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notebook.tex
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% Default to the notebook output style
% Inherit from the specified cell style.
\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
% Nicer default font (+ math font) than Computer Modern for most use cases
\usepackage{mathpazo}
% Basic figure setup, for now with no caption control since it's done
% automatically by Pandoc (which extracts  syntax from Markdown).
\usepackage{graphicx}
% We will generate all images so they have a width \maxwidth. This means
% that they will get their normal width if they fit onto the page, but
% are scaled down if they would overflow the margins.
\makeatletter
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth
\else\Gin@nat@width\fi}
\makeatother
\let\Oldincludegraphics\includegraphics
% Set max figure width to be 80% of text width, for now hardcoded.
\renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}}
% Ensure that by default, figures have no caption (until we provide a
% proper Figure object with a Caption API and a way to capture that
% in the conversion process - todo).
\usepackage{caption}
\DeclareCaptionLabelFormat{nolabel}{}
\captionsetup{labelformat=nolabel}
\usepackage{adjustbox} % Used to constrain images to a maximum size
\usepackage{xcolor} % Allow colors to be defined
\usepackage{enumerate} % Needed for markdown enumerations to work
\usepackage{geometry} % Used to adjust the document margins
\usepackage{amsmath} % Equations
\usepackage{amssymb} % Equations
\usepackage{textcomp} % defines textquotesingle
% Hack from http://tex.stackexchange.com/a/47451/13684:
\AtBeginDocument{%
\def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code
}
\usepackage{upquote} % Upright quotes for verbatim code
\usepackage{eurosym} % defines \euro
\usepackage[mathletters]{ucs} % Extended unicode (utf-8) support
\usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document
\usepackage{fancyvrb} % verbatim replacement that allows latex
\usepackage{grffile} % extends the file name processing of package graphics
% to support a larger range
% The hyperref package gives us a pdf with properly built
% internal navigation ('pdf bookmarks' for the table of contents,
% internal cross-reference links, web links for URLs, etc.)
\usepackage{hyperref}
\usepackage{longtable} % longtable support required by pandoc >1.10
\usepackage{booktabs} % table support for pandoc > 1.12.2
\usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment)
\usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout)
% normalem makes italics be italics, not underlines
% Colors for the hyperref package
\definecolor{urlcolor}{rgb}{0,.145,.698}
\definecolor{linkcolor}{rgb}{.71,0.21,0.01}
\definecolor{citecolor}{rgb}{.12,.54,.11}
% ANSI colors
\definecolor{ansi-black}{HTML}{3E424D}
\definecolor{ansi-black-intense}{HTML}{282C36}
\definecolor{ansi-red}{HTML}{E75C58}
\definecolor{ansi-red-intense}{HTML}{B22B31}
\definecolor{ansi-green}{HTML}{00A250}
\definecolor{ansi-green-intense}{HTML}{007427}
\definecolor{ansi-yellow}{HTML}{DDB62B}
\definecolor{ansi-yellow-intense}{HTML}{B27D12}
\definecolor{ansi-blue}{HTML}{208FFB}
\definecolor{ansi-blue-intense}{HTML}{0065CA}
\definecolor{ansi-magenta}{HTML}{D160C4}
\definecolor{ansi-magenta-intense}{HTML}{A03196}
\definecolor{ansi-cyan}{HTML}{60C6C8}
\definecolor{ansi-cyan-intense}{HTML}{258F8F}
\definecolor{ansi-white}{HTML}{C5C1B4}
\definecolor{ansi-white-intense}{HTML}{A1A6B2}
% commands and environments needed by pandoc snippets
% extracted from the output of `pandoc -s`
\providecommand{\tightlist}{%
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
% Add ',fontsize=\small' for more characters per line
\newenvironment{Shaded}{}{}
\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}}
\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}}
\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}}
\newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}}
\newcommand{\RegionMarkerTok}[1]{{#1}}
\newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\NormalTok}[1]{{#1}}
% Additional commands for more recent versions of Pandoc
\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}}
\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}}
\newcommand{\ImportTok}[1]{{#1}}
\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}}
\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}}
\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}}
\newcommand{\BuiltInTok}[1]{{#1}}
\newcommand{\ExtensionTok}[1]{{#1}}
\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}}
\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}}
\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
% Define a nice break command that doesn't care if a line doesn't already
% exist.
\def\br{\hspace*{\fill} \\* }
% Math Jax compatability definitions
\def\gt{>}
\def\lt{<}
% Document parameters
\title{Untitled}
% Pygments definitions
\makeatletter
\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax%
\let\PY@ul=\relax \let\PY@tc=\relax%
\let\PY@bc=\relax \let\PY@ff=\relax}
\def\PY@tok#1{\csname PY@tok@#1\endcsname}
\def\PY@toks#1+{\ifx\relax#1\empty\else%
\PY@tok{#1}\expandafter\PY@toks\fi}
\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{%
\PY@it{\PY@bf{\PY@ff{#1}}}}}}}
\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}}
\expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@fm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
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\expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
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\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
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\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit}
\expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@nn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
\expandafter\def\csname PY@tok@ow\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}}
\expandafter\def\csname PY@tok@gh\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@cp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.74,0.48,0.00}{##1}}}
\expandafter\def\csname PY@tok@bp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
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\expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}}
\expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@no\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.00,0.00}{##1}}}
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\expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
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\expandafter\def\csname PY@tok@kr\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
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\expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf}
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\expandafter\def\csname PY@tok@o\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}}
\expandafter\def\csname PY@tok@sc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@sb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@nv\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}}
\expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@nt\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@vm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@nb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}}
\expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@nf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
\expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@sx\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\def\PYZbs{\char`\\}
\def\PYZus{\char`\_}
\def\PYZob{\char`\{}
\def\PYZcb{\char`\}}
\def\PYZca{\char`\^}
\def\PYZam{\char`\&}
\def\PYZlt{\char`\<}
\def\PYZgt{\char`\>}
\def\PYZsh{\char`\#}
\def\PYZpc{\char`\%}
\def\PYZdl{\char`\$}
\def\PYZhy{\char`\-}
\def\PYZsq{\char`\'}
\def\PYZdq{\char`\"}
\def\PYZti{\char`\~}
% for compatibility with earlier versions
\def\PYZat{@}
\def\PYZlb{[}
\def\PYZrb{]}
\makeatother
% Exact colors from NB
\definecolor{incolor}{rgb}{0.0, 0.0, 0.5}
\definecolor{outcolor}{rgb}{0.545, 0.0, 0.0}
% Prevent overflowing lines due to hard-to-break entities
\sloppy
% Setup hyperref package
\hypersetup{
breaklinks=true, % so long urls are correctly broken across lines
colorlinks=true,
urlcolor=urlcolor,
linkcolor=linkcolor,
citecolor=citecolor,
}
% Slightly bigger margins than the latex defaults
\geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
\begin{document}
\maketitle
\textbf{Advanced Lane Finding Project}
The goals / steps of this project are the following:
\begin{itemize}
\tightlist
\item
Compute the camera calibration matrix and distortion coefficients
given a set of chessboard images.
\item
Apply a distortion correction to raw images.
\item
Use color transforms, gradients, etc., to create a thresholded binary
image.
\item
Apply a perspective transform to rectify binary image (``birds-eye
view'').
\item
Detect lane pixels and fit to find the lane boundary.
\item
Determine the curvature of the lane and vehicle position with respect
to center.
\item
Warp the detected lane boundaries back onto the original image.
\item
Output visual display of the lane boundaries and numerical estimation
of lane curvature and vehicle position.
\end{itemize}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}1}]:} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np}
\PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt}
\PY{k+kn}{import} \PY{n+nn}{cv2}
\PY{k+kn}{import} \PY{n+nn}{glob}
\end{Verbatim}
\hypertarget{camera-calibration}{%
\subsubsection{Camera Calibration}\label{camera-calibration}}
I start by preparing ``object points'', which will be the (x, y, z)
coordinates of the chessboard corners in the world. Here I am assuming
the chessboard is fixed on the (x, y) plane at z=0, such that the object
points are the same for each calibration image. Thus, \texttt{obj} is
just a replicated array of coordinates, and \texttt{object\_points} will
be appended with a copy of it every time I successfully detect all
chessboard corners in a test image. \texttt{image\_points} will be
appended with the (x, y) pixel position of each of the corners in the
image plane with each successful chessboard detection.
I then used the output \texttt{object\_points} and
\texttt{image\_points} to compute the camera calibration and distortion
coefficients using the \texttt{cv2.calibrateCamera()} function.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}2}]:} \PY{k}{def} \PY{n+nf}{calibrate\PYZus{}camera}\PY{p}{(}\PY{n}{path}\PY{p}{)}\PY{p}{:}
\PY{n}{object\PYZus{}points}\PY{o}{=}\PY{p}{[}\PY{p}{]}
\PY{n}{image\PYZus{}points}\PY{o}{=}\PY{p}{[}\PY{p}{]}
\PY{n}{images}\PY{o}{=}\PY{n}{glob}\PY{o}{.}\PY{n}{glob}\PY{p}{(}\PY{n}{path}\PY{p}{)}
\PY{n}{img\PYZus{}size}\PY{o}{=}\PY{p}{(}\PY{p}{)}
\PY{n}{obj}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{p}{(}\PY{l+m+mi}{9}\PY{o}{*}\PY{l+m+mi}{6}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{,}\PY{n}{np}\PY{o}{.}\PY{n}{float32}\PY{p}{)}
\PY{n}{obj}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{mgrid}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{:}\PY{l+m+mi}{9}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{:}\PY{l+m+mi}{6}\PY{p}{]}\PY{o}{.}\PY{n}{T}\PY{o}{.}\PY{n}{reshape}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}
\PY{k}{for} \PY{n}{idx}\PY{p}{,}\PY{n}{image} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{images}\PY{p}{)}\PY{p}{:}
\PY{n}{img}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{imread}\PY{p}{(}\PY{n}{image}\PY{p}{)}
\PY{n}{gray}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{img}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2GRAY}\PY{p}{)}
\PY{n}{ret}\PY{p}{,}\PY{n}{corners}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{findChessboardCorners}\PY{p}{(}\PY{n}{gray}\PY{p}{,}\PY{p}{(}\PY{l+m+mi}{9}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{)}\PY{p}{,}\PY{k+kc}{None}\PY{p}{)}
\PY{k}{if} \PY{n}{ret}\PY{p}{:}
\PY{n}{image\PYZus{}points}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{corners}\PY{p}{)}
\PY{n}{object\PYZus{}points}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{obj}\PY{p}{)}
\PY{n}{img\PYZus{}size}\PY{o}{=}\PY{p}{(}\PY{n}{img}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,}\PY{n}{img}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
\PY{n}{ret}\PY{p}{,}\PY{n}{mtx}\PY{p}{,}\PY{n}{dist}\PY{p}{,}\PY{n}{rvecs}\PY{p}{,}\PY{n}{tvecs}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{calibrateCamera}\PY{p}{(}\PY{n}{object\PYZus{}points}\PY{p}{,}\PY{n}{image\PYZus{}points}\PY{p}{,}\PY{n}{img\PYZus{}size}\PY{p}{,}\PY{k+kc}{None}\PY{p}{,}\PY{k+kc}{None}\PY{p}{)}
\PY{k}{return} \PY{n}{mtx}\PY{p}{,}\PY{n}{dist}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}3}]:} \PY{n}{mtx}\PY{p}{,}\PY{n}{dist}\PY{o}{=}\PY{n}{calibrate\PYZus{}camera}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{./camera\PYZus{}cal/calibration*.jpg}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
In the previous step I calculated \emph{Camera Matrix} and
\emph{Distortion Coefficients} using \texttt{cv2.calibrateCamera} now I
can use these values to undistort any image taken from the same camera
using \texttt{cv2.undistort}. The result after distorting image looks
like this:
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}4}]:} \PY{n}{test\PYZus{}image}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{imread}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{./camera\PYZus{}cal/calibration2.jpg}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{undistort}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{undistort}\PY{p}{(}\PY{n}{test\PYZus{}image}\PY{p}{,}\PY{n}{mtx}\PY{p}{,}\PY{n}{dist}\PY{p}{,}\PY{k+kc}{None}\PY{p}{,}\PY{n}{mtx}\PY{p}{)}
\PY{n}{f}\PY{p}{,} \PY{p}{(}\PY{n}{ax1}\PY{p}{,} \PY{n}{ax2}\PY{p}{)} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{20}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{)}\PY{p}{)}
\PY{n}{ax1}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{test\PYZus{}image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2RGB}\PY{p}{)}\PY{p}{)}
\PY{n}{ax1}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Original Image}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{30}\PY{p}{)}
\PY{n}{ax2}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{undistort}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2RGB}\PY{p}{)}\PY{p}{)}
\PY{n}{ax2}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Undistorted Image}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{30}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}4}]:} <matplotlib.text.Text at 0x17646c80be0>
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_6_1.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{perspective-transform}{%
\subsubsection{Perspective Transform}\label{perspective-transform}}
I started with choosing four reference points in the image to use them
as \texttt{src\_points} and four points for \texttt{dest\_points}. The
source points reflects on destination points after the perspective
transform. The first step is to calculate the transformation matrix
using \texttt{cv2.getPerspectiveTransform()} this function takes source
and destination points as input.
\begin{longtable}[]{@{}cc@{}}
\toprule
Source & Destination\tabularnewline
\midrule
\endhead
200, 720 & 300, 720\tabularnewline
600, 447 & 300, 0\tabularnewline
679, 447 & 900, 0\tabularnewline
1100,720 & 900, 720\tabularnewline
\bottomrule
\end{longtable}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}5}]:} \PY{c+c1}{\PYZsh{}function to calculate transformation matrix for perspective transform.}
\PY{k}{def} \PY{n+nf}{get\PYZus{}transformation\PYZus{}matrix}\PY{p}{(}\PY{n}{src}\PY{p}{,}\PY{n}{dest}\PY{p}{)}\PY{p}{:}
\PY{n}{transformation\PYZus{}matrix}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{getPerspectiveTransform}\PY{p}{(}\PY{n}{src}\PY{p}{,}\PY{n}{dest}\PY{p}{)}
\PY{k}{return} \PY{n}{transformation\PYZus{}matrix}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}6}]:} \PY{c+c1}{\PYZsh{}warp the image}
\PY{k}{def} \PY{n+nf}{perspective\PYZus{}transform}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{transformation\PYZus{}matrix}\PY{p}{)}\PY{p}{:}
\PY{n}{img\PYZus{}size}\PY{o}{=}\PY{p}{(}\PY{n}{image}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,}\PY{n}{image}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
\PY{n}{transformed\PYZus{}image}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{warpPerspective}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{transformation\PYZus{}matrix}\PY{p}{,}\PY{n}{img\PYZus{}size}\PY{p}{,}\PY{n}{flags}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{INTER\PYZus{}LINEAR}\PY{p}{)}
\PY{k}{return} \PY{n}{transformed\PYZus{}image}
\end{Verbatim}
\hypertarget{perform-perspective-transform}{%
\paragraph{Perform Perspective
Transform}\label{perform-perspective-transform}}
Once we have the transformation matrix we can use
\texttt{cv2.warpPerspective} to perform perspective transform of an
image. The result after the transform looks like this.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}7}]:} \PY{c+c1}{\PYZsh{}undistort Image}
\PY{n}{transformation\PYZus{}test}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{imread}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{./frames/frame2.jpg}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{undistort}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{undistort}\PY{p}{(}\PY{n}{transformation\PYZus{}test}\PY{p}{,}\PY{n}{mtx}\PY{p}{,}\PY{n}{dist}\PY{p}{,}\PY{k+kc}{None}\PY{p}{,}\PY{n}{mtx}\PY{p}{)}
\PY{c+c1}{\PYZsh{}src\PYZus{}points=np.float32([[790,490],[1090,670],[250,670],[515,490]])}
\PY{c+c1}{\PYZsh{}dest\PYZus{}points=np.float32([[1100,0],[1100,720],[200,720],[200,0]])}
\PY{c+c1}{\PYZsh{}src\PYZus{}points=np.float32([[800,490],[1100,650],[210,650],[500,490]])}
\PY{c+c1}{\PYZsh{}dest\PYZus{}points=np.float32([[1100,0],[1100,720],[200,720],[200,0]])}
\PY{c+c1}{\PYZsh{}perform perspective transform}
\PY{n}{src\PYZus{}points} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{float32}\PY{p}{(}\PY{p}{[}\PY{p}{[}\PY{l+m+mi}{200}\PY{p}{,}\PY{l+m+mi}{720}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{600}\PY{p}{,} \PY{l+m+mi}{447}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{679}\PY{p}{,}\PY{l+m+mi}{447}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{1100}\PY{p}{,}\PY{l+m+mi}{720}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{dest\PYZus{}points} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{float32}\PY{p}{(}\PY{p}{[}\PY{p}{[}\PY{l+m+mi}{300}\PY{p}{,} \PY{l+m+mi}{720}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{300}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{900}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{900}\PY{p}{,} \PY{l+m+mi}{720}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{transformation\PYZus{}matrix}\PY{o}{=}\PY{n}{get\PYZus{}transformation\PYZus{}matrix}\PY{p}{(}\PY{n}{src\PYZus{}points}\PY{p}{,}\PY{n}{dest\PYZus{}points}\PY{p}{)}
\PY{n}{transformed\PYZus{}image}\PY{o}{=}\PY{n}{perspective\PYZus{}transform}\PY{p}{(}\PY{n}{undistort}\PY{p}{,}\PY{n}{transformation\PYZus{}matrix}\PY{p}{)}
\PY{n}{f}\PY{p}{,} \PY{p}{(}\PY{n}{ax1}\PY{p}{,} \PY{n}{ax2}\PY{p}{)} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{20}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{)}\PY{p}{)}
\PY{n}{ax1}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{transformation\PYZus{}test}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2RGB}\PY{p}{)}\PY{p}{)}
\PY{n}{ax1}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Original Image}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{30}\PY{p}{)}
\PY{n}{ax2}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{transformed\PYZus{}image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2RGB}\PY{p}{)}\PY{p}{)}
\PY{n}{ax2}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Transformed Image}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{30}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}7}]:} <matplotlib.text.Text at 0x17646dbe358>
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_11_1.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{image-thresholding}{%
\subsubsection{Image Thresholding}\label{image-thresholding}}
After trying different strategies to apply thresholding finally I
applied HLS Colour space and Sobel thresholding to fecth features of
interest from the frame, here features of intrest are Lane lines. I used
Sobel along the X axis that is \texttt{sobelx} and later applied
thresholding over it, and I also applied thresholding over HLS colour
space to get a binary image. \emph{Values for Thresholding}
\begin{longtable}[]{@{}cc@{}}
\toprule
Applied On & Range\tabularnewline
\midrule
\endhead
Sobel X & 25 - 120\tabularnewline
l\_channel & 70 - 255\tabularnewline
s\_channel & 90 - 255\tabularnewline
\bottomrule
\end{longtable}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}8}]:} \PY{k}{def} \PY{n+nf}{apply\PYZus{}sobel}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{thresholds}\PY{p}{,}\PY{n}{kernel\PYZus{}size}\PY{o}{=}\PY{l+m+mi}{3}\PY{p}{,}\PY{n}{Color\PYZus{}Encoding}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{RGB}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{:}
\PY{k}{if}\PY{p}{(}\PY{n}{Color\PYZus{}Encoding}\PY{o}{==}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{BGR}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{:}
\PY{n}{gray}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2GRAY}\PY{p}{)}
\PY{k}{else}\PY{p}{:}
\PY{n}{gray}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}RGB2GRAY}\PY{p}{)}
\PY{n}{sobelx}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{Sobel}\PY{p}{(}\PY{n}{gray}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{CV\PYZus{}64F}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{,}\PY{n}{ksize}\PY{o}{=}\PY{n}{kernel\PYZus{}size}\PY{p}{)}
\PY{n}{sobel\PYZus{}scaled}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{uint8}\PY{p}{(}\PY{l+m+mi}{255}\PY{o}{*}\PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{n}{sobelx}\PY{p}{)}\PY{o}{/}\PY{n}{np}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{n}{sobelx}\PY{p}{)}\PY{p}{)}
\PY{n}{binary\PYZus{}image}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{zeros\PYZus{}like}\PY{p}{(}\PY{n}{sobel\PYZus{}scaled}\PY{p}{)}
\PY{n}{binary\PYZus{}image}\PY{p}{[}\PY{p}{(}\PY{n}{sobel\PYZus{}scaled}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{n}{thresholds}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{sobel\PYZus{}scaled}\PY{o}{\PYZlt{}}\PY{o}{=}\PY{n}{thresholds}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{]}\PY{o}{=}\PY{l+m+mi}{1}
\PY{k}{return} \PY{n}{binary\PYZus{}image}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}9}]:} \PY{k}{def} \PY{n+nf}{apply\PYZus{}sobel\PYZus{}and\PYZus{}color\PYZus{}thresholding}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{thresholds\PYZus{}sobel}\PY{p}{,}\PY{n}{threshold\PYZus{}l}\PY{p}{,}\PY{n}{thresholds\PYZus{}s}\PY{p}{,}\PY{n}{kernel\PYZus{}size}\PY{o}{=}\PY{l+m+mi}{3}\PY{p}{,}\PY{n}{Color\PYZus{}Encoding}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{RGB}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{:}
\PY{k}{if}\PY{p}{(}\PY{n}{Color\PYZus{}Encoding}\PY{o}{==}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{BGR}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{:}
\PY{n}{gray}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2GRAY}\PY{p}{)}
\PY{n}{hls}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2HLS}\PY{p}{)}
\PY{k}{else}\PY{p}{:}
\PY{n}{gray}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}RGB2GRAY}\PY{p}{)}
\PY{n}{hls}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}RGB2HLS}\PY{p}{)}
\PY{n}{s\PYZus{}channel}\PY{o}{=}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{l\PYZus{}channel}\PY{o}{=}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}
\PY{n}{sobelx}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{Sobel}\PY{p}{(}\PY{n}{gray}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{CV\PYZus{}64F}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{,}\PY{n}{ksize}\PY{o}{=}\PY{n}{kernel\PYZus{}size}\PY{p}{)}
\PY{n}{scaled\PYZus{}sobel}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{uint8}\PY{p}{(}\PY{l+m+mi}{255}\PY{o}{*}\PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{n}{sobelx}\PY{p}{)}\PY{o}{/}\PY{n}{np}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{n}{sobelx}\PY{p}{)}\PY{p}{)}
\PY{n}{binary\PYZus{}image}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{zeros\PYZus{}like}\PY{p}{(}\PY{n}{scaled\PYZus{}sobel}\PY{p}{)}
\PY{n}{binary\PYZus{}image}\PY{p}{[}\PY{p}{(}\PY{p}{(}\PY{n}{scaled\PYZus{}sobel}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{n}{thresholds\PYZus{}sobel}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{scaled\PYZus{}sobel}\PY{o}{\PYZlt{}}\PY{o}{=}\PY{n}{thresholds\PYZus{}sobel}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{o}{|}\PY{p}{(}\PY{p}{(}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{]}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{n}{thresholds\PYZus{}s}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{]}\PY{o}{\PYZlt{}}\PY{o}{=}\PY{n}{thresholds\PYZus{}s}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{n}{threshold\PYZus{}l}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{\PYZlt{}}\PY{o}{=}\PY{n}{threshold\PYZus{}l}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{p}{]}\PY{o}{=}\PY{l+m+mi}{1}
\PY{k}{return} \PY{n}{binary\PYZus{}image}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}10}]:} \PY{k}{def} \PY{n+nf}{apply\PYZus{}sobel\PYZus{}direction}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{thresholds\PYZus{}sobel}\PY{p}{,}\PY{n}{thresholds\PYZus{}direction}\PY{p}{,}\PY{n}{kernel\PYZus{}size}\PY{o}{=}\PY{l+m+mi}{3}\PY{p}{,}\PY{n}{Color\PYZus{}Encoding}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{RGB}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{:}
\PY{k}{if}\PY{p}{(}\PY{n}{Color\PYZus{}Encoding}\PY{o}{==}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{BGR}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{:}
\PY{n}{gray}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2GRAY}\PY{p}{)}
\PY{k}{else}\PY{p}{:}
\PY{n}{gray}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}RGB2GRAY}\PY{p}{)}
\PY{n}{sobelx}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{Sobel}\PY{p}{(}\PY{n}{gray}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{CV\PYZus{}64F}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{,}\PY{n}{ksize}\PY{o}{=}\PY{n}{kernel\PYZus{}size}\PY{p}{)}
\PY{n}{sobely}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{Sobel}\PY{p}{(}\PY{n}{gray}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{CV\PYZus{}64F}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{,}\PY{n}{ksize}\PY{o}{=}\PY{n}{kernel\PYZus{}size}\PY{p}{)}
\PY{n}{sobel\PYZus{}direction}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{arctan2}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{n}{sobelx}\PY{p}{)}\PY{p}{,}\PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{n}{sobely}\PY{p}{)}\PY{p}{)}
\PY{n}{sobel\PYZus{}scaled}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{uint8}\PY{p}{(}\PY{l+m+mi}{255}\PY{o}{*}\PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{n}{sobelx}\PY{p}{)}\PY{o}{/}\PY{n}{np}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{n}{sobelx}\PY{p}{)}\PY{p}{)}
\PY{n}{binary\PYZus{}image}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{zeros\PYZus{}like}\PY{p}{(}\PY{n}{sobel\PYZus{}scaled}\PY{p}{)}
\PY{n}{binary\PYZus{}image}\PY{p}{[}\PY{p}{(}\PY{n}{sobel\PYZus{}direction}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{n}{thresholds\PYZus{}direction}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{sobel\PYZus{}direction}\PY{o}{\PYZlt{}}\PY{o}{=}\PY{n}{thresholds\PYZus{}direction}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}}\PY{p}{(}\PY{n}{sobel\PYZus{}scaled}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{n}{thresholds\PYZus{}sobel}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{sobel\PYZus{}scaled}\PY{o}{\PYZlt{}}\PY{o}{=}\PY{n}{thresholds\PYZus{}sobel}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{]}\PY{o}{=}\PY{l+m+mi}{1}
\PY{k}{return} \PY{n}{binary\PYZus{}image}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}11}]:} \PY{k}{def} \PY{n+nf}{color\PYZus{}thresholding}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{l\PYZus{}threshold}\PY{p}{,}\PY{n}{s\PYZus{}threshold}\PY{p}{)}\PY{p}{:}
\PY{n}{hls}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2HLS}\PY{p}{)}
\PY{n}{binary\PYZus{}image}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{zeros\PYZus{}like}\PY{p}{(}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
\PY{n}{binary\PYZus{}image}\PY{p}{[}\PY{p}{(}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{]}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{n}{s\PYZus{}threshold}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{]}\PY{o}{\PYZlt{}}\PY{o}{=}\PY{n}{s\PYZus{}threshold}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{n}{l\PYZus{}threshold}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{hls}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{\PYZlt{}}\PY{o}{=}\PY{n}{l\PYZus{}threshold}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{]}\PY{o}{=}\PY{l+m+mi}{1}
\PY{k}{return} \PY{n}{binary\PYZus{}image}
\end{Verbatim}
\hypertarget{test-thresholding}{%
\paragraph{Test Thresholding}\label{test-thresholding}}
Below is the image that my function returns after applying thresholding
over it:
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}12}]:} \PY{n}{binary\PYZus{}image}\PY{o}{=}\PY{n}{apply\PYZus{}sobel\PYZus{}and\PYZus{}color\PYZus{}thresholding}\PY{p}{(}\PY{n}{transformation\PYZus{}test}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{25}\PY{p}{,}\PY{l+m+mi}{120}\PY{p}{]}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{70}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{]}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{90}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{]}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{binary\PYZus{}image}\PY{p}{,}\PY{n}{cmap}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{gray}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}12}]:} <matplotlib.image.AxesImage at 0x17646e6d940>
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_18_1.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{thresholding-and-perspective-transform}{%
\subsubsection{Thresholding and Perspective
Transform}\label{thresholding-and-perspective-transform}}
Below is the result that my pipeline returned after applying
thresholding and later performing perspective transform:
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}13}]:} \PY{n}{transformed\PYZus{}image}\PY{o}{=}\PY{n}{perspective\PYZus{}transform}\PY{p}{(}\PY{n}{binary\PYZus{}image}\PY{p}{,}\PY{n}{transformation\PYZus{}matrix}\PY{p}{)}
\PY{n}{output\PYZus{}image}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{dstack}\PY{p}{(}\PY{p}{(}\PY{n}{transformed\PYZus{}image}\PY{p}{,}\PY{n}{transformed\PYZus{}image}\PY{p}{,}\PY{n}{transformed\PYZus{}image}\PY{p}{)}\PY{p}{)}\PY{o}{*}\PY{l+m+mi}{255}
\PY{n}{f}\PY{p}{,} \PY{p}{(}\PY{n}{ax1}\PY{p}{,} \PY{n}{ax2}\PY{p}{)} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{20}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{)}\PY{p}{)}
\PY{n}{ax1}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{cv2}\PY{o}{.}\PY{n}{cvtColor}\PY{p}{(}\PY{n}{transformation\PYZus{}test}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{COLOR\PYZus{}BGR2RGB}\PY{p}{)}\PY{p}{)}
\PY{n}{ax1}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Original Image}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{30}\PY{p}{)}
\PY{n}{ax2}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{output\PYZus{}image}\PY{p}{)}
\PY{n}{ax2}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Transformed \PYZam{} Thresholded Image}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{30}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}13}]:} <matplotlib.text.Text at 0x17645732128>
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_20_1.png}
\end{center}
{ \hspace*{\fill} \\}
\hypertarget{pipeline}{%
\subsubsection{Pipeline}\label{pipeline}}
I used a class to retain the data from previous frames, my pipeline
function is also a member of this class. Steps performed: 1. For the
First Frame calculate Camera matrix, distortion Coefficients,
transformation matrix and inverse transformation matrix. 2. Undistort
the Image 3. Apply Thresholding 4. Take Perspective Transform 5. Find
out the pixel indices that are part of lane lines. 6. Fit the polynomial
to the left and right lane pixels. 7. Take the mean of the previous
polynomial coefficients and the coefficeint calculated in step 6. 8.
Calculate the x points for each value of Y(0-719) using the equation
AY\^{}2+BY+C. 9. Then using \texttt{cv2.fillPoly()} fill the lane line
area. 10. Take the inverse Perspective transform of the image received
from step 9. 11. Add the original image and image from step 10. 12.
Calculate Radius of curvature and deviation from center and put it over
the image received after step 12.
\hypertarget{deviation-from-center}{%
\subsubsection{Deviation from center}\label{deviation-from-center}}
To calculate the deviation from center I assumed that the center of the
image is the center of the car, then I simply calculated the center of
the lane lines and the differnce between center of the image and center
of the lane lines is required deviation.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}22}]:} \PY{k}{class} \PY{n+nc}{LaneLineFinding}\PY{p}{(}\PY{n+nb}{object}\PY{p}{)}\PY{p}{:}
\PY{c+c1}{\PYZsh{}prev\PYZus{}left\PYZus{}x=np.array([])}
\PY{c+c1}{\PYZsh{}prev\PYZus{}left\PYZus{}y=np.array([])}
\PY{c+c1}{\PYZsh{}prev\PYZus{}right\PYZus{}x=np.array([])}
\PY{c+c1}{\PYZsh{}prev\PYZus{}right\PYZus{}y=np.array([])}
\PY{n}{prev\PYZus{}left\PYZus{}coeff}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{p}{]}\PY{p}{)}
\PY{n}{prev\PYZus{}right\PYZus{}coeff}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{p}{]}\PY{p}{)}
\PY{n}{last\PYZus{}left\PYZus{}fit}\PY{o}{=}\PY{p}{[}\PY{p}{]}
\PY{n}{last\PYZus{}right\PYZus{}fit}\PY{o}{=}\PY{p}{[}\PY{p}{]}
\PY{n}{mtx}\PY{o}{=}\PY{k+kc}{None}
\PY{n}{dist}\PY{o}{=}\PY{k+kc}{None}
\PY{n}{trans\PYZus{}matrix}\PY{o}{=}\PY{k+kc}{None}
\PY{n}{inverse\PYZus{}trans\PYZus{}matrix}\PY{o}{=}\PY{k+kc}{None}
\PY{n}{flag}\PY{o}{=}\PY{k+kc}{True}
\PY{k}{def} \PY{n+nf}{pipeline}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,}\PY{n}{image}\PY{p}{)}\PY{p}{:}
\PY{k}{if}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{flag}\PY{p}{)}\PY{p}{:}
\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{mtx}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{dist}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{trans\PYZus{}matrix}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{inverse\PYZus{}trans\PYZus{}matrix}\PY{o}{=}\PY{n}{get\PYZus{}variables}\PY{p}{(}\PY{p}{)}
\PY{n}{undistort}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{undistort}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{mtx}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{dist}\PY{p}{,}\PY{k+kc}{None}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{mtx}\PY{p}{)}
\PY{c+c1}{\PYZsh{}binary\PYZus{}image=apply\PYZus{}sobel\PYZus{}and\PYZus{}color\PYZus{}thresholding(transformed\PYZus{}image,[12,170],[48,255])}
\PY{c+c1}{\PYZsh{}binary\PYZus{}image=color\PYZus{}thresholding(undistort,[75,255],[85,255])}
\PY{n}{binary\PYZus{}image}\PY{o}{=}\PY{n}{apply\PYZus{}sobel\PYZus{}and\PYZus{}color\PYZus{}thresholding}\PY{p}{(}\PY{n}{undistort}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{25}\PY{p}{,}\PY{l+m+mi}{120}\PY{p}{]}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{70}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{]}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{90}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{]}\PY{p}{)}\PY{c+c1}{\PYZsh{}[70,120],[120,255],[90,255])\PYZsh{}[70,120],[100,255],[90,255])\PYZsh{}[25,150],[90,255],[90,255])}
\PY{n}{transformed\PYZus{}image}\PY{o}{=}\PY{n}{perspective\PYZus{}transform}\PY{p}{(}\PY{n}{binary\PYZus{}image}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{trans\PYZus{}matrix}\PY{p}{)}
\PY{k}{if}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{flag}\PY{p}{)}\PY{p}{:}
\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{flag}\PY{o}{=}\PY{k+kc}{False}
\PY{n}{left\PYZus{}x}\PY{p}{,}\PY{n}{left\PYZus{}y}\PY{p}{,}\PY{n}{right\PYZus{}x}\PY{p}{,}\PY{n}{right\PYZus{}y}\PY{o}{=}\PY{n}{sliding\PYZus{}window}\PY{p}{(}\PY{n}{transformed\PYZus{}image}\PY{p}{)}
\PY{k}{else}\PY{p}{:}
\PY{n}{left\PYZus{}x}\PY{p}{,}\PY{n}{left\PYZus{}y}\PY{p}{,}\PY{n}{right\PYZus{}x}\PY{p}{,}\PY{n}{right\PYZus{}y}\PY{o}{=}\PY{n}{find\PYZus{}lane\PYZus{}lines}\PY{p}{(}\PY{n}{transformed\PYZus{}image}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{last\PYZus{}left\PYZus{}fit}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{last\PYZus{}right\PYZus{}fit}\PY{p}{)}
\PY{c+c1}{\PYZsh{}output= np.dstack((transformed\PYZus{}image,np.zeros\PYZus{}like(binary\PYZus{}image),np.zeros\PYZus{}like(binary\PYZus{}image)))*255}
\PY{c+c1}{\PYZsh{}plt.imshow(binary\PYZus{}image)}
\PY{c+c1}{\PYZsh{}print(output)}
\PY{c+c1}{\PYZsh{}if(len(self.prev\PYZus{}left\PYZus{}x)\PYZgt{}=720*10):}
\PY{c+c1}{\PYZsh{} self.prev\PYZus{}left\PYZus{}x=self.prev\PYZus{}left\PYZus{}x[720:len(self.prev\PYZus{}left\PYZus{}x)]}
\PY{c+c1}{\PYZsh{}if(len(self.prev\PYZus{}right\PYZus{}x)\PYZgt{}=720*10):}
\PY{c+c1}{\PYZsh{} self.prev\PYZus{}right\PYZus{}x=self.prev\PYZus{}right\PYZus{}x[720:len(self.prev\PYZus{}right\PYZus{}x)]}
\PY{c+c1}{\PYZsh{}if(len(self.prev\PYZus{}left\PYZus{}y)\PYZgt{}=720*10):}
\PY{c+c1}{\PYZsh{} self.prev\PYZus{}left\PYZus{}y=self.prev\PYZus{}left\PYZus{}y[720:len(self.prev\PYZus{}left\PYZus{}y)]}
\PY{c+c1}{\PYZsh{}if(len(self.prev\PYZus{}right\PYZus{}y)\PYZgt{}=720*10):}
\PY{c+c1}{\PYZsh{} self.prev\PYZus{}right\PYZus{}y=self.prev\PYZus{}right\PYZus{}y[720:len(self.prev\PYZus{}right\PYZus{}y)]}
\PY{c+c1}{\PYZsh{}self.prev\PYZus{}left\PYZus{}x=np.append(self.prev\PYZus{}left\PYZus{}x,left\PYZus{}x)}
\PY{c+c1}{\PYZsh{}self.prev\PYZus{}left\PYZus{}y=np.append(self.prev\PYZus{}left\PYZus{}y,left\PYZus{}y)}
\PY{c+c1}{\PYZsh{}self.prev\PYZus{}right\PYZus{}x=np.append(self.prev\PYZus{}right\PYZus{}x,right\PYZus{}x)}
\PY{c+c1}{\PYZsh{}self.prev\PYZus{}right\PYZus{}y=np.append(self.prev\PYZus{}right\PYZus{}y,right\PYZus{}y)}
\PY{c+c1}{\PYZsh{}left\PYZus{}fit=np.polyfit(self.prev\PYZus{}left\PYZus{}y, self.prev\PYZus{}left\PYZus{}x,2)}
\PY{c+c1}{\PYZsh{}right\PYZus{}fit=np.polyfit(self.prev\PYZus{}right\PYZus{}y,self.prev\PYZus{}right\PYZus{}x,2)}
\PY{n}{left\PYZus{}fit}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{polyfit}\PY{p}{(}\PY{n}{left\PYZus{}y}\PY{p}{,} \PY{n}{left\PYZus{}x}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}
\PY{n}{right\PYZus{}fit}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{polyfit}\PY{p}{(}\PY{n}{right\PYZus{}y}\PY{p}{,}\PY{n}{right\PYZus{}x}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}
\PY{k}{if}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}left\PYZus{}coeff}\PY{p}{)}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{l+m+mi}{10}\PY{o}{*}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{:}
\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}left\PYZus{}coeff}\PY{o}{=}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}left\PYZus{}coeff}\PY{p}{[}\PY{l+m+mi}{3}\PY{p}{:}\PY{n+nb}{len}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}left\PYZus{}coeff}\PY{p}{)}\PY{p}{]}
\PY{k}{if}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}right\PYZus{}coeff}\PY{p}{)}\PY{o}{\PYZgt{}}\PY{o}{=}\PY{l+m+mi}{3}\PY{o}{*}\PY{l+m+mi}{10}\PY{p}{)}\PY{p}{:}
\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}right\PYZus{}coeff}\PY{o}{=}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}right\PYZus{}coeff}\PY{p}{[}\PY{l+m+mi}{3}\PY{p}{:}\PY{n+nb}{len}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}right\PYZus{}coeff}\PY{p}{)}\PY{p}{]}
\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}right\PYZus{}coeff}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}right\PYZus{}coeff}\PY{p}{,}\PY{n}{right\PYZus{}fit}\PY{p}{)}
\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}left\PYZus{}coeff}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}left\PYZus{}coeff}\PY{p}{,}\PY{n}{left\PYZus{}fit}\PY{p}{)}
\PY{n}{left\PYZus{}fit}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}left\PYZus{}coeff}\PY{o}{.}\PY{n}{reshape}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{,}\PY{n}{axis}\PY{o}{=}\PY{l+m+mi}{0}\PY{p}{)}
\PY{n}{right\PYZus{}fit}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{prev\PYZus{}right\PYZus{}coeff}\PY{o}{.}\PY{n}{reshape}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{,}\PY{n}{axis}\PY{o}{=}\PY{l+m+mi}{0}\PY{p}{)}
\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{last\PYZus{}left\PYZus{}fit}\PY{o}{=}\PY{n}{left\PYZus{}fit}
\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{last\PYZus{}right\PYZus{}fit}\PY{o}{=}\PY{n}{right\PYZus{}fit}
\PY{n}{ploty} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{linspace}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{n}{image}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,} \PY{n}{image}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{p}{)}
\PY{n}{left\PYZus{}fitx} \PY{o}{=} \PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{n}{ploty}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} \PY{o}{+} \PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{*}\PY{n}{ploty} \PY{o}{+} \PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{right\PYZus{}fitx} \PY{o}{=} \PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{n}{ploty}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} \PY{o}{+} \PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{*}\PY{n}{ploty} \PY{o}{+} \PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{output\PYZus{}image}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{zeros\PYZus{}like}\PY{p}{(}\PY{n}{image}\PY{p}{)}
\PY{n}{pts\PYZus{}left} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{n}{np}\PY{o}{.}\PY{n}{transpose}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{vstack}\PY{p}{(}\PY{p}{[}\PY{n}{left\PYZus{}fitx}\PY{p}{,} \PY{n}{ploty}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{p}{]}\PY{p}{)}
\PY{n}{pts\PYZus{}right} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{n}{np}\PY{o}{.}\PY{n}{flipud}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{transpose}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{vstack}\PY{p}{(}\PY{p}{[}\PY{n}{right\PYZus{}fitx}\PY{p}{,} \PY{n}{ploty}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{p}{)}\PY{p}{]}\PY{p}{)}
\PY{n}{pts} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{hstack}\PY{p}{(}\PY{p}{(}\PY{n}{pts\PYZus{}left}\PY{p}{,} \PY{n}{pts\PYZus{}right}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Draw the lane onto the warped blank image}
\PY{n}{cv2}\PY{o}{.}\PY{n}{fillPoly}\PY{p}{(}\PY{n}{output\PYZus{}image}\PY{p}{,} \PY{n}{np}\PY{o}{.}\PY{n}{int\PYZus{}}\PY{p}{(}\PY{p}{[}\PY{n}{pts}\PY{p}{]}\PY{p}{)}\PY{p}{,} \PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{255}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{)}\PY{p}{)}
\PY{n}{final\PYZus{}image}\PY{o}{=}\PY{n}{perspective\PYZus{}transform}\PY{p}{(}\PY{n}{output\PYZus{}image}\PY{p}{,}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{inverse\PYZus{}trans\PYZus{}matrix}\PY{p}{)}
\PY{n}{output\PYZus{}image}\PY{o}{=}\PY{n}{cv2}\PY{o}{.}\PY{n}{addWeighted}\PY{p}{(}\PY{n}{image}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{,}\PY{n}{final\PYZus{}image}\PY{p}{,}\PY{l+m+mf}{0.5}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{)}
\PY{n}{left\PYZus{}curverad}\PY{p}{,}\PY{n}{right\PYZus{}curverad}\PY{o}{=}\PY{n}{calculate\PYZus{}radius\PYZus{}of\PYZus{}curvature}\PY{p}{(}\PY{n}{left\PYZus{}fit}\PY{p}{,}\PY{n}{right\PYZus{}fit}\PY{p}{,}\PY{n}{np}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{n}{ploty}\PY{p}{)}\PY{p}{)}
\PY{n}{cv2}\PY{o}{.}\PY{n}{putText}\PY{p}{(}\PY{n}{output\PYZus{}image}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Radius Of Curvature = }\PY{l+s+si}{\PYZob{}0:.2f\PYZcb{}}\PY{l+s+s1}{(m)}\PY{l+s+s1}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{[}\PY{n}{left\PYZus{}curverad}\PY{p}{,}\PY{n}{right\PYZus{}curverad}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{p}{,}\PY{p}{(}\PY{l+m+mi}{50}\PY{p}{,}\PY{l+m+mi}{50}\PY{p}{)}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,}\PY{p}{(}\PY{l+m+mi}{255}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{)}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{LINE\PYZus{}AA}\PY{p}{)}
\PY{n}{deviation\PYZus{}from\PYZus{}center}\PY{o}{=}\PY{p}{(}\PY{p}{(}\PY{n}{image}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{p}{(}\PY{p}{(}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{n}{right\PYZus{}fitx}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{\PYZhy{}}\PY{n}{left\PYZus{}fitx}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{+}\PY{n}{left\PYZus{}fitx}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{o}{*}\PY{p}{(}\PY{l+m+mf}{3.7}\PY{o}{/}\PY{l+m+mi}{600}\PY{p}{)}
\PY{k}{if}\PY{p}{(}\PY{n}{deviation\PYZus{}from\PYZus{}center}\PY{o}{\PYZgt{}}\PY{l+m+mi}{0}\PY{p}{)}\PY{p}{:}
\PY{n}{cv2}\PY{o}{.}\PY{n}{putText}\PY{p}{(}\PY{n}{output\PYZus{}image}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{vehicle is }\PY{l+s+si}{\PYZob{}0:.2f\PYZcb{}}\PY{l+s+s1}{(m) left from the center}\PY{l+s+s1}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{n}{deviation\PYZus{}from\PYZus{}center}\PY{p}{)}\PY{p}{)}\PY{p}{,}\PY{p}{(}\PY{l+m+mi}{50}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{)}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,}\PY{p}{(}\PY{l+m+mi}{255}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{)}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{LINE\PYZus{}AA}\PY{p}{)}
\PY{k}{else}\PY{p}{:}
\PY{n}{cv2}\PY{o}{.}\PY{n}{putText}\PY{p}{(}\PY{n}{output\PYZus{}image}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{vehicle is }\PY{l+s+si}{\PYZob{}0:.2f\PYZcb{}}\PY{l+s+s1}{(m) right from the center}\PY{l+s+s1}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{n}{deviation\PYZus{}from\PYZus{}center}\PY{p}{)}\PY{p}{)}\PY{p}{,}\PY{p}{(}\PY{l+m+mi}{50}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{)}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,}\PY{p}{(}\PY{l+m+mi}{255}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{,}\PY{l+m+mi}{255}\PY{p}{)}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{cv2}\PY{o}{.}\PY{n}{LINE\PYZus{}AA}\PY{p}{)}
\PY{k}{return} \PY{n}{output\PYZus{}image}
\end{Verbatim}
\hypertarget{sliding-window}{%
\subsubsection{Sliding Window}\label{sliding-window}}
I have used sliding window approach to find out the indices of the
pixels those are part of the lane lines. This approach uses a window and
only considers nonzero pixels within that window, in my implementaion I
have used 9 windows hence there will be 9 windows for left lane and 9
windows for right lane, each of 80 pixel height and 200 pixels width.
This function returns the \texttt{left\_x},\texttt{left\_y} for left
lane and \texttt{right\_x},\texttt{right\_y} for right lane. These
points I used in Pipeline to fit a polynomial.
Sliding window is not being used by each frame, since consecutive frames
will not have much difference in lane line positions, hence we are
serching in a given margin for the next frame say 100 in my case. I have
defined \texttt{find\_lane\_lines()} for this purpose this function also
returns the \texttt{left\_x},\texttt{left\_y} for left lane and
\texttt{right\_x},\texttt{right\_y} for right lane. These points I used
in Pipeline to fit a polynomial.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}15}]:} \PY{k}{def} \PY{n+nf}{sliding\PYZus{}window}\PY{p}{(}\PY{n}{binary\PYZus{}warped}\PY{p}{,}\PY{n}{visualize}\PY{o}{=}\PY{k+kc}{False}\PY{p}{)}\PY{p}{:}
\PY{n}{histogram}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{n}{binary\PYZus{}warped}\PY{p}{[}\PY{n}{binary\PYZus{}warped}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{/}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{:}\PY{p}{,}\PY{p}{:}\PY{p}{]}\PY{p}{,}\PY{n}{axis}\PY{o}{=}\PY{l+m+mi}{0}\PY{p}{)}
\PY{n}{out\PYZus{}img} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{dstack}\PY{p}{(}\PY{p}{(}\PY{n}{binary\PYZus{}warped}\PY{p}{,} \PY{n}{binary\PYZus{}warped}\PY{p}{,} \PY{n}{binary\PYZus{}warped}\PY{p}{)}\PY{p}{)}\PY{o}{*}\PY{l+m+mi}{255}
\PY{c+c1}{\PYZsh{} Find the peak of the left and right halves of the histogram}
\PY{c+c1}{\PYZsh{} These will be the starting point for the left and right lines}
\PY{n}{midpoint} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{int}\PY{p}{(}\PY{n}{histogram}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{/}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{)}
\PY{n}{leftx\PYZus{}base} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{argmax}\PY{p}{(}\PY{n}{histogram}\PY{p}{[}\PY{p}{:}\PY{n}{midpoint}\PY{p}{]}\PY{p}{)}
\PY{n}{rightx\PYZus{}base} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{argmax}\PY{p}{(}\PY{n}{histogram}\PY{p}{[}\PY{n}{midpoint}\PY{p}{:}\PY{p}{]}\PY{p}{)} \PY{o}{+} \PY{n}{midpoint}
\PY{c+c1}{\PYZsh{} Choose the number of sliding windows}
\PY{n}{nwindows} \PY{o}{=} \PY{l+m+mi}{9}
\PY{c+c1}{\PYZsh{} Set height of windows}
\PY{n}{window\PYZus{}height} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{int}\PY{p}{(}\PY{n}{binary\PYZus{}warped}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{/}\PY{o}{/}\PY{n}{nwindows}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Identify the x and y positions of all nonzero pixels in the image}
\PY{n}{nonzero} \PY{o}{=} \PY{n}{binary\PYZus{}warped}\PY{o}{.}\PY{n}{nonzero}\PY{p}{(}\PY{p}{)}
\PY{n}{nonzeroy} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{n}{nonzero}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
\PY{n}{nonzerox} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{n}{nonzero}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Current positions to be updated for each window}
\PY{n}{leftx\PYZus{}current} \PY{o}{=} \PY{n}{leftx\PYZus{}base}
\PY{n}{rightx\PYZus{}current} \PY{o}{=} \PY{n}{rightx\PYZus{}base}
\PY{c+c1}{\PYZsh{} Set the width of the windows +/\PYZhy{} margin}
\PY{n}{margin} \PY{o}{=} \PY{l+m+mi}{100}
\PY{c+c1}{\PYZsh{} Set minimum number of pixels found to recenter window}
\PY{n}{minpix} \PY{o}{=} \PY{l+m+mi}{50}
\PY{c+c1}{\PYZsh{} Create empty lists to receive left and right lane pixel indices}
\PY{n}{left\PYZus{}lane\PYZus{}inds} \PY{o}{=} \PY{p}{[}\PY{p}{]}
\PY{n}{right\PYZus{}lane\PYZus{}inds} \PY{o}{=} \PY{p}{[}\PY{p}{]}
\PY{c+c1}{\PYZsh{} Step through the windows one by one}
\PY{k}{for} \PY{n}{window} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{nwindows}\PY{p}{)}\PY{p}{:}
\PY{c+c1}{\PYZsh{} Identify window boundaries in x and y (and right and left)}
\PY{n}{win\PYZus{}y\PYZus{}low} \PY{o}{=} \PY{n}{binary\PYZus{}warped}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{p}{(}\PY{n}{window}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{window\PYZus{}height}
\PY{n}{win\PYZus{}y\PYZus{}high} \PY{o}{=} \PY{n}{binary\PYZus{}warped}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{window}\PY{o}{*}\PY{n}{window\PYZus{}height}
\PY{n}{win\PYZus{}xleft\PYZus{}low} \PY{o}{=} \PY{n}{leftx\PYZus{}current} \PY{o}{\PYZhy{}} \PY{n}{margin}
\PY{n}{win\PYZus{}xleft\PYZus{}high} \PY{o}{=} \PY{n}{leftx\PYZus{}current} \PY{o}{+} \PY{n}{margin}
\PY{n}{win\PYZus{}xright\PYZus{}low} \PY{o}{=} \PY{n}{rightx\PYZus{}current} \PY{o}{\PYZhy{}} \PY{n}{margin}
\PY{n}{win\PYZus{}xright\PYZus{}high} \PY{o}{=} \PY{n}{rightx\PYZus{}current} \PY{o}{+} \PY{n}{margin}
\PY{c+c1}{\PYZsh{} Draw the windows on the visualization image}
\PY{c+c1}{\PYZsh{}cv2.rectangle(out\PYZus{}img,(win\PYZus{}xleft\PYZus{}low,win\PYZus{}y\PYZus{}low),(win\PYZus{}xleft\PYZus{}high,win\PYZus{}y\PYZus{}high),}
\PY{c+c1}{\PYZsh{}(0,255,0), 2) }
\PY{c+c1}{\PYZsh{}cv2.rectangle(out\PYZus{}img,(win\PYZus{}xright\PYZus{}low,win\PYZus{}y\PYZus{}low),(win\PYZus{}xright\PYZus{}high,win\PYZus{}y\PYZus{}high),}
\PY{c+c1}{\PYZsh{}(0,255,0), 2) }
\PY{c+c1}{\PYZsh{} Identify the nonzero pixels in x and y within the window}
\PY{n}{good\PYZus{}left\PYZus{}inds} \PY{o}{=} \PY{p}{(}\PY{p}{(}\PY{n}{nonzeroy} \PY{o}{\PYZgt{}}\PY{o}{=} \PY{n}{win\PYZus{}y\PYZus{}low}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{nonzeroy} \PY{o}{\PYZlt{}} \PY{n}{win\PYZus{}y\PYZus{}high}\PY{p}{)} \PY{o}{\PYZam{}}
\PY{p}{(}\PY{n}{nonzerox} \PY{o}{\PYZgt{}}\PY{o}{=} \PY{n}{win\PYZus{}xleft\PYZus{}low}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{nonzerox} \PY{o}{\PYZlt{}} \PY{n}{win\PYZus{}xleft\PYZus{}high}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{nonzero}\PY{p}{(}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}
\PY{n}{good\PYZus{}right\PYZus{}inds} \PY{o}{=} \PY{p}{(}\PY{p}{(}\PY{n}{nonzeroy} \PY{o}{\PYZgt{}}\PY{o}{=} \PY{n}{win\PYZus{}y\PYZus{}low}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{nonzeroy} \PY{o}{\PYZlt{}} \PY{n}{win\PYZus{}y\PYZus{}high}\PY{p}{)} \PY{o}{\PYZam{}}
\PY{p}{(}\PY{n}{nonzerox} \PY{o}{\PYZgt{}}\PY{o}{=} \PY{n}{win\PYZus{}xright\PYZus{}low}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{nonzerox} \PY{o}{\PYZlt{}} \PY{n}{win\PYZus{}xright\PYZus{}high}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{nonzero}\PY{p}{(}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}
\PY{c+c1}{\PYZsh{} Append these indices to the lists}
\PY{n}{left\PYZus{}lane\PYZus{}inds}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{good\PYZus{}left\PYZus{}inds}\PY{p}{)}
\PY{n}{right\PYZus{}lane\PYZus{}inds}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{good\PYZus{}right\PYZus{}inds}\PY{p}{)}
\PY{c+c1}{\PYZsh{} If you found \PYZgt{} minpix pixels, recenter next window on their mean position}
\PY{k}{if} \PY{n+nb}{len}\PY{p}{(}\PY{n}{good\PYZus{}left\PYZus{}inds}\PY{p}{)} \PY{o}{\PYZgt{}} \PY{n}{minpix}\PY{p}{:}
\PY{n}{leftx\PYZus{}current} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{int}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{n}{nonzerox}\PY{p}{[}\PY{n}{good\PYZus{}left\PYZus{}inds}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{k}{if} \PY{n+nb}{len}\PY{p}{(}\PY{n}{good\PYZus{}right\PYZus{}inds}\PY{p}{)} \PY{o}{\PYZgt{}} \PY{n}{minpix}\PY{p}{:}
\PY{n}{rightx\PYZus{}current} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{int}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{n}{nonzerox}\PY{p}{[}\PY{n}{good\PYZus{}right\PYZus{}inds}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Concatenate the arrays of indices}
\PY{n}{left\PYZus{}lane\PYZus{}inds} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{concatenate}\PY{p}{(}\PY{n}{left\PYZus{}lane\PYZus{}inds}\PY{p}{)}
\PY{n}{right\PYZus{}lane\PYZus{}inds} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{concatenate}\PY{p}{(}\PY{n}{right\PYZus{}lane\PYZus{}inds}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Extract left and right line pixel positions}
\PY{n}{leftx} \PY{o}{=} \PY{n}{nonzerox}\PY{p}{[}\PY{n}{left\PYZus{}lane\PYZus{}inds}\PY{p}{]}
\PY{n}{lefty} \PY{o}{=} \PY{n}{nonzeroy}\PY{p}{[}\PY{n}{left\PYZus{}lane\PYZus{}inds}\PY{p}{]}
\PY{n}{rightx} \PY{o}{=} \PY{n}{nonzerox}\PY{p}{[}\PY{n}{right\PYZus{}lane\PYZus{}inds}\PY{p}{]}
\PY{n}{righty} \PY{o}{=} \PY{n}{nonzeroy}\PY{p}{[}\PY{n}{right\PYZus{}lane\PYZus{}inds}\PY{p}{]}
\PY{k}{if}\PY{p}{(}\PY{n}{visualize}\PY{p}{)}\PY{p}{:}
\PY{c+c1}{\PYZsh{} Fit a second order polynomial to each}
\PY{n}{left\PYZus{}fit} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{polyfit}\PY{p}{(}\PY{n}{lefty}\PY{p}{,} \PY{n}{leftx}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{)}
\PY{n}{right\PYZus{}fit} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{polyfit}\PY{p}{(}\PY{n}{righty}\PY{p}{,} \PY{n}{rightx}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{)}
\PY{n}{ploty} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{linspace}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{n}{binary\PYZus{}warped}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,} \PY{n}{binary\PYZus{}warped}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{p}{)}
\PY{n}{left\PYZus{}fitx} \PY{o}{=} \PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{n}{ploty}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} \PY{o}{+} \PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{*}\PY{n}{ploty} \PY{o}{+} \PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{right\PYZus{}fitx} \PY{o}{=} \PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{n}{ploty}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} \PY{o}{+} \PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{*}\PY{n}{ploty} \PY{o}{+} \PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{out\PYZus{}img}\PY{p}{[}\PY{n}{nonzeroy}\PY{p}{[}\PY{n}{left\PYZus{}lane\PYZus{}inds}\PY{p}{]}\PY{p}{,} \PY{n}{nonzerox}\PY{p}{[}\PY{n}{left\PYZus{}lane\PYZus{}inds}\PY{p}{]}\PY{p}{]} \PY{o}{=} \PY{p}{[}\PY{l+m+mi}{255}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}
\PY{n}{out\PYZus{}img}\PY{p}{[}\PY{n}{nonzeroy}\PY{p}{[}\PY{n}{right\PYZus{}lane\PYZus{}inds}\PY{p}{]}\PY{p}{,} \PY{n}{nonzerox}\PY{p}{[}\PY{n}{right\PYZus{}lane\PYZus{}inds}\PY{p}{]}\PY{p}{]} \PY{o}{=} \PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{255}\PY{p}{]}
\PY{n}{plt}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{out\PYZus{}img}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{left\PYZus{}fitx}\PY{p}{,} \PY{n}{ploty}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{yellow}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{right\PYZus{}fitx}\PY{p}{,} \PY{n}{ploty}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{yellow}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlim}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1280}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylim}\PY{p}{(}\PY{l+m+mi}{720}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{)}
\PY{k}{return} \PY{k+kc}{None}
\PY{k}{return} \PY{n}{leftx}\PY{p}{,}\PY{n}{lefty}\PY{p}{,}\PY{n}{rightx}\PY{p}{,}\PY{n}{righty}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}16}]:} \PY{k}{def} \PY{n+nf}{find\PYZus{}lane\PYZus{}lines}\PY{p}{(}\PY{n}{binary\PYZus{}warped}\PY{p}{,}\PY{n}{left\PYZus{}fit}\PY{p}{,}\PY{n}{right\PYZus{}fit}\PY{p}{)}\PY{p}{:}
\PY{n}{nonzero} \PY{o}{=} \PY{n}{binary\PYZus{}warped}\PY{o}{.}\PY{n}{nonzero}\PY{p}{(}\PY{p}{)}
\PY{n}{nonzeroy} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{n}{nonzero}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
\PY{n}{nonzerox} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{n}{nonzero}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}
\PY{n}{margin} \PY{o}{=} \PY{l+m+mi}{100}
\PY{n}{left\PYZus{}lane\PYZus{}inds} \PY{o}{=} \PY{p}{(}\PY{p}{(}\PY{n}{nonzerox} \PY{o}{\PYZgt{}} \PY{p}{(}\PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{p}{(}\PY{n}{nonzeroy}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)} \PY{o}{+} \PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{*}\PY{n}{nonzeroy} \PY{o}{+}
\PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{margin}\PY{p}{)}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{nonzerox} \PY{o}{\PYZlt{}} \PY{p}{(}\PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{p}{(}\PY{n}{nonzeroy}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)} \PY{o}{+}
\PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{*}\PY{n}{nonzeroy} \PY{o}{+} \PY{n}{left\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]} \PY{o}{+} \PY{n}{margin}\PY{p}{)}\PY{p}{)}\PY{p}{)}
\PY{n}{right\PYZus{}lane\PYZus{}inds} \PY{o}{=} \PY{p}{(}\PY{p}{(}\PY{n}{nonzerox} \PY{o}{\PYZgt{}} \PY{p}{(}\PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{p}{(}\PY{n}{nonzeroy}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)} \PY{o}{+} \PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{*}\PY{n}{nonzeroy} \PY{o}{+}
\PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{margin}\PY{p}{)}\PY{p}{)} \PY{o}{\PYZam{}} \PY{p}{(}\PY{n}{nonzerox} \PY{o}{\PYZlt{}} \PY{p}{(}\PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{p}{(}\PY{n}{nonzeroy}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)} \PY{o}{+}
\PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{*}\PY{n}{nonzeroy} \PY{o}{+} \PY{n}{right\PYZus{}fit}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]} \PY{o}{+} \PY{n}{margin}\PY{p}{)}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Again, extract left and right line pixel positions}
\PY{n}{leftx} \PY{o}{=} \PY{n}{nonzerox}\PY{p}{[}\PY{n}{left\PYZus{}lane\PYZus{}inds}\PY{p}{]}
\PY{n}{lefty} \PY{o}{=} \PY{n}{nonzeroy}\PY{p}{[}\PY{n}{left\PYZus{}lane\PYZus{}inds}\PY{p}{]}
\PY{n}{rightx} \PY{o}{=} \PY{n}{nonzerox}\PY{p}{[}\PY{n}{right\PYZus{}lane\PYZus{}inds}\PY{p}{]}
\PY{n}{righty} \PY{o}{=} \PY{n}{nonzeroy}\PY{p}{[}\PY{n}{right\PYZus{}lane\PYZus{}inds}\PY{p}{]}
\PY{c+c1}{\PYZsh{} Fit a second order polynomial to each}
\PY{c+c1}{\PYZsh{}left\PYZus{}fit = np.polyfit(lefty, leftx, 2)}
\PY{c+c1}{\PYZsh{}right\PYZus{}fit = np.polyfit(righty, rightx, 2)}
\PY{c+c1}{\PYZsh{} Generate x and y values for plotting}
\PY{c+c1}{\PYZsh{}ploty = np.linspace(0, binary\PYZus{}warped.shape[0]\PYZhy{}1, binary\PYZus{}warped.shape[0] )}
\PY{c+c1}{\PYZsh{}left\PYZus{}fitx = left\PYZus{}fit[0]*ploty**2 + left\PYZus{}fit[1]*ploty + left\PYZus{}fit[2]}
\PY{c+c1}{\PYZsh{}right\PYZus{}fitx = right\PYZus{}fit[0]*ploty**2 + right\PYZus{}fit[1]*ploty + right\PYZus{}fit[2]}
\PY{k}{return} \PY{n}{leftx}\PY{p}{,}\PY{n}{lefty}\PY{p}{,}\PY{n}{rightx}\PY{p}{,}\PY{n}{righty}
\end{Verbatim}
\hypertarget{fit-the-polynomial}{%
\paragraph{Fit the Polynomial}\label{fit-the-polynomial}}
Below is the result after identifying the lane line points and fitting a
polynomial to them.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}17}]:} \PY{n}{sliding\PYZus{}window}\PY{p}{(}\PY{n}{transformed\PYZus{}image}\PY{p}{,}\PY{n}{visualize}\PY{o}{=}\PY{k+kc}{True}\PY{p}{)}
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_27_0.png}
\end{center}
{ \hspace*{\fill} \\}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}18}]:} \PY{k}{def} \PY{n+nf}{get\PYZus{}variables}\PY{p}{(}\PY{p}{)}\PY{p}{:}
\PY{n}{mtx}\PY{p}{,}\PY{n}{dist}\PY{o}{=}\PY{n}{calibrate\PYZus{}camera}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{./camera\PYZus{}cal/calibration*.jpg}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{}1src\PYZus{}points=np.float32([[800,470],[1100,720],[210,720],[500,470]])}
\PY{c+c1}{\PYZsh{}1dest\PYZus{}points=np.float32([[1100,0],[1100,720],[200,720],[200,0]])}
\PY{c+c1}{\PYZsh{}src\PYZus{}points=np.float32([[790,490],[1090,670],[250,670],[515,490]])}
\PY{c+c1}{\PYZsh{}dest\PYZus{}points=np.float32([[1100,0],[1100,720],[200,720],[200,0]])}
\PY{n}{src\PYZus{}points} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{float32}\PY{p}{(}\PY{p}{[}\PY{p}{[}\PY{l+m+mi}{200}\PY{p}{,}\PY{l+m+mi}{720}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{600}\PY{p}{,} \PY{l+m+mi}{447}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{679}\PY{p}{,}\PY{l+m+mi}{447}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{1100}\PY{p}{,}\PY{l+m+mi}{720}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{dest\PYZus{}points} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{float32}\PY{p}{(}\PY{p}{[}\PY{p}{[}\PY{l+m+mi}{300}\PY{p}{,} \PY{l+m+mi}{720}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{300}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{900}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{900}\PY{p}{,} \PY{l+m+mi}{720}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{transformation\PYZus{}matrix}\PY{o}{=}\PY{n}{get\PYZus{}transformation\PYZus{}matrix}\PY{p}{(}\PY{n}{src\PYZus{}points}\PY{p}{,}\PY{n}{dest\PYZus{}points}\PY{p}{)}
\PY{n}{inverse\PYZus{}transformation\PYZus{}matrix}\PY{o}{=}\PY{n}{get\PYZus{}transformation\PYZus{}matrix}\PY{p}{(}\PY{n}{dest\PYZus{}points}\PY{p}{,}\PY{n}{src\PYZus{}points}\PY{p}{)}
\PY{k}{return} \PY{n}{mtx}\PY{p}{,}\PY{n}{dist}\PY{p}{,}\PY{n}{transformation\PYZus{}matrix}\PY{p}{,}\PY{n}{inverse\PYZus{}transformation\PYZus{}matrix}
\end{Verbatim}
\hypertarget{radius-of-curvature}{%
\subsubsection{Radius of curvature}\label{radius-of-curvature}}
Once we have the polynomial coefficients we can use them to find out the
radius of curvature. I have scaled the Radius of curvature in the
meters.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}19}]:} \PY{k}{def} \PY{n+nf}{calculate\PYZus{}radius\PYZus{}of\PYZus{}curvature}\PY{p}{(}\PY{n}{left\PYZus{}fit\PYZus{}cr}\PY{p}{,}\PY{n}{right\PYZus{}fit\PYZus{}cr}\PY{p}{,}\PY{n}{y\PYZus{}eval}\PY{p}{)}\PY{p}{:}
\PY{n}{ym\PYZus{}per\PYZus{}pix} \PY{o}{=} \PY{l+m+mi}{40}\PY{o}{/}\PY{l+m+mi}{720} \PY{c+c1}{\PYZsh{} meters per pixel in y dimension}
\PY{n}{xm\PYZus{}per\PYZus{}pix} \PY{o}{=} \PY{l+m+mf}{3.7}\PY{o}{/}\PY{l+m+mi}{600} \PY{c+c1}{\PYZsh{} meters per pixel in x dimension}
\PY{c+c1}{\PYZsh{} Fit new polynomials to x,y in world space}
\PY{c+c1}{\PYZsh{}left\PYZus{}fit\PYZus{}cr = np.polyfit(ploty*ym\PYZus{}per\PYZus{}pix, leftx*xm\PYZus{}per\PYZus{}pix, 2)}
\PY{c+c1}{\PYZsh{}right\PYZus{}fit\PYZus{}cr = np.polyfit(ploty*ym\PYZus{}per\PYZus{}pix, rightx*xm\PYZus{}per\PYZus{}pix, 2)}
\PY{c+c1}{\PYZsh{} Calculate the new radii of curvature}
\PY{n}{left\PYZus{}curverad} \PY{o}{=} \PY{p}{(}\PY{p}{(}\PY{l+m+mi}{1} \PY{o}{+} \PY{p}{(}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{left\PYZus{}fit\PYZus{}cr}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{n}{y\PYZus{}eval}\PY{o}{*}\PY{n}{ym\PYZus{}per\PYZus{}pix} \PY{o}{+} \PY{n}{left\PYZus{}fit\PYZus{}cr}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mf}{1.5}\PY{p}{)} \PY{o}{/} \PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{left\PYZus{}fit\PYZus{}cr}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
\PY{n}{right\PYZus{}curverad} \PY{o}{=} \PY{p}{(}\PY{p}{(}\PY{l+m+mi}{1} \PY{o}{+} \PY{p}{(}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{right\PYZus{}fit\PYZus{}cr}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{*}\PY{n}{y\PYZus{}eval}\PY{o}{*}\PY{n}{ym\PYZus{}per\PYZus{}pix} \PY{o}{+} \PY{n}{right\PYZus{}fit\PYZus{}cr}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mf}{1.5}\PY{p}{)} \PY{o}{/} \PY{n}{np}\PY{o}{.}\PY{n}{absolute}\PY{p}{(}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{right\PYZus{}fit\PYZus{}cr}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Now our radius of curvature is in meters}
\PY{k}{return} \PY{n}{left\PYZus{}curverad}\PY{p}{,}\PY{n}{right\PYZus{}curverad}
\end{Verbatim}
\hypertarget{pipeline-output}{%
\subsubsection{Pipeline Output}\label{pipeline-output}}
Below is the example of Pipeline output for a frame.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}23}]:} \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{image} \PY{k}{as} \PY{n+nn}{matimage}
\PY{n}{test}\PY{o}{=}\PY{n}{LaneLineFinding}\PY{p}{(}\PY{p}{)}
\PY{n}{test\PYZus{}image}\PY{o}{=}\PY{n}{matimage}\PY{o}{.}\PY{n}{imread}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{./test\PYZus{}images/straight\PYZus{}lines1.jpg}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{test\PYZus{}output}\PY{o}{=}\PY{n}{test}\PY{o}{.}\PY{n}{pipeline}\PY{p}{(}\PY{n}{test\PYZus{}image}\PY{p}{)}
\PY{n}{f}\PY{p}{,} \PY{p}{(}\PY{n}{ax1}\PY{p}{,} \PY{n}{ax2}\PY{p}{)} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{20}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{)}\PY{p}{)}
\PY{n}{ax1}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{test\PYZus{}image}\PY{p}{)}
\PY{n}{ax1}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Original Image}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{30}\PY{p}{)}
\PY{n}{ax2}\PY{o}{.}\PY{n}{imshow}\PY{p}{(}\PY{n}{test\PYZus{}output}\PY{p}{)}
\PY{n}{ax2}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Final Image}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{30}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}23}]:} <matplotlib.text.Text at 0x1764c5c9780>
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_32_1.png}
\end{center}
{ \hspace*{\fill} \\}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}24}]:} \PY{k+kn}{from} \PY{n+nn}{moviepy}\PY{n+nn}{.}\PY{n+nn}{editor} \PY{k}{import} \PY{n}{VideoFileClip}
\PY{k+kn}{from} \PY{n+nn}{IPython}\PY{n+nn}{.}\PY{n+nn}{display} \PY{k}{import} \PY{n}{HTML}
\PY{n}{video\PYZus{}processor}\PY{o}{=}\PY{n}{LaneLineFinding}\PY{p}{(}\PY{p}{)}
\PY{n}{white\PYZus{}output} \PY{o}{=} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{project\PYZus{}video\PYZus{}output.mp4}\PY{l+s+s1}{\PYZsq{}}
\PY{n}{clip1} \PY{o}{=} \PY{n}{VideoFileClip}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{project\PYZus{}video.mp4}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{white\PYZus{}clip} \PY{o}{=} \PY{n}{clip1}\PY{o}{.}\PY{n}{fl\PYZus{}image}\PY{p}{(}\PY{n}{video\PYZus{}processor}\PY{o}{.}\PY{n}{pipeline}\PY{p}{)} \PY{c+c1}{\PYZsh{}NOTE: this function expects color images!!}
\PY{o}{\PYZpc{}}\PY{k}{time} white\PYZus{}clip.write\PYZus{}videofile(white\PYZus{}output, audio=False)
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
[MoviePy] >>>> Building video project\_video\_output.mp4
[MoviePy] Writing video project\_video\_output.mp4
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
100\%|█████████████████████████████████████████████████████████████████████████████▉| 1260/1261 [03:14<00:00, 7.79it/s]
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
[MoviePy] Done.
[MoviePy] >>>> Video ready: project\_video\_output.mp4
Wall time: 3min 16s
\end{Verbatim}
% Add a bibliography block to the postdoc
\end{document}