[VC] Catch up

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janishutz committed 2026-09-26 08:15:50 +02:00
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\shortdefinition[Scale Space] Collection of img at diff scales \& smooth.
\shortremark Finite diff. for $\frac{\partial f(x, y)}{\partial x} \approx \frac{f(x + 1, y) - f(x, y)}{1}$,\\
filter: $[1, -1]$. Can use par der. for edge detection
\shortdefinition[Gradient] $\nabla f = [\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}]$, dir of most rapid change.
\bi{Edge strength} (magnitude): $M(x, y) = ||\nabla f||$.\\
Noise makes edge detection hard, smooth first, then edge is peak in $\pardiff{x}(h * f)$.
\bi{Angle} $\alpha(x, y) = \arctan \left( \frac{\partial f}{\partial y} \div \frac{\partial f}{\partial x} \right)$
\shorttheorem $\pardiff{x}(h * f) = \left( \pardiff{x} h \right) * f$
\shortdefinition[Laplacian] $\nabla^2 f = \frac{\partial^2 f}{\partial^2 x} + \frac{\partial^2 f}{\partial^2 y}$
\shortdefinition[LoG] $\nabla^2 G(x, y) = \frac{1}{2\pi \sigma^2} \left( \frac{x^2 + y^2 - 2\sigma^2}{\sigma^2} \right)\exp\left( -\frac{x^2 + y^2}{2 \sigma^2} \right)$\\
Edge is at zero-crossing of $\left( \pardiffn{x}{2} h \right) * f$. $\sigma$ affects scale of edges detected (larger $\sigma$ = stronger edges)
\shortdefinition[Canny E.D.] \bi{1} smooth w/ Gaussian, \bi{2} gradient magnitude \& angle, \bi{3} Nonmaxima suppression to gradient mag. image,
\bi{4} double thresholding to detect strong and weak edge pixels, \bi{5} reject weak edge pixels not connected with strong edge pixels
\shortdefinition[Non-Max-Suppression] Quantize edge normal to four dir, if $M(x, y)$ smaller than either neighbour in dir, suppress, else keep
\shortdefinition[Thresholding] Via thresholds $\theta_\text{high} \div \theta_\text{low} \in [2, 3]$ (typ)
\subsubsection{Line Fitting}
Generally challenging, missing information
\shortdefinition[RANSAC] Random Sample Consensus:
\begin{enumerate}
\item Rand. sel. \textit{seed group} of p. w/ base transf. est.
\item Compute transformation from seed group
\item Find \textit{inliers} to this transformation
\item If inliers sufficiently large, recompute least-squares estimate of transformation on all inliers
\end{enumerate}
Sample count: $w$ frac of inliers, $n$ points define hypothesis ($n = 2$ for lines), $k$ samples chosen.
Prob. sample of $n$ points correct: $w^n$, prob all $k$ samples fail: $(1 - w^n)^k$, i.e. \hl{choose $k$ high to keep below failure rate}
\shortdefinition[Hough Transform] Voting technique, main idea:
\begin{enumerate}
\item Vote for all possible lines on which edge could lie
\item Look for line candidates that get many votes
\item Noise features votes should be inconsistent
\end{enumerate}
% TODO: Explore how it works in detail
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\subsection{Digital Image} \subsection{Digital Image}
\input{parts/00_computer-vision/00_digital-image.tex} \input{parts/00_computer-vision/00_digital-image.tex}
\subsection{Filtering} \subsection{Filtering \& Convolution}
\input{parts/00_computer-vision/01_filtering.tex} \input{parts/00_computer-vision/01_filtering.tex}
\subsection{Convolution} \subsection{Edge Detection}
\input{parts/00_computer-vision/02_convolution/00_basics.tex} \input{parts/00_computer-vision/02_edge-detection.tex}
% \input{parts/00_computer-vision/} % \input{parts/00_computer-vision/}
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\renewcommand{\theoremShortNamingEN}{Thm} \renewcommand{\theoremShortNamingEN}{Thm}
\renewcommand{\descriptorNameDisplay}[1]{\textbf{#1}} \renewcommand{\descriptorNameDisplay}[1]{\textbf{#1}}
\setupCheatSheet{Visual Computing} \setupCheatSheet[0.5cm]{Visual Computing}
\begin{document} \begin{document}
\startDocument \startDocument
\noverticalspacing \noverticalspacing
% TODO: Shorten significantly
\input{parts/00_computer-vision/main.tex} \input{parts/00_computer-vision/main.tex}