Q:

How to convert a JPEG image into SVG format using ImageMagick?

How to convert a JPEG image into SVG format using ImageMagick?

A:

you'll need to use potrace and convert to a bitmap first.
$convert input.jpg output.ppm
$potrace -s output.ppm -o svgout.svg

A:

Actually, with a complete installation of a recent version of ImageMagick it should be as easy as:
convert  some.jpeg  some.svg

Of course, ImageMagick cannot do it all by itself -- it uses delegates (helper programs) to handle SVG input or output. (This has been pointed out by other answers already.)
To see a (partial) list of all delegates (and their respective commands), run
convert  -list delegate

To see the config file where all the delegate secrets hide, see 
convert  -list delegate | grep delegates.xml

To see a (partial) list of SVG handling delegates, run
convert  -list delegate | grep -i svg

However, ImageMagick likes to put some of its external helper utilities into 'stealth' mode and doesn't necessarily reveal their presence when using above commands.
Just look into the delegates.xml file itself. On my system it's:
grep -i svg /opt/local/etc/ImageMagick/delegates.xml | grep -i --color stealth

  <delegate decode="autotrace" stealth="True" \
            command="&quot;/opt/local/bin/convert&quot; &quot;%i&quot; \
            &quot;pnm:%u&quot;\n\
            &quot;/opt/local/bin/autotrace&quot; \
           -input-format pnm \
           -output-format svg \
           -output-file &quot;%o&quot; &quot;%u&quot;"/>

  <delegate decode="svg:decode" stealth="True" \
            command="&quot;/opt/local/bin/inkscape&quot; &quot;%s&quot; \
            --export-png=&quot;%s&quot; \
            --export-dpi=&quot;%s&quot; \
            --export-background=&quot;%s&quot; \
            --export-background-opacity=&quot;%s&quot; \
            &gt; &quot;%s&quot; 2&gt;&amp;1"/>

As you may see, on my system the ImageMagick installation automatically uses (amongst others)...

...inkscape to convert SVG to PNG;
...autotrace to convert PNM to SVG;

Of course, one could argue the benefits of rather using autotrace directly -- but that would require to manually convert the whatever-input-format to PNM first. So for this preliminary step you'd probably use ImageMagick anyway...

A:

You'll actually need some software or code to vectorize your image in between, as jpg is a raster format, while SVG is a vector format. I don't think imagemagick alone can do that for you.

