the practical session. 2. Repeat basic linear algebra (below). 3. Possibly start on [3D Mathematics]() - probably not though. ## Vectors and Points + A *point* in space $\mathbf{X} = [X_1,X_2,X_3]^\mathrm{T}\in\mathbb{R}^3$ + A *bound vector*, from $\mathbf{X}$ to $\mathbf{Y}$: $\vect{\mathbf{XY}}$ + A *free vector* is the same difference, but without any specific anchor point + represented as $\mathbf{Y} - \mathbf{X}$ + Set of free vectors form a linear vector space + **note** points do not + The sum of two vectors is another vector + The sum of two points is not a point ## Dot product (inner product) $$x=\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}\quad y=\begin{bmatrix}y_1\\y_2\\y_3\end{bmatrix}$$ **Inner product** $$\langle x,y\rangle = x^\mathrm{T}y = x_1y_1+x_2y_2+x_3y_3$$ Euclidean **Norm** $$||x|| = \sqrt{\langle x,x\rangle}$$ **Orthogonal vectors** when $\langle x,y\rangle=0$ ## Cross product $$x\times y = \begin{bmatrix} x_2y_3 - x_3y_2 \\ x_3y_1 - x_1y_3 \\ x_1y_2 - x_2y_1 \end{bmatrix} \in \mathbb{R}^3$$ Observe that + $y\times x = -x\times y$ + $\langle x\times y, y\rangle= \langle x\times y, x\rangle$ $$x\times y = \hat xy \quad\text{where}\quad \hat x = \begin{bmatrix} 0 -x_3 x_2 \\ x_3 0 -x_1 \\ -x_2 x_1 0 \end{bmatrix} \in \mathbb{R}^{3\times3}$$ $\hat x$ is a **skew-symmetric** matrix because $\hat x=-\hat x^\mathrm{T}$ ## Right Hand Rule **TODO** ## Skew-Symmetric Matrix **TODO** ## Change of Basis **TODO**