From eeb319841769d24227a2d427f93402772a98f5cd Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Mon, 20 Apr 2026 16:41:38 +0200 Subject: [PATCH] [AMR] Vision intro --- .../autonomous-mobile-robots-cheatsheet.pdf | Bin 554398 -> 562480 bytes .../autonomous-mobile-robots-cheatsheet.tex | 6 ++++ .../amr/parts/04_vision/00_keypoints.tex | 18 ++++++++++ .../amr/parts/04_vision/01_bootstrapping.tex | 33 ++++++++++++++++++ .../parts/04_vision/02_place-recognition.tex | 3 ++ 5 files changed, 60 insertions(+) create mode 100644 electives/others/amr/parts/04_vision/00_keypoints.tex create mode 100644 electives/others/amr/parts/04_vision/01_bootstrapping.tex create mode 100644 electives/others/amr/parts/04_vision/02_place-recognition.tex diff --git a/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf b/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf index 937957931fe29f4fc277e283a7d9f43d6e1b499b..fd009d1562bf847b4d37c373d4a2d9bfb23d9d82 100644 GIT binary patch delta 149994 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zRUoeImI7)=@h6ue|CeZ|9{FQn)sDr;r#*Cq$biS*&pKa4p&i2a6k`7khvx=XTa3r$di5@&$lXz~Po17ZP%?lN S7y^8}y!>bk407u7X#WG7dDhkd diff --git a/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex b/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex index 2bb6d4b..af4d5d2 100644 --- a/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex +++ b/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex @@ -71,4 +71,10 @@ \input{parts/03_multi-sensor-estimation/06_extended-kalman-filter.tex} % \input{parts/03_multi-sensor-estimation/} +\section{SLAM to Spatial AI} +\input{parts/04_vision/00_keypoints.tex} +\input{parts/04_vision/01_bootstrapping.tex} +\input{parts/04_vision/02_place-recognition.tex} +% \input{parts/04_vision/} + \end{document} diff --git a/electives/others/amr/parts/04_vision/00_keypoints.tex b/electives/others/amr/parts/04_vision/00_keypoints.tex new file mode 100644 index 0000000..1b6d956 --- /dev/null +++ b/electives/others/amr/parts/04_vision/00_keypoints.tex @@ -0,0 +1,18 @@ +\subsection{Keypoints} +\bi{Corner det.} $SSD(\Delta_x, \Delta_y) \approx [\Delta_x \; \Delta_y] \mat{M} [\Delta_x \; \Delta_y]^\top$ +with $\mat{M} = \mat{R}^\top \text{diag}(\lambda_1, \lambda_2) \mat{R}$; $\lambda_i$ E.V. of $M$; +$\mat{R} = \det(M) - \kappa \cdot \text{trace}(M)^2 = \lambda_1\lambda_2 - \kappa(\lambda_1 + \lambda_2)^2$; +$\displaystyle M = \sum_{x, y \in P} \begin{bmatrix} + I_x^2 & I_x I_y \\ + I_x I_y & I_y^2 + \end{bmatrix}$ + + +\shade{gray}{Blob Detection} ($I$ is the image) + +\bi{Laplacian of Gaussian} (LoG): $L = g(x, y, t) \cdot I(x, y)$. +Then apply Laplacian Operator $\nabla_\text{norm}^2 L = t\left( \frac{\partial^2 L}{\partial x^2} + \frac{\partial L}{\partial y^2} \right)$ + +\bi{Diff. of Gaussians} (DoG): $\Delta L = L(x, y, t) - L(x, y, kt)$ + +\bi{SIFT Detector} \bi{(1)} Subsample + Blur \bi{(2)} DoG on each res. image \bi{(3)} Keypoints extrema in DoG pyramid diff --git a/electives/others/amr/parts/04_vision/01_bootstrapping.tex b/electives/others/amr/parts/04_vision/01_bootstrapping.tex new file mode 100644 index 0000000..22ae033 --- /dev/null +++ b/electives/others/amr/parts/04_vision/01_bootstrapping.tex @@ -0,0 +1,33 @@ +\subsection{Bootstrapping} + +\bi{PnP Problem} {\scriptsize Persp. n-P.} +Find sol. for camera pose \textit{directly} + +\bi{RANSAC} {\scriptsize RANdom SAmpling Consensus} for find. outliers \& correct + +\bi{Stereo Triang.} Given two rays (known poses for points in 2D). +Find good point in 3D. Fast sol: \bi{Midpoint Method}: + +\bi{1} Find p. along ray w/ min. dist (Lin. Least Squares) +\rmvspace[0.7] +\[ + \vec{\lambda}\! =\! [\lambda_1 \; \lambda_2]^\top\! = \! \argmin{} ||({_W}\vec{t}_{C_2} + \lambda_2 {_W}\vec{e}_2) - ({_W}\vec{t}_{C_1} + \lambda_1 {_W}\vec{e}_2)||^2 +\] + +\rmvspace[1] +\bi{2} Solve normal equation $\mat{A} \vec{\lambda} = \vec{b}$ with $\vec{q} = -{_W}\vec{e}^\top_1 {_W}\vec{e}_2$: +\rmvspace[0.7] +\[ + \mat{A} = \begin{bmatrix} + 1 & \vec{q} \\ + \vec{q} & 1 + \end{bmatrix} + \quad + \vec{b} = \begin{bmatrix} + \vec{e}_1^\top \cdot ({_W}\vec{t}_{C_2} - {_W}\vec{t}_{C_1}) \\ + -\vec{e}_2^\top \cdot ({_W}\vec{t}_{C_2} - {_W}\vec{t}_{C_1}) + \end{bmatrix} +\] + +\rmvspace[0.7] +\bi{3} Pick midp. ${_W}\vec{t}_P \! = \! 0.5(\tau_1 \! + \! \tau_2)$; $\tau_n \! = \! {_W}\vec{t}_{C_n} + \lambda_n{_W}\vec{e}_n)$ diff --git a/electives/others/amr/parts/04_vision/02_place-recognition.tex b/electives/others/amr/parts/04_vision/02_place-recognition.tex new file mode 100644 index 0000000..36d8d6c --- /dev/null +++ b/electives/others/amr/parts/04_vision/02_place-recognition.tex @@ -0,0 +1,3 @@ +\subsection{Place Recognition} +Idea: Build vocab from ``visual words'' (in Training). +\bi{Runtime} Detect keypoints; Extract descriptors; Build histogram; Query DB for similarity; If no match, insert into DB, else use to compute with e.g. RANSAC