ImageMagick convert produces a darker CMYK PDF than PhotoShop
<p>The ImageMagick (IM) result of this command  </p>

<pre><code>convert myRGB.png -colorspace cmyk cmyk.pdf &lt;br&gt;
</code></pre>

<p>is not as bright or as close to the screen colors as a Photoshop produced CMYK PDF. <code>myRGB.png</code> is a PNG file produced using GIMP.<p>
I don't own Photoshop, and would like to stick with open source tools. 
The current Ubuntu release of of IM is 6.7.7. That IM version produces very dark, totally unusable, CMYK PDF.
<p>
I built 7.0.2-6 Q16 from source on Ubuntu 14.0.4, after also building LCMS package from source, and the above command works better, but the CMYK PDF as stated above is less bright and less close to the screen colors than the similar Photoshop output. E.g. blacks are not totally black; the sky color is dull blue instead of bright blue/cyan.
<p>I've tried using ICC files downloaded from Adobe as in the following <br></p>

<pre><code>convert myRGB.png -colorspace cmyk -profile WebCoatedSWOP2006Grade5.icc cmyk.pdf
</code></pre>

<p><p>
I've tried this command with all 14 Adobe ICC files and there is no difference in any of them. Although, I admit I do not understand under what circumstances the ICC comes into play or if it is appropriate to this problem at all.
<p>The simple question is why does IM convert tool not match the Photoshop results for CMYK? <br>
The second question is, if IM can't be made to do it: is there any open source tool or tools that can match the Photoshop results for producing a CMYK PDF from and RGB PNG?</p>