Scale image to align with hanging caption text

Question

How to automatically scale a centred image to be (at the same time to being centred) left aligned with a hanging caption?

MWE with guessed image widths:

\documentclass{book}

\usepackage{graphicx}   
\usepackage{caption}                

\captionsetup{%
    singlelinecheck=false,
    format=hang
}

\begin{document}

\chapter{test}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=.7\textwidth]{example-image}
    \caption{Text}
\end{figure}

\setcounter{figure}{1000}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=.62\textwidth]{example-image}
    \caption{Text}
\end{figure}


\end{document}

Answer 1

Due to a missunderstanding in my first answer I adapted the caption to the image. Here the image width is adapted to the caption. It works with different label formats.

For this a new caption format was written, which is a copy of the original hang plus a macro to calculate the \imagewidth. The caption must be known before the image, so the command \captionafter sets it into a box. The latter is then printed with \printcaption after the image.

Using these macros will result in this:

The code:

\documentclass{book}
\usepackage[showframe]{geometry} % just for checking centering
\usepackage{etoolbox}
\usepackage{graphicx}   
\usepackage{caption}                

\makeatletter
\newlength{\imagewidth}

\newcommand*{\set@imagewidth}{%
    \global\imagewidth\dimexpr\textwidth-2\caption@hangindent
}

% copoied from caption3.sty, renamed and added \set@imagewidth
\DeclareCaptionFormat{myhang}[#1#2#3\par]{%
  \caption@ifin@list\caption@lsepcrlist\caption@lsepname
    {\caption@Error{%
       The option `labelsep=\caption@lsepname' does not work\MessageBreak
       with `format=hang'}}%
    {\@hangfrom{#1#2}%
     \advance\caption@parindent\hangindent
     \advance\caption@hangindent\hangindent
     % added
     \set@imagewidth
     \caption@@par#3\par}}

% caption must be known to set \imagewidth, so store it in a box
\newbox\captionafterbox
\newcommand{\captionafter}[2][]{%
    \setbox\captionafterbox\vbox{\caption[#1]{#2}}%
}
% and print it later
\newcommand{\printcaption}{\box\captionafterbox}

\makeatother

\captionsetup{%
    singlelinecheck=false,
    format=myhang
}

% just for testing
\setcounter{totalnumber}{4}

\begin{document}

\chapter{test}

\begin{figure}[htbp]
    \centering
    \captionafter{Text}
    \includegraphics[width=\imagewidth,height=1cm]{example-image}
    \printcaption
\end{figure}

\begin{figure}[htbp]
    \centering
    \captionsetup{labelfont=bf}
    \captionafter{Text}
    \includegraphics[width=\imagewidth,height=1cm]{example-image}
    \printcaption
\end{figure}

\setcounter{figure}{1000}

\begin{figure}[htbp]
    \centering
    \captionafter{A very long caption text, which needs more than one line. Just some more text to fill it.}
    \includegraphics[width=\imagewidth,height=1cm]{example-image}
    \printcaption
\end{figure}

\setcounter{figure}{1000000}

\begin{figure}[htbp]
    \centering
    \captionafter{A very long caption text, which needs more than one line. Just some more text to fill it. Amd make it even longer.}
    \includegraphics[width=\imagewidth,height=1cm]{example-image}
    \printcaption
\end{figure}

\end{document}

Answer 2

As long as you set the width of the image manually (or know it), you can use this:

Edit: added a command to set up caption so it ocupies the rest of the line.

Edit 2: added onside to \captionsetup in \captionimagewidth;
added a new command \capimagewidth, which corrects width and indent, so for wide images the label ("Figure 1.1") doesn't move into the left margin.

\documentclass{book}
\usepackage[showframe]{geometry} % just for checking centering
\usepackage{etoolbox}
\usepackage{graphicx}   
\usepackage{caption}                

\captionsetup{%
    singlelinecheck=false,
}

\DeclareCaptionLabelFormat{myfigure}{\llap{#1 #2:\ }}
\captionsetup{labelformat=myfigure}

% Edit
\newlength{\capindent}
\newlength{\capwidth}
\newcommand{\captionimagewidth}[1]{%
    \capindent\dimexpr0.5\textwidth-#1/2\relax
    \capwidth\dimexpr\textwidth-\capindent
    \captionsetup{width=\capwidth,margin={\capindent,0pt},oneside}%
}

% Edit 2: added `oneside` to \captionsetup
%         correction for wide images
\newcommand{\capimagewidth}[1]{%
    \capindent\dimexpr0.5\textwidth-#1/2\relax
    % from your answer
    \addtocounter{figure}{1}%
    \settowidth{\capwidth}{%
        \figurename~\thefigure:\space% 
    }%
    \addtocounter{figure}{-1}%
    %
    \ifdim\capindent<\capwidth
        \capindent\capwidth
    \fi
    \capwidth\dimexpr\textwidth-\capindent
    \captionsetup{width=\capwidth,margin={\capindent,0pt},oneside}%
}

\begin{document}

\chapter{test}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.3\textwidth]{example-image}
    \captionsetup{width=0.3\textwidth}
    \caption{Text}
\end{figure}

\setcounter{figure}{1000}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.5\textwidth]{example-image}
    % old
    %\captionsetup{width=0.5\textwidth}
    % Edit
    \captionimagewidth{0.5\textwidth}
    \caption{A very long caption text, which needs more than one line. Just some more text to fill it.}
\end{figure}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.9\textwidth]{example-image}
    \capimagewidth{0.9\textwidth}
    \caption{A very long caption text, which needs more than one line. Just some more text to fill it. Amd make it even longer.}
\end{figure}

\end{document}

Result after edit:

But for wide images, the label moves into the margin:

With new command from second edit:

Old result:

Answer 3

The following solution is a bit clumsy as it calculates the hanging indent of the caption by emulating the caption label ... this has the big drawback that it does not automatically adjust to the format of the caption, the font size and style.

\documentclass{book}

\usepackage{etoolbox}
\usepackage{graphicx}   
\usepackage{caption}                

\captionsetup{%
    singlelinecheck=false,
    format=hang
}

% calculate idention of caption
\newlength{\captionindent}
\AtBeginEnvironment{figure}{%
    \addtocounter{figure}{1}%
    \settowidth{\captionindent}{%
        Figure\space\thefigure:\space% 
    }%
    \addtocounter{figure}{-1}%
}

\begin{document}

\chapter{test}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=\dimexpr\textwidth-2\captionindent\relax]{example-image}
    \caption{Text}
\end{figure}

\end{document}